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Sample records for quantum stress tensor

  1. Tensor Network Quantum Virtual Machine (TNQVM)

    SciTech Connect

    McCaskey, Alexander J.

    2016-11-18

    There is a lack of state-of-the-art quantum computing simulation software that scales on heterogeneous systems like Titan. Tensor Network Quantum Virtual Machine (TNQVM) provides a quantum simulator that leverages a distributed network of GPUs to simulate quantum circuits in a manner that leverages recent results from tensor network theory.

  2. Quantum stress tensor for a massive vector field in the space-time of a cylindrical black hole

    SciTech Connect

    Fernandez Piedra, Owen Pavel; Matyjasek, Jerzy

    2010-09-15

    The components of the renormalized quantum energy-momentum tensor for a massive vector field coupled to the gravitational field configuration of static 3+1 dimensional black strings in anti-de Sitter space are analytically evaluated using the Schwinger-DeWitt approximation. The general results are employed to investigate the pointwise energy conditions for the quantized matter field, and it is shown that they are violated at some regions of the space-time, in particular the horizon of the black hole.

  3. Local recovery of lithospheric stress tensor from GOCE gravitational tensor

    NASA Astrophysics Data System (ADS)

    Eshagh, Mehdi

    2017-01-01

    SUMMARYThe sub-lithospheric <span class="hlt">stress</span> due to mantle convection can be computed from gravity data and propagated through the lithosphere by solving the boundary-value problem of elasticity for the Earth's lithosphere. In this case, a full <span class="hlt">tensor</span> of <span class="hlt">stress</span> can be computed at any point inside this elastic layer. Here, we present mathematical foundations for recovering such a <span class="hlt">tensor</span> from gravitational <span class="hlt">tensor</span> measured at satellite altitudes. The mathematical relations will be much simpler in this way than the case of using gravity data as no derivative of spherical harmonics or Legendre polynomials is involved in the expressions. Here, new relations between the spherical harmonic coefficients of the <span class="hlt">stress</span> and gravitational <span class="hlt">tensor</span> elements are presented. Thereafter integral equations are established from them to recover the elements of <span class="hlt">stress</span> <span class="hlt">tensor</span> from those of the gravitational <span class="hlt">tensor</span>. The integrals have no closed-form kernels, but they are easy to invert and their spatial truncation errors are reducible. The integral equations are used to invert the real data of the gravity field and steady-state ocean circulation explorer (GOCE) mission, in November 2009, over the South American plate and its surroundings to recover the <span class="hlt">stress</span> <span class="hlt">tensor</span> at a depth of 35 km. The recovered <span class="hlt">stress</span> fields are in good agreement with the tectonic and geological features of the area.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017APS..APR.M6003A','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017APS..APR.M6003A"><span>Method to compute the <span class="hlt">stress</span>-energy <span class="hlt">tensor</span> for a <span class="hlt">quantum</span> field outside a black hole that forms from collapse</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Anderson, Paul; Evans, Charles</p> <p>2017-01-01</p> <p>A method to compute the <span class="hlt">stress</span>-energy <span class="hlt">tensor</span> for a quantized massless minimally coupled scalar field outside the event horizon of a 4-D black hole that forms from the collapse of a spherically symmetric null shell is given. The method is illustrated in the corresponding 2-D case which is mathematically similar but is simple enough that the calculations can be done analytically. The approach to the Unruh state at late times is discussed. National Science Foundation Grant No. PHY-1505875 to Wake Forest University and National Science Foundation Grant No. PHY-1506182 to the University of North Carolina, Chapel Hill</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2014PhRvL.113c0501F','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2014PhRvL.113c0501F"><span><span class="hlt">Tensor</span> Networks and <span class="hlt">Quantum</span> Error Correction</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Ferris, Andrew J.; Poulin, David</p> <p>2014-07-01</p> <p>We establish several relations between <span class="hlt">quantum</span> error correction (QEC) and <span class="hlt">tensor</span> network (TN) methods of <span class="hlt">quantum</span> many-body physics. We exhibit correspondences between well-known families of QEC codes and TNs, and demonstrate a formal equivalence between decoding a QEC code and contracting a TN. We build on this equivalence to propose a new family of <span class="hlt">quantum</span> codes and decoding algorithms that generalize and improve upon <span class="hlt">quantum</span> polar codes and successive cancellation decoding in a natural way.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/26124254','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/26124254"><span><span class="hlt">Quantum</span> theory with bold operator <span class="hlt">tensors</span>.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Hardy, Lucien</p> <p>2015-08-06</p> <p>In this paper, we present a formulation of <span class="hlt">quantum</span> theory in terms of bold operator <span class="hlt">tensors</span>. A circuit is built up of operations where an operation corresponds to a use of an apparatus. We associate collections of operator <span class="hlt">tensors</span> (which together comprise a bold operator) with these apparatus uses. We give rules for combining bold operator <span class="hlt">tensors</span> such that, for a circuit, they give a probability distribution over the possible outcomes. If we impose certain physicality constraints on the bold operator <span class="hlt">tensors</span>, then we get exactly the <span class="hlt">quantum</span> formalism. We provide both symbolic and diagrammatic ways to represent these calculations. This approach is manifestly covariant in that it does not require us to foliate the circuit into time steps and then evolve a state. Thus, the approach forms a natural starting point for an operational approach to <span class="hlt">quantum</span> field theory.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/22711865','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/22711865"><span>The operator <span class="hlt">tensor</span> formulation of <span class="hlt">quantum</span> theory.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Hardy, Lucien</p> <p>2012-07-28</p> <p>In this paper, we provide what might be regarded as a manifestly covariant presentation of discrete <span class="hlt">quantum</span> theory. A typical <span class="hlt">quantum</span> experiment has a bunch of apparatuses placed so that <span class="hlt">quantum</span> systems can pass between them. We regard each use of an apparatus, along with some given outcome on the apparatus (a certain detector click or a certain meter reading for example), as an operation. An operation (e.g. B(b(2)a(3))(a(1))) can have zero or more <span class="hlt">quantum</span> systems inputted into it and zero or more <span class="hlt">quantum</span> systems outputted from it. The operation B(b(2)a(3))(a(1)) has one system of type a inputted, and one system of type b and one system of type a outputted. We can wire together operations to form circuits, for example, A(a(1))B(b(2)a(3))(a(1))C(b(2)a(3)). Each repeated integer label here denotes a wire connecting an output to an input of the same type. As each operation in a circuit has an outcome associated with it, a circuit represents a set of outcomes that can happen in a run of the experiment. In the operator <span class="hlt">tensor</span> formulation of <span class="hlt">quantum</span> theory, each operation corresponds to an operator <span class="hlt">tensor</span>. For example, the operation B(b(2)a(3))(a(1)) corresponds to the operator <span class="hlt">tensor</span> B(b(2)a(3))(a(1)). Further, the probability for a general circuit is given by replacing operations with corresponding operator <span class="hlt">tensors</span> as in Prob(A(a(1))B(b(2)a(3))(a(1))C(b(2)a(3))) = Â(a(1))B(b(2)a(3))(a(1))C(b(2)a(3)). Repeated integer labels indicate that we multiply in the associated subspace and then take the partial trace over that subspace. Operator <span class="hlt">tensors</span> must be physical (namely, they must have positive input transpose and satisfy a certain normalization condition).</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017JHEP...03..056K','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017JHEP...03..056K"><span><span class="hlt">Quantum</span> chaos and holographic <span class="hlt">tensor</span> models</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Krishnan, Chethan; Sanyal, Sambuddha; Subramanian, P. N. Bala</p> <p>2017-03-01</p> <p>A class of <span class="hlt">tensor</span> models were recently outlined as potentially calculable examples of holography: their perturbative large- N behavior is similar to the Sachdev-Ye-Kitaev (SYK) model, but they are fully <span class="hlt">quantum</span> mechanical (in the sense that there is no quenched disorder averaging). These facts make them intriguing tentative models for <span class="hlt">quantum</span> black holes. In this note, we explicitly diagonalize the simplest non-trivial Gurau-Witten <span class="hlt">tensor</span> model and study its spectral and late-time properties. We find parallels to (a single sample of) SYK where some of these features were recently attributed to random matrix behavior and <span class="hlt">quantum</span> chaos. In particular, the spectral form factor exhibits a dip-ramp-plateau structure after a running time average, in qualitative agreement with SYK. But we also observe that even though the spectrum has a unique ground state, it has a huge (quasi-?)degeneracy of intermediate energy states, not seen in SYK. If one ignores the delta function due to the degeneracies however, there is level repulsion in the unfolded spacing distribution hinting chaos. Furthermore, there are gaps in the spectrum. The system also has a spectral mirror symmetry which we trace back to the presence of a unitary operator with which the Hamiltonian anticommutes. We use it to argue that to the extent that the model exhibits random matrix behavior, it is controlled not by the Dyson ensembles, but by the BDI (chiral orthogonal) class in the Altland-Zirnbauer classification.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://eric.ed.gov/?q=electric+AND+current&pg=5&id=EJ963896','ERIC'); return false;" href="http://eric.ed.gov/?q=electric+AND+current&pg=5&id=EJ963896"><span>Radiation Forces and Torques without <span class="hlt">Stress</span> (<span class="hlt">Tensors</span>)</span></a></p> <p><a target="_blank" href="http://www.eric.ed.gov/ERICWebPortal/search/extended.jsp?_pageLabel=advanced">ERIC Educational Resources Information Center</a></p> <p>Bohren, Craig F.</p> <p>2011-01-01</p> <p>To understand radiation forces and torques or to calculate them does not require invoking photon or electromagnetic field momentum transfer or <span class="hlt">stress</span> <span class="hlt">tensors</span>. According to continuum electromagnetic theory, forces and torques exerted by radiation are a consequence of electric and magnetic fields acting on charges and currents that the fields induce…</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2008LMaPh..86..209L','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2008LMaPh..86..209L"><span>On Endomorphisms of <span class="hlt">Quantum</span> <span class="hlt">Tensor</span> Space</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Lehrer, Gustav Isaac; Zhang, Ruibin</p> <p>2008-12-01</p> <p>We give a presentation of the endomorphism algebra End_{mathcal {U}q(mathfrak {sl}2)}(V^{⊗ r}) , where V is the three-dimensional irreducible module for <span class="hlt">quantum</span> {mathfrak {sl}_2} over the function field {mathbb {C}(q^{1/2})} . This will be as a quotient of the Birman-Wenzl-Murakami algebra BMW r ( q) : = BMW r ( q -4, q 2 - q -2) by an ideal generated by a single idempotent Φ q . Our presentation is in analogy with the case where V is replaced by the two-dimensional irreducible {mathcal {U}_q(mathfrak {sl}2)} -module, the BMW algebra is replaced by the Hecke algebra H r ( q) of type A r-1, Φ q is replaced by the <span class="hlt">quantum</span> alternator in H 3( q), and the endomorphism algebra is the classical realisation of the Temperley-Lieb algebra on <span class="hlt">tensor</span> space. In particular, we show that all relations among the endomorphisms defined by the R-matrices on {V^{⊗ r}} are consequences of relations among the three R-matrices acting on {V^{⊗ 4}}. The proof makes extensive use of the theory of cellular algebras. Potential applications include the decomposition of <span class="hlt">tensor</span> powers when q is a root of unity.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2010AGUFM.T13E..01S','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2010AGUFM.T13E..01S"><span>Complete <span class="hlt">stress</span> <span class="hlt">tensor</span> determination by microearthquake analysis</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Slunga, R.</p> <p>2010-12-01</p> <p>Jones 1984 found that half of the shallow strike-slip EQ in California had at least one M>2 foreshock. By the Gutenberg law this means at least 3-20 M>0 (low b-value 0.4-0.8). deformations within the crust. This was confirmed by observations in Iceland after 1990 when anew seismic network in Iceland operated by IMO started. Like the Parkfield project in California the SIL network in Iceland was established in an area predicted (Einarsson et al 1981, Stefansson and Halldorsson 1988) to be struck by major EQs within decades of years. The area of main interest have a detection threshold of M=0. A physical approach was chosen to the earthquake warning problem (Stefansson et al 1993) and therefore all microearthquakes were analyzed for FPS by the spectral amplitude method (Slunga 1981). As the shear slip is caused by the in situ <span class="hlt">stress</span> it is logical to investigate what bounds the FPS puts on the <span class="hlt">stress</span> <span class="hlt">tensor</span>. McKenzie 1969 assumed that the earthquake takes place in a crust containing only one fracture, the fault plane. He found that in s uch a case only very weak constraints could be put on the <span class="hlt">stress</span>. This was widely accepted t o be valid also for microearthquakes in the real crust and lead to methods (Angelier 1978, G ephart and Forsythe 1984 etc) to put four constraints on the <span class="hlt">stress</span> <span class="hlt">tensor</span> by assuming that the same <span class="hlt">stress</span> <span class="hlt">tensor</span> is causing the slip on four or more different fractures. Another and more realistic approach is to assume that the crust have frequent fractures with almost all orientations. In such a case one can rely on Coulomb's failure criterion for isotropic mat erial (gives four constraints) instead of the weaker Bolt's criterion (giving only one const raint). One obvious fifth constraint is to require the vertical <span class="hlt">stress</span> to equal the lithosta tic pressure. A sixth constraint is achieved by requiring that the deviatoric elastic energy is minimized. The water pressure is also needed for the fourth constraint by Coulomb (CFS=0 ). It can be related to</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2013MeSol..48..546R','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2013MeSol..48..546R"><span>Asymptotic axes of <span class="hlt">stress</span> <span class="hlt">tensors</span> and strain increment <span class="hlt">tensors</span> in mechanics of compressible continua</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Radaev, Yu. N.</p> <p>2013-09-01</p> <p>New <span class="hlt">tensor</span> representations of the <span class="hlt">stress</span> state and the kinematics of compressible flows are obtained in the paper with the use of the notion of asymptotic directions of the symmetric <span class="hlt">stress</span> <span class="hlt">tensor</span> and the strain increment <span class="hlt">tensor</span>. The exposition is based on terminology and notation typical of the mathematical theory of plasticity, but all main results remain valid for <span class="hlt">stresses</span> and strains in compressible continua. The simplest and most efficient forms of the <span class="hlt">stress</span> <span class="hlt">tensor</span> for "completely plastic," "semiplastic," and "nonplastic" spatial <span class="hlt">stress</span> states are found, where the asymptotic <span class="hlt">stress</span> axes serve as the most natural reference frame ensuring new symmetric <span class="hlt">tensor</span> representations of <span class="hlt">stresses</span> different from the spectral ones. Similar representations can be extended to the <span class="hlt">stress</span> increment <span class="hlt">tensor</span>. Two-dimensional curvilinear grids such that the strain rates of their elements are always zero are chosen on the surfaces orthogonal to the directions of the "intermediate" principal strain increment. Incremental relations for the sliding rates along the grid lines are obtained, and these relations generalize the Geiringer equations along the characteristic lines, which are well known in the theory of plane deformation of perfectly plastic bodies. The generalization readily applies to spatial flows, and the possible flow compressibility is taken into account as well.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2011cqvz.book..323M','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2011cqvz.book..323M"><span>Local ζ -functions, <span class="hlt">stress</span>-energy <span class="hlt">tensor</span>, field fluctuations, and all that, in curved static spacetime</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Moretti, Valter</p> <p></p> <p>This is a quick review on some technology concerning the local zeta function applied to <span class="hlt">Quantum</span> Field Theory in curved static (thermal) spacetime to regularize the <span class="hlt">stress</span> energy <span class="hlt">tensor</span> and the field fluctuations. Dedicated to Prof. Emilio Elizalde on the occasion of his 60th birthday.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016APS..APRJ15006K','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016APS..APRJ15006K"><span><span class="hlt">Stress</span>-Energy <span class="hlt">Tensor</span> in Einstein-Cartan Theory</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Kur, Eugene</p> <p>2016-03-01</p> <p>We present a proof connecting the Noether <span class="hlt">stress</span>-energy <span class="hlt">tensor</span> with the Hilbert <span class="hlt">stress</span>-energy <span class="hlt">tensor</span> for theories coupled to an arbitrary background metric. In particular, we show how applying Noether's theorem to spacetime diffeomorphisms leads to Hilbert's formula Tμν ~δS/δgμν . The proof immediately yields the symmetry of the <span class="hlt">stress</span>-energy <span class="hlt">tensor</span> as well as the vanishing of its covariant divergence. In the case that the theory is coupled to a background tetrad and a background connection, we show that the <span class="hlt">stress</span>-energy <span class="hlt">tensor</span> receives contributions from the torsion of the background connection and the spin current of the matter. We discuss the applications of these results to fermions coupled to Einstein-Cartan gravity and to theories of gravity with no matter coupling.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/6372003','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/6372003"><span>Discussion of <span class="hlt">stress</span> <span class="hlt">tensor</span> nonuniqueness with application to nonuniform, particulate systems</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Aidun, J.B.</p> <p>1993-01-01</p> <p>The indeterminacy of the mechanical <span class="hlt">stress</span> <span class="hlt">tensor</span> has been noted in several developments of expressions for <span class="hlt">stress</span> in a system of particles. It is generally agreed that physical quantities related to the <span class="hlt">stress</span> <span class="hlt">tensor</span> must be insensitive to this nonuniqueness, but there is no definitive prescription for insuring it. Kroener's <span class="hlt">tensor</span> decomposition theorem is applied to the mechanical <span class="hlt">stress</span> <span class="hlt">tensor</span> [sup [sigma</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2014APS..DFDM24006A','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2014APS..DFDM24006A"><span>Non-Newtonian <span class="hlt">stress</span> <span class="hlt">tensor</span> and thermal conductivity <span class="hlt">tensor</span> in granular plane shear flow</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Alam, Meheboob; Saha, Saikat</p> <p>2014-11-01</p> <p>The non-Newtonian <span class="hlt">stress</span> <span class="hlt">tensor</span> and the heat flux in the plane shear flow of smooth inelastic disks are analysed from the Grad-level moment equations using the anisotropic Gaussian as a reference. Closed-form expressions for shear viscosity, pressure, first normal <span class="hlt">stress</span> difference (N1) and the dissipation rate are given as functions of (i) the density or the area fraction (ν), (ii) the restitution coefficient (e), (iii) the dimensionless shear rate (R), (iv) the temperature anisotropy [ η, the difference between the principal eigenvalues of the second moment <span class="hlt">tensor</span>] and (v) the angle (ϕ) between the principal directions of the shear <span class="hlt">tensor</span> and the second moment <span class="hlt">tensor</span>. Particle simulation data for a sheared hard-disk system is compared with theoretical results, with good agreement for p, μ and N1 over a large range of density. In contrast, the predictions from a Navier-Stokes order constitutive model are found to deviate significantly from both the simulation and the moment theory even at moderate values of e. We show that the gradient of the deviatoric part of the kinetic <span class="hlt">stress</span> drives a heat current and the thermal conductivity is characterized by an anisotropic 2nd rank <span class="hlt">tensor</span> for which explicit expressions are derived.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/28067221','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/28067221"><span><span class="hlt">Quantum</span>-chemical insights from deep <span class="hlt">tensor</span> neural networks.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Schütt, Kristof T; Arbabzadah, Farhad; Chmiela, Stefan; Müller, Klaus R; Tkatchenko, Alexandre</p> <p>2017-01-09</p> <p>Learning from data has led to paradigm shifts in a multitude of disciplines, including web, text and image search, speech recognition, as well as bioinformatics. Can machine learning enable similar breakthroughs in understanding <span class="hlt">quantum</span> many-body systems? Here we develop an efficient deep learning approach that enables spatially and chemically resolved insights into <span class="hlt">quantum</span>-mechanical observables of molecular systems. We unify concepts from many-body Hamiltonians with purpose-designed deep <span class="hlt">tensor</span> neural networks, which leads to size-extensive and uniformly accurate (1 kcal mol(-1)) predictions in compositional and configurational chemical space for molecules of intermediate size. As an example of chemical relevance, the model reveals a classification of aromatic rings with respect to their stability. Further applications of our model for predicting atomic energies and local chemical potentials in molecules, reliable isomer energies, and molecules with peculiar electronic structure demonstrate the potential of machine learning for revealing insights into complex <span class="hlt">quantum</span>-chemical systems.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017NatCo...813890S','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017NatCo...813890S"><span><span class="hlt">Quantum</span>-chemical insights from deep <span class="hlt">tensor</span> neural networks</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Schütt, Kristof T.; Arbabzadah, Farhad; Chmiela, Stefan; Müller, Klaus R.; Tkatchenko, Alexandre</p> <p>2017-01-01</p> <p>Learning from data has led to paradigm shifts in a multitude of disciplines, including web, text and image search, speech recognition, as well as bioinformatics. Can machine learning enable similar breakthroughs in understanding <span class="hlt">quantum</span> many-body systems? Here we develop an efficient deep learning approach that enables spatially and chemically resolved insights into <span class="hlt">quantum</span>-mechanical observables of molecular systems. We unify concepts from many-body Hamiltonians with purpose-designed deep <span class="hlt">tensor</span> neural networks, which leads to size-extensive and uniformly accurate (1 kcal mol-1) predictions in compositional and configurational chemical space for molecules of intermediate size. As an example of chemical relevance, the model reveals a classification of aromatic rings with respect to their stability. Further applications of our model for predicting atomic energies and local chemical potentials in molecules, reliable isomer energies, and molecules with peculiar electronic structure demonstrate the potential of machine learning for revealing insights into complex <span class="hlt">quantum</span>-chemical systems.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2013PhRvL.111x6102K','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2013PhRvL.111x6102K"><span>Unified <span class="hlt">Stress</span> <span class="hlt">Tensor</span> of the Hydration Water Layer</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Kim, Bongsu; Kim, QHwan; Kwon, Soyoung; An, Sangmin; Lee, Kunyoung; Lee, Manhee; Jhe, Wonho</p> <p>2013-12-01</p> <p>We present the general <span class="hlt">stress</span> <span class="hlt">tensor</span> of the ubiquitous hydration water layer (HWL), based on the empirical hydration force, by combining the elasticity and hydrodynamics theories. The tapping and shear component of the <span class="hlt">tensor</span> describe the elastic and damping properties of the HWL, respectively, in good agreement with experiments. In particular, a unified understanding of HWL dynamics provides the otherwise unavailable intrinsic parameters of the HWL, which offer additional but unexplored aspects to the supercooled liquidity of the confined HWL. Our results may allow deeper insight on systems where the HWL is critical.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/24483679','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/24483679"><span>Unified <span class="hlt">stress</span> <span class="hlt">tensor</span> of the hydration water layer.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Kim, Bongsu; Kim, Qhwan; Kwon, Soyoung; An, Sangmin; Lee, Kunyoung; Lee, Manhee; Jhe, Wonho</p> <p>2013-12-13</p> <p>We present the general <span class="hlt">stress</span> <span class="hlt">tensor</span> of the ubiquitous hydration water layer (HWL), based on the empirical hydration force, by combining the elasticity and hydrodynamics theories. The tapping and shear component of the <span class="hlt">tensor</span> describe the elastic and damping properties of the HWL, respectively, in good agreement with experiments. In particular, a unified understanding of HWL dynamics provides the otherwise unavailable intrinsic parameters of the HWL, which offer additional but unexplored aspects to the supercooled liquidity of the confined HWL. Our results may allow deeper insight on systems where the HWL is critical.</p> </li> </ol> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li class="active"><span>1</span></li> <li><a href="#" onclick='return showDiv("page_2");'>2</a></li> <li><a href="#" onclick='return showDiv("page_3");'>3</a></li> <li><a href="#" onclick='return showDiv("page_4");'>4</a></li> <li><a href="#" onclick='return showDiv("page_5");'>5</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div><!-- col-sm-12 --> </div><!-- row --> </div><!-- page_1 --> <div id="page_2" class="hiddenDiv"> <div class="row"> <div class="col-sm-12"> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_1");'>1</a></li> <li class="active"><span>2</span></li> <li><a href="#" onclick='return showDiv("page_3");'>3</a></li> <li><a href="#" onclick='return showDiv("page_4");'>4</a></li> <li><a href="#" onclick='return showDiv("page_5");'>5</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div> </div> <div class="row"> <div class="col-sm-12"> <ol class="result-class" start="21"> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/1987PhDT.......137H','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/1987PhDT.......137H"><span>Irreducible <span class="hlt">Tensor</span> Operators and Multiple-<span class="hlt">Quantum</span> NMR.</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Hutchison, Wayne Douglas</p> <p></p> <p>The aim of the work detailed in this thesis, is to provide a concise, and illuminating, mathematical description of multiple <span class="hlt">quantum</span> nuclear magnetic resonance (MQNMR) experiments, on essentially isolated (non-coupled) nuclei. The treatment used is based on irreducible <span class="hlt">tensor</span> operators, which form an orthonormal basis set. Such operators can be used to detail the state of the nuclear ensemble (density matrix) during every stage, preparation, evolution and detection, of a MQNMR experiment. Moreover, such operators can be also used to provide a rigorous analysis of pulsed NMR experiments, on oriented nuclei at low temperatures, where the initial density matrix is far from trivial. The specific topics dealt with in this thesis are as follows. In the first place the properties of irreducible <span class="hlt">tensor</span> operators are discussed in some detail. In particular, symmetric and anti-symmetric combinations of <span class="hlt">tensor</span> operators are introduced, to reflect the Hermitian nature of the nuclear Hamiltonian and density matrix. Secondly, the creation of multipolar nuclear states using hard, non-selective rf pulses, is detailed for spin I = 1, 3/2, 2 and 5/2 nuclei, subject to an axially symmetric quadrupole interaction. Results are also given for general I. Thirdly, some experimental results, verifying the production of a triple <span class="hlt">quantum</span> NMR state, for the I = 3/2 ^{23}Na nuclei in a single crystal of NaIO_4 are presented and discussed. Fourthly, the treatment of MQNMR experiments is extended to the low temperature regime where the initial density matrix includes Fano statistical <span class="hlt">tensors</span> other than rank one. In particular, it is argued that MQNMR techniques could be used to enhance the anisotropy of gamma-ray emission from oriented nuclei at low temperatures. Fifthly, the effect of a more general quadrupole Hamiltonian (including an asymmetry term) on MQNMR experiments is considered for spins I = 1 and 3/2. In particular, it is shown that double <span class="hlt">quantum</span> states evolve to give longitudinal NMR</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017CPL...667...25X','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017CPL...667...25X"><span>A <span class="hlt">stress</span> <span class="hlt">tensor</span> eigenvector projection space for the (H2O)5 potential energy surface</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Xu, Tianlv; Farrell, James; Momen, Roya; Azizi, Alireza; Kirk, Steven R.; Jenkins, Samantha; Wales, David J.</p> <p>2017-01-01</p> <p>A <span class="hlt">stress</span> <span class="hlt">tensor</span> eigenvector projection space is created to describe reaction pathways on the (H2O)5 MP2 potential energy surface. Evidence for the stabilizing role of the O--O bonding interactions is found from the length of the recently introduced <span class="hlt">stress</span> <span class="hlt">tensor</span> trajectory in the <span class="hlt">stress</span> <span class="hlt">tensor</span> eigenvector projection space. The <span class="hlt">stress</span> <span class="hlt">tensor</span> trajectories demonstrate coupling behavior of the adjoining covalent (σ) O-H and hydrogen bonds due to sharing of covalent character. Additionally, the <span class="hlt">stress</span> <span class="hlt">tensor</span> trajectories can show dynamic coupling effects of pairs of σ bonds and of pairs of hydrogen bonds.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2015IJGMM..1250031G','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015IJGMM..1250031G"><span>Covariant diagonalization of the perfect fluid <span class="hlt">stress</span>-energy <span class="hlt">tensor</span></span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Garat, Alcides</p> <p>2015-02-01</p> <p>We introduce new tetrads that manifestly and covariantly diagonalize the <span class="hlt">stress</span>-energy <span class="hlt">tensor</span> for a perfect fluid with vorticity at every spacetime point. This new tetrad can be applied to introduce simplification in the analysis of astrophysical relativistic problems where vorticity is present through the Carter-Lichnerowicz equation. We also discuss the origin of inertia in this special case from the standpoint of our new local tetrads.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=5228054','PMC'); return false;" href="https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=5228054"><span><span class="hlt">Quantum</span>-chemical insights from deep <span class="hlt">tensor</span> neural networks</span></a></p> <p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pmc">PubMed Central</a></p> <p>Schütt, Kristof T.; Arbabzadah, Farhad; Chmiela, Stefan; Müller, Klaus R.; Tkatchenko, Alexandre</p> <p>2017-01-01</p> <p>Learning from data has led to paradigm shifts in a multitude of disciplines, including web, text and image search, speech recognition, as well as bioinformatics. Can machine learning enable similar breakthroughs in understanding <span class="hlt">quantum</span> many-body systems? Here we develop an efficient deep learning approach that enables spatially and chemically resolved insights into <span class="hlt">quantum</span>-mechanical observables of molecular systems. We unify concepts from many-body Hamiltonians with purpose-designed deep <span class="hlt">tensor</span> neural networks, which leads to size-extensive and uniformly accurate (1 kcal mol−1) predictions in compositional and configurational chemical space for molecules of intermediate size. As an example of chemical relevance, the model reveals a classification of aromatic rings with respect to their stability. Further applications of our model for predicting atomic energies and local chemical potentials in molecules, reliable isomer energies, and molecules with peculiar electronic structure demonstrate the potential of machine learning for revealing insights into complex <span class="hlt">quantum</span>-chemical systems. PMID:28067221</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016PhRvD..93h5017M','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016PhRvD..93h5017M"><span><span class="hlt">Stress</span> <span class="hlt">tensor</span> for a scalar field in a spatially varying background potential: Divergences, "renormalization", anomalies, and Casimir forces</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Milton, Kimball A.; Fulling, Stephen A.; Parashar, Prachi; Kalauni, Pushpa; Murphy, Taylor</p> <p>2016-04-01</p> <p>Motivated by a desire to understand <span class="hlt">quantum</span> fluctuation energy densities and <span class="hlt">stress</span> within a spatially varying dielectric medium, we examine the vacuum expectation value for the <span class="hlt">stress</span> <span class="hlt">tensor</span> of a scalar field with arbitrary conformal parameter, in the background of a given potential that depends on only one spatial coordinate. We regulate the expressions by incorporating a temporal-spatial cutoff in the (imaginary) time and transverse-spatial directions. The divergences are captured by the zeroth- and second-order WKB approximations. Then the <span class="hlt">stress</span> <span class="hlt">tensor</span> is "renormalized" by omitting the terms that depend on the cutoff. The ambiguities that inevitably arise in this procedure are both duly noted and restricted by imposing certain physical conditions; one result is that the renormalized <span class="hlt">stress</span> <span class="hlt">tensor</span> exhibits the expected trace anomaly. The renormalized <span class="hlt">stress</span> <span class="hlt">tensor</span> exhibits no pressure anomaly, in that the principle of virtual work is satisfied for motions in a transverse direction. We then consider a potential that defines a wall, a one-dimensional potential that vanishes for z <0 and rises like zα, α >0 , for z >0 . Previously, the <span class="hlt">stress</span> <span class="hlt">tensor</span> had been computed outside of the wall, whereas now we compute all components of the <span class="hlt">stress</span> <span class="hlt">tensor</span> in the interior of the wall. The full finite <span class="hlt">stress</span> <span class="hlt">tensor</span> is computed numerically for the two cases where explicit solutions to the differential equation are available, α =1 and 2. The energy density exhibits an inverse linear divergence as the boundary is approached from the inside for a linear potential, and a logarithmic divergence for a quadratic potential. Finally, the interaction between two such walls is computed, and it is shown that the attractive Casimir pressure between the two walls also satisfies the principle of virtual work (i.e., the pressure equals the negative derivative of the energy with respect to the distance between the walls).</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017JPhA...50dLT02T','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017JPhA...50dLT02T"><span><span class="hlt">Tensor</span> product of no-signaling boxes in the framework of <span class="hlt">quantum</span> logics</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Tylec, T. I.; Kuś, M.</p> <p>2017-01-01</p> <p>In the <span class="hlt">quantum</span> logic framework we show that the no-signaling box model is a particular type of <span class="hlt">tensor</span> product with single box logics. Such notion of a <span class="hlt">tensor</span> product is too strong to apply in the category of logics of <span class="hlt">quantum</span> mechanical systems. In the light of the obtained results, the statement that no-signaling box models are generalizations of <span class="hlt">quantum</span> models is questionable.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/scitech/biblio/250826','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/250826"><span>Detailed <span class="hlt">stress</span> <span class="hlt">tensor</span> measurements in a centrifugal compressor vaneless diffuser</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Pinarbasi, A.; Johnson, M.W.</p> <p>1996-04-01</p> <p>Detailed flow measurements have been made in the vaneless diffuser of a large low-speed centrifugal compressor using hot-wire anemometry. The three time mean velocity components and full <span class="hlt">stress</span> <span class="hlt">tensor</span> distributions have been determined on eight measurement plans within the diffuser. High levels of Reynolds <span class="hlt">stress</span> result in the rapid mixing out of the blade wake. Although high levels of turbulent kinetic energy are found in the passage wake, they are not associated with strong Reynolds <span class="hlt">stresses</span> and hence the passage wake mixes out only slowly. Low-frequency meandering of the wake position is therefore likely to be responsible for the high kinetic energy levels. The anisotropic nature of the turbulence suggests that Reynolds <span class="hlt">stress</span> turbulence models are required for CFD modeling of diffuser flows.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/27709640','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/27709640"><span>Distinguishing and quantifying the torquoselectivity in competitive ring-opening reactions using the <span class="hlt">stress</span> <span class="hlt">tensor</span> and QTAIM.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Guo, Huan; Morales-Bayuelo, Alejandro; Xu, Tianlv; Momen, Roya; Wang, Lingling; Yang, Ping; Kirk, Steven R; Jenkins, Samantha</p> <p>2016-12-05</p> <p>Currently the theories to explain and predict the classification of the electronic reorganization due to the torquoselectivity of a ring-opening reaction cannot accommodate the directional character of the reaction pathway; the torquoselectivity is a type of stereoselectivity and therefore is dependent on the pathway. Therefore, in this investigation we introduced new measures from <span class="hlt">quantum</span> theory of atoms in molecules and the <span class="hlt">stress</span> <span class="hlt">tensor</span> to clearly distinguish and quantify the transition states of the inward (TSIC) and outward (TSOC) conrotations of competitive ring-opening reactions of 3-(trifluoromethyl)cyclobut-1-ene and 1-cyano-1-methylcyclobutene. We find the metallicity ξ(rb ) of the ring-opening bond does not occur exactly at the transition state in agreement with transition state theory. The vector-based <span class="hlt">stress</span> <span class="hlt">tensor</span> response βσ was used to distinguish the effect of the CN, CH3 , and CF3 groups on the TSIC and TSOC paths that was consistent with the ellipticity ε, the total local energy density H(rb ) and the <span class="hlt">stress</span> <span class="hlt">tensor</span> stiffness Sσ . We determine the directional properties of the TSIC and TSOC ring-opening reactions by constructing a <span class="hlt">stress</span> <span class="hlt">tensor</span> UσTS space with trajectories TσTS (s) with length l in real space, longer l correlated with the lowest density functional theory-evaluated total energy barrier and hence will be more thermodynamically favored. © 2016 Wiley Periodicals, Inc.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017PhRvD..95b5007L','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017PhRvD..95b5007L"><span>Renormalized <span class="hlt">stress</span>-energy <span class="hlt">tensor</span> for stationary black holes</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Levi, Adam</p> <p>2017-01-01</p> <p>We continue the presentation of the pragmatic mode-sum regularization (PMR) method for computing the renormalized <span class="hlt">stress</span>-energy <span class="hlt">tensor</span> (RSET). We show in detail how to employ the t -splitting variant of the method, which was first presented for ⟨ϕ2⟩ren , to compute the RSET in a stationary, asymptotically flat background. This variant of the PMR method was recently used to compute the RSET for an evaporating spinning black hole. As an example for regularization, we demonstrate here the computation of the RSET for a minimally coupled, massless scalar field on Schwarzschild background in all three vacuum states. We discuss future work and possible improvements of the regularization schemes in the PMR method.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/10159007','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/10159007"><span>Discussion of <span class="hlt">stress</span> <span class="hlt">tensor</span> nonuniqueness with application to nonuniform, particulate systems</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Aidun, J.B.</p> <p>1993-06-01</p> <p>The indeterminacy of the mechanical <span class="hlt">stress</span> <span class="hlt">tensor</span> has been noted in several developments of expressions for <span class="hlt">stress</span> in a system of particles. It is generally agreed that physical quantities related to the <span class="hlt">stress</span> <span class="hlt">tensor</span> must be insensitive to this nonuniqueness, but there is no definitive prescription for insuring it. Kroener`s <span class="hlt">tensor</span> decomposition theorem is applied to the mechanical <span class="hlt">stress</span> <span class="hlt">tensor</span> {sup {sigma}}{sub ij} to show that its complete determination requires specification of its ``incompatibility,`` {epsilon}{sub ijk} {epsilon}{sub lmn} {sup {partial_derivative}}{sub j} {sup {partial_derivative}}{sub m} {sup {sigma}}{sub kn}, in addition to its divergence, which is obtained from the momentum conservation relation. For a particulate system, <span class="hlt">stress</span> <span class="hlt">tensor</span> incompatibility is shown to vanish to recover the correct expression for macroscopically observable traction. This result removes concern about nonuniqueness without requiring equilibrium or arbitrarily-defined force lines.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/1986isi..rept.....B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/1986isi..rept.....B"><span>Behavior of a vorticity-influenced asymmetric <span class="hlt">stress</span> <span class="hlt">tensor</span> in fluid flow</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Berdahl, C. H.; Strang, W. Z.</p> <p>1986-10-01</p> <p>The Navier Stokes momentum equations describe the general movement of a Newtonian fluid. In classic derivation of these equations, an entity called the <span class="hlt">stress</span> <span class="hlt">tensor</span> is postulated to exist. Classic thought allowed the <span class="hlt">stress</span> to depend on dilation and deformation but assumed no effect of vorticity on <span class="hlt">stress</span>. Because the complete Navier Stokes equations had not yielded to numerical solution until the last few years, it has been impractical to test the validity of assuming no influence of vorticity on <span class="hlt">stress</span>. However, the arrival of powerful computers has now made their numerical solution possible. Consequently, an investigation was made into the relative behavior of the classic <span class="hlt">stress</span> <span class="hlt">tensor</span> as compared to a vorticity influenced <span class="hlt">stress</span> <span class="hlt">tensor</span>. In this work, a vorticity influenced <span class="hlt">stress</span> <span class="hlt">tensor</span> is derived. Behavior of its principal axes is examined. Within the context of a linearized one dimensional momentum equation, the asymmetric <span class="hlt">stress</span> <span class="hlt">tensor</span> is shown to display a forcing function behavior in phase space under some conditions. Classic heuristic arguments are discussed for assuming no influence of vorticity on <span class="hlt">stress</span>. Lastly, the behavior of a two dimensional, low speed free shear layer is computed as it transitions from laminar to turbulent flow under the influence of the Stokesian <span class="hlt">tensor</span> and then the vorticity-influenced <span class="hlt">tensor</span>. The MacCormack, two dimensional, explicit, time accurate, compressible code is used for this study.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2004APS..MARY26010L','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2004APS..MARY26010L"><span>Theory of electron g-<span class="hlt">tensor</span> in bulk and <span class="hlt">quantum</span>-well semiconductors</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Lau, Wayne H.; Flatte', Michael E.</p> <p>2004-03-01</p> <p>We present quantitative calculations for the electron g-<span class="hlt">tensors</span> in bulk and <span class="hlt">quantum</span>-well semiconductors based on a generalized P.p envelope function theory solved in a fourteen-band restricted basis set. The dependences of g-<span class="hlt">tensor</span> on structure, magnetic field, carrier density, temperature, and spin polarization have been explored and will be described. It is found that at temperatures of a few Kelvin and fields of a few Tesla, the g-<span class="hlt">tensors</span> for bulk semiconductors develop quasi-steplike dependences on carrier density or magnetic field due to magnetic quantization, and this effect is even more pronounced in <span class="hlt">quantum</span>-well semiconductors due to the additional electric quantization along the growth direction. The influence of <span class="hlt">quantum</span> confinement on the electron g-<span class="hlt">tensors</span> in QWs is studied by examining the dependence of electron g-<span class="hlt">tensors</span> on well width. Excellent agreement between these calculated electron g-<span class="hlt">tensors</span> and measurements [1-2] is found for GaAs/AlGaAs QWs. This work was supported by DARPA/ARO. [1] A. Malinowski and R. T. Harley, Phys. Rev. B 62, 2051 (2000);[2] Le Jeune et al., Semicond. Sci. Technol. 12, 380 (1997).</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016JSeis..20..669H','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016JSeis..20..669H"><span><span class="hlt">Stress</span> <span class="hlt">tensor</span> and focal mechanisms in the Dead Sea basin</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Hofstetter, A.; Dorbath, C.; Dorbath, L.; Braeuer, B.; Weber, M.</p> <p>2016-04-01</p> <p>We use the recorded seismicity, confined to the Dead Sea basin and its boundaries, by the Dead Sea Integrated Research (DESIRE) portable seismic network and the Israel and Jordan permanent seismic networks for studying the mechanisms of earthquakes in the Dead Sea basin. The observed seismicity in the Dead Sea basin is divided into nine regions according to the spatial distribution of the earthquakes and the known tectonic features. The large number of recording stations and the adequate station distribution allowed the reliable determinations of 494 earthquake focal mechanisms. For each region, based on the inversion of the observed polarities of the earthquakes, we determine the focal mechanisms and the associated <span class="hlt">stress</span> <span class="hlt">tensor</span>. For 159 earthquakes, out of the 494 focal mechanisms, we could determine compatible fault planes. On the eastern side, the focal mechanisms are mainly strike-slip mechanism with nodal planes in the N-S and E-W directions. The azimuths of the <span class="hlt">stress</span> axes are well constrained presenting minimal variability in the inversion of the data, which is in agreement with the Eastern Boundary fault on the east side of the Dead Sea basin and what we had expected from the regional geodynamics. However, larger variabilities of the azimuthal and dip angles are observed on the western side of the basin. Due to the wider range of azimuths of the fault planes, we observe the switching of σ1 and σ2 or the switching of σ2 and σ3 as major horizontal <span class="hlt">stress</span> directions. This observed switching of <span class="hlt">stress</span> axes allows having dip-slip and normal mechanisms in a region that is dominated by strike-slip motion.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016CPL...652..112M','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016CPL...652..112M"><span>11-cis retinal torsion: A QTAIM and <span class="hlt">stress</span> <span class="hlt">tensor</span> analysis of the S1 excited state</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Maza, Julio R.; Jenkins, Samantha; Kirk, Steven R.</p> <p>2016-05-01</p> <p>We investigate torsion about the C11-C12 bond mid-point for the S1 state of 11-cis retinal, using a QTAIM and <span class="hlt">stress</span> <span class="hlt">tensor</span> analysis. The QTAIM and <span class="hlt">stress</span> <span class="hlt">tensor</span> responses to a torsion ±α increase at a faster rate for the preferred direction of torsion though the CI seam. A QTAIM and <span class="hlt">stress</span> <span class="hlt">tensor</span> vector-based analysis provides an alternative way of characterising the asymmetry of the S1 potential energy surface. In the vicinity of the CI seam the ellipticity ε attained minimum values. The application of this analysis to molecular rotary motors is briefly discussed.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016EGUGA..18.1441D','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016EGUGA..18.1441D"><span>Use of non-fault fractures in <span class="hlt">stress</span> <span class="hlt">tensor</span> reconstruction using the Mohr Circle with the Win-<span class="hlt">tensor</span> program</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Delvaux, Damien</p> <p>2016-04-01</p> <p>Paleostress inversion of geological fault-slip data is usually done using the directional part of the applied <span class="hlt">stress</span> <span class="hlt">tensor</span> on a slip plane and comparing it with the observed slip lines. However, this method do not fully exploit the brittle data sets as those are composed of shear and tension fractures, in addition to faults. Brittle deformation can be decomposed in two steps. An initial fracture/failure in previously intact rock generate extension/tensile fractures or shear fractures, both without visible opening or displacement. This first step may or not be followed by fracture opening to form tension joints, frictional shearing to form shear faults, or a combination of opening and shearing which produces hybrid fractures. Fractured rock outcrop contain information of the <span class="hlt">stress</span> conditions that acted during both brittle deformation steps. The purpose here is to investigate how the fracture pattern generated during the initial fracture/failure step might be used in paleostress reconstruction. Each fracture is represented on the Mohr Circle by its resolved normal and shear <span class="hlt">stress</span> magnitudes. We consider the typical domains on the Mohr circle where the different types de fractures nucleate (tension, hybrid, shear and compression fractures), as well the domain which contain reactivated fractures (faults reactivating an initial fracture plane). In function of the fracture type defined in the field, a "distance" is computed on the Mohr circle between each point and its expected corresponding nucleation/reactivation domain. This "Mohr Distance" is then used as function to minimize during the inversion. We implemented this new function in the Win-<span class="hlt">Tensor</span> program, and tested it with natural and synthetic data sets from different <span class="hlt">stress</span> regimes. It can be used alone using only the Mohr Distance on each plane (function F10), or combined with the angular misfit between observed striae and resolved shear directions (composite function F11). When used alone (F10), only the 3</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016JHEP...02..102B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016JHEP...02..102B"><span>Flavour fields in steady state: <span class="hlt">stress</span> <span class="hlt">tensor</span> and free energy</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Banerjee, Avik; Kundu, Arnab; Kundu, Sandipan</p> <p>2016-02-01</p> <p>The dynamics of a probe brane in a given gravitational background is governed by the Dirac-Born-Infeld action. The corresponding open string metric arises naturally in studying the fluctuations on the probe. In Gauge-String duality, it is known that in the presence of a constant electric field on the worldvolume of the probe, the open string metric acquires an event horizon and therefore the fluctuation modes on the probe experience an effective temperature. In this article, we bring together various properties of such a system to a formal definition and a subsequent narration of the effective thermodynamics and the <span class="hlt">stress</span> <span class="hlt">tensor</span> of the corresponding flavour fields, also including a non-vanishing chemical potential. In doing so, we point out a potentially infinitely-degenerate scheme-dependence of regularizing the free energy, which nevertheless yields a universal contribution in certain cases. This universal piece appears as the coefficient of a log-divergence in free energy when a space-filling probe brane is embedded in AdS d+1-background, for d = 2, 4, and is related to conformal anomaly. For the special case of d = 2, the universal factor has a striking resemblance to the well-known heat current formula in (1 + 1)-dimensional conformal field theory in steady-state, which endows a plausible physical interpretation to it. Interestingly, we observe a vanishing conformal anomaly in d = 6.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/scitech/biblio/982172','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/982172"><span>Performance Optimization of <span class="hlt">Tensor</span> Contraction Expressions for Many Body Methods in <span class="hlt">Quantum</span> Chemistry</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Krishnamoorthy, Sriram; Bernholdt, David E; Pitzer, R. M.; Sadayappan, Ponnuswamy</p> <p>2009-01-01</p> <p>Complex <span class="hlt">tensor</span> contraction expressions arise in accurate electronic structure models in <span class="hlt">quantum</span> chemistry, such as the coupled cluster method. This paper addresses two complementary aspects of performance optimization of such <span class="hlt">tensor</span> contraction expressions. Transformations using algebraic properties of commutativity and associativity can be used to significantly decrease the number of arithmetic operations required for evaluation of these expressions. The identification of common subexpressions among a set of <span class="hlt">tensor</span> contraction expressions can result in a reduction of the total number of operations required to evaluate the <span class="hlt">tensor</span> contractions. The first part of the paper describes an effective algorithm for operation minimization with common subexpression identification and demonstrates its effectiveness on <span class="hlt">tensor</span> contraction expressions for coupled cluster equations. The second part of the paper highlights the importance of data layout transformation in the optimization of <span class="hlt">tensor</span> contraction computations on modern processors. A number of considerations, such as minimization of cache misses and utilization of multimedia vector instructions, are discussed. A library for efficient index permutation of multidimensional <span class="hlt">tensors</span> is described, and experimental performance data is provided that demonstrates its effectiveness.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/scitech/biblio/973715','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/973715"><span>Performance Optimization of <span class="hlt">Tensor</span> Contraction Expressions for Many Body Methods in <span class="hlt">Quantum</span> Chemistry</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Hartono, Albert; Lu, Qingda; henretty, thomas; Krishnamoorthy, Sriram; zhang, huaijian; Baumgartner, Gerald; Bernholdt, David E.; Nooijen, Marcel; Pitzer, Russell M.; Ramanujam, J.; Sadayappan, Ponnuswamy</p> <p>2009-11-12</p> <p>Complex <span class="hlt">tensor</span> contraction expressions arise in accurate electronic structure models in <span class="hlt">quantum</span> chemistry, such as the coupled cluster method. This paper addresses two complementary aspects of performance optimization of such <span class="hlt">tensor</span> contraction expressions. Transformations using algebraic properties of commutativity and associativity can be used to significantly decrease the number of arithmetic operations required for evaluation of these expressions. The identification of common subexpressions among a set of <span class="hlt">tensor</span> contraction expressions can result in a reduction of the total number of operations required to evaluate the <span class="hlt">tensor</span> contractions. The first part of the paper describes an effective algorithm for operation minimization with common subexpression identification and demonstrates its effectiveness on <span class="hlt">tensor</span> contraction expressions for coupled cluster equations. The second part of the paper highlights the importance of data layout transformation in the optimization of <span class="hlt">tensor</span> contraction computations on modern processors. A number of considerations such as minimization of cache misses and utilization of multimedia vector instructions are discussed. A library for efficient index permutation of multi-dimensional <span class="hlt">tensors</span> is described and experimental performance data is provided that demonstrates its effectiveness.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/19888780','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/19888780"><span>Performance optimization of <span class="hlt">tensor</span> contraction expressions for many-body methods in <span class="hlt">quantum</span> chemistry.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Hartono, Albert; Lu, Qingda; Henretty, Thomas; Krishnamoorthy, Sriram; Zhang, Huaijian; Baumgartner, Gerald; Bernholdt, David E; Nooijen, Marcel; Pitzer, Russell; Ramanujam, J; Sadayappan, P</p> <p>2009-11-12</p> <p>Complex <span class="hlt">tensor</span> contraction expressions arise in accurate electronic structure models in <span class="hlt">quantum</span> chemistry, such as the coupled cluster method. This paper addresses two complementary aspects of performance optimization of such <span class="hlt">tensor</span> contraction expressions. Transformations using algebraic properties of commutativity and associativity can be used to significantly decrease the number of arithmetic operations required for evaluation of these expressions. The identification of common subexpressions among a set of <span class="hlt">tensor</span> contraction expressions can result in a reduction of the total number of operations required to evaluate the <span class="hlt">tensor</span> contractions. The first part of the paper describes an effective algorithm for operation minimization with common subexpression identification and demonstrates its effectiveness on <span class="hlt">tensor</span> contraction expressions for coupled cluster equations. The second part of the paper highlights the importance of data layout transformation in the optimization of <span class="hlt">tensor</span> contraction computations on modern processors. A number of considerations, such as minimization of cache misses and utilization of multimedia vector instructions, are discussed. A library for efficient index permutation of multidimensional <span class="hlt">tensors</span> is described, and experimental performance data is provided that demonstrates its effectiveness.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/scitech/biblio/20935276','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/20935276"><span><span class="hlt">Stress</span> <span class="hlt">tensor</span> of a quark moving through N=4 thermal plasma</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Friess, Joshua J.; Gubser, Steven S.; Michalogiorgakis, Georgios; Pufu, Silviu S.</p> <p>2007-05-15</p> <p>We develop the linear equations that describe graviton perturbations of AdS{sub 5}-Schwarzschild generated by a string trailing behind an external quark moving with constant velocity. Solving these equations allows us to evaluate the <span class="hlt">stress</span> <span class="hlt">tensor</span> in the boundary gauge theory. Components of the <span class="hlt">stress</span> <span class="hlt">tensor</span> exhibit directional structures in Fourier space at both large and small momenta. We comment on the possible relevance of our results to relativistic heavy-ion collisions.</p> </li> </ol> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_1");'>1</a></li> <li class="active"><span>2</span></li> <li><a href="#" onclick='return showDiv("page_3");'>3</a></li> <li><a href="#" onclick='return showDiv("page_4");'>4</a></li> <li><a href="#" onclick='return showDiv("page_5");'>5</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div><!-- col-sm-12 --> </div><!-- row --> </div><!-- page_2 --> <div id="page_3" class="hiddenDiv"> <div class="row"> <div class="col-sm-12"> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_1");'>1</a></li> <li><a href="#" onclick='return showDiv("page_2");'>2</a></li> <li class="active"><span>3</span></li> <li><a href="#" onclick='return showDiv("page_4");'>4</a></li> <li><a href="#" onclick='return showDiv("page_5");'>5</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div> </div> <div class="row"> <div class="col-sm-12"> <ol class="result-class" start="41"> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/scitech/biblio/22157106','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/22157106"><span>Conservation laws and <span class="hlt">stress</span>-energy-momentum <span class="hlt">tensors</span> for systems with background fields</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Gratus, Jonathan; Obukhov, Yuri N.; Tucker, Robin W.</p> <p>2012-10-15</p> <p>This article attempts to delineate the roles played by non-dynamical background structures and Killing symmetries in the construction of <span class="hlt">stress</span>-energy-momentum <span class="hlt">tensors</span> generated from a diffeomorphism invariant action density. An intrinsic coordinate independent approach puts into perspective a number of spurious arguments that have historically lead to the main contenders, viz the Belinfante-Rosenfeld <span class="hlt">stress</span>-energy-momentum <span class="hlt">tensor</span> derived from a Noether current and the Einstein-Hilbert <span class="hlt">stress</span>-energy-momentum <span class="hlt">tensor</span> derived in the context of Einstein's theory of general relativity. Emphasis is placed on the role played by non-dynamical background (phenomenological) structures that discriminate between properties of these <span class="hlt">tensors</span> particularly in the context of electrodynamics in media. These <span class="hlt">tensors</span> are used to construct conservation laws in the presence of Killing Lie-symmetric background fields. - Highlights: Black-Right-Pointing-Pointer The role of background fields in diffeomorphism invariant actions is demonstrated. Black-Right-Pointing-Pointer Interrelations between different <span class="hlt">stress</span>-energy-momentum <span class="hlt">tensors</span> are emphasised. Black-Right-Pointing-Pointer The Abraham and Minkowski electromagnetic <span class="hlt">tensors</span> are discussed in this context. Black-Right-Pointing-Pointer Conservation laws in the presence of nondynamic background fields are formulated. Black-Right-Pointing-Pointer The discussion is facilitated by the development of a new variational calculus.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2012IJMPS..14..403K','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2012IJMPS..14..403K"><span>Optical Probes of the <span class="hlt">Quantum</span> Vacuum: the Photon Polarization <span class="hlt">Tensor</span> in External Fields</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Karbstein, Felix; Roessler, Lars; Döbrich, Babette; Gies, Holger</p> <p>2012-07-01</p> <p>The photon polarization <span class="hlt">tensor</span> is the central building block of an effective theory description of photon propagation in the <span class="hlt">quantum</span> vacuum. It accounts for the vacuum fluctuations of the underlying theory, and in the presence of external electromagnetic fields, gives rise to such striking phenomena as vacuum birefringence and dichroism. Standard approximations of the polarization <span class="hlt">tensor</span> are often restricted to on-the-light-cone dynamics in homogeneous electromagnetic fields, and are limited to certain momentum regimes only. We devise two different strategies to go beyond these limitations: First, we aim at obtaining novel analytical insights into the photon polarization <span class="hlt">tensor</span> for homogeneous fields, while retaining its full momentum dependence. Second, we employ wordline numerical methods to surpass the constant-field limit.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2015JCAP...10..052Z','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015JCAP...10..052Z"><span>Scalar and <span class="hlt">tensor</span> perturbations in loop <span class="hlt">quantum</span> cosmology: high-order corrections</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Zhu, Tao; Wang, Anzhong; Cleaver, Gerald; Kirsten, Klaus; Sheng, Qin; Wu, Qiang</p> <p>2015-10-01</p> <p>Loop <span class="hlt">quantum</span> cosmology (LQC) provides promising resolutions to the trans-Planckian issue and initial singularity arising in the inflationary models of general relativity. In general, due to different quantization approaches, LQC involves two types of <span class="hlt">quantum</span> corrections, the holonomy and inverse-volume, to both of the cosmological background evolution and perturbations. In this paper, using the third-order uniform asymptotic approximations, we derive explicitly the observational quantities of the slow-roll inflation in the framework of LQC with these <span class="hlt">quantum</span> corrections. We calculate the power spectra, spectral indices, and running of the spectral indices for both scalar and <span class="hlt">tensor</span> perturbations, whereby the <span class="hlt">tensor</span>-to-scalar ratio is obtained. We expand all the observables at the time when the inflationary mode crosses the Hubble horizon. As the upper error bounds for the uniform asymptotic approximation at the third-order are lesssim 0.15%, these results represent the most accurate results obtained so far in the literature. It is also shown that with the inverse-volume corrections, both scalar and <span class="hlt">tensor</span> spectra exhibit a deviation from the usual shape at large scales. Then, using the Planck, BAO and SN data we obtain new constraints on <span class="hlt">quantum</span> gravitational effects from LQC corrections, and find that such effects could be within the detection of the forthcoming experiments.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/scitech/biblio/22525226','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/22525226"><span>Scalar and <span class="hlt">tensor</span> perturbations in loop <span class="hlt">quantum</span> cosmology: high-order corrections</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Zhu, Tao; Wang, Anzhong; Wu, Qiang; Cleaver, Gerald; Kirsten, Klaus; Sheng, Qin E-mail: anzhong_wang@baylor.edu E-mail: klaus_kirsten@baylor.edu E-mail: wuq@zjut.edu.cn</p> <p>2015-10-01</p> <p>Loop <span class="hlt">quantum</span> cosmology (LQC) provides promising resolutions to the trans-Planckian issue and initial singularity arising in the inflationary models of general relativity. In general, due to different quantization approaches, LQC involves two types of <span class="hlt">quantum</span> corrections, the holonomy and inverse-volume, to both of the cosmological background evolution and perturbations. In this paper, using the third-order uniform asymptotic approximations, we derive explicitly the observational quantities of the slow-roll inflation in the framework of LQC with these <span class="hlt">quantum</span> corrections. We calculate the power spectra, spectral indices, and running of the spectral indices for both scalar and <span class="hlt">tensor</span> perturbations, whereby the <span class="hlt">tensor</span>-to-scalar ratio is obtained. We expand all the observables at the time when the inflationary mode crosses the Hubble horizon. As the upper error bounds for the uniform asymptotic approximation at the third-order are ∼< 0.15%, these results represent the most accurate results obtained so far in the literature. It is also shown that with the inverse-volume corrections, both scalar and <span class="hlt">tensor</span> spectra exhibit a deviation from the usual shape at large scales. Then, using the Planck, BAO and SN data we obtain new constraints on <span class="hlt">quantum</span> gravitational effects from LQC corrections, and find that such effects could be within the detection of the forthcoming experiments.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016PhRvL.116w7201W','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016PhRvL.116w7201W"><span>Positive <span class="hlt">Tensor</span> Network Approach for Simulating Open <span class="hlt">Quantum</span> Many-Body Systems</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Werner, A. H.; Jaschke, D.; Silvi, P.; Kliesch, M.; Calarco, T.; Eisert, J.; Montangero, S.</p> <p>2016-06-01</p> <p>Open <span class="hlt">quantum</span> many-body systems play an important role in <span class="hlt">quantum</span> optics and condensed matter physics, and capture phenomena like transport, the interplay between Hamiltonian and incoherent dynamics, and topological order generated by dissipation. We introduce a versatile and practical method to numerically simulate one-dimensional open <span class="hlt">quantum</span> many-body dynamics using <span class="hlt">tensor</span> networks. It is based on representing mixed <span class="hlt">quantum</span> states in a locally purified form, which guarantees that positivity is preserved at all times. Moreover, the approximation error is controlled with respect to the trace norm. Hence, this scheme overcomes various obstacles of the known numerical open-system evolution schemes. To exemplify the functioning of the approach, we study both stationary states and transient dissipative behavior, for various open <span class="hlt">quantum</span> systems ranging from few to many bodies.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/27341253','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/27341253"><span>Positive <span class="hlt">Tensor</span> Network Approach for Simulating Open <span class="hlt">Quantum</span> Many-Body Systems.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Werner, A H; Jaschke, D; Silvi, P; Kliesch, M; Calarco, T; Eisert, J; Montangero, S</p> <p>2016-06-10</p> <p>Open <span class="hlt">quantum</span> many-body systems play an important role in <span class="hlt">quantum</span> optics and condensed matter physics, and capture phenomena like transport, the interplay between Hamiltonian and incoherent dynamics, and topological order generated by dissipation. We introduce a versatile and practical method to numerically simulate one-dimensional open <span class="hlt">quantum</span> many-body dynamics using <span class="hlt">tensor</span> networks. It is based on representing mixed <span class="hlt">quantum</span> states in a locally purified form, which guarantees that positivity is preserved at all times. Moreover, the approximation error is controlled with respect to the trace norm. Hence, this scheme overcomes various obstacles of the known numerical open-system evolution schemes. To exemplify the functioning of the approach, we study both stationary states and transient dissipative behavior, for various open <span class="hlt">quantum</span> systems ranging from few to many bodies.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016PhRvB..94x5126P','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016PhRvB..94x5126P"><span>First-principles calculation of <span class="hlt">stress</span> <span class="hlt">tensor</span> in the LSDA+U formalism</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Park, Se Young; Choi, Hyoung Joon</p> <p>2016-12-01</p> <p>We derive the <span class="hlt">stress-tensor</span> formula within the LSDA+U scheme by differentiating analytically the LSDA+U total-energy function with respect to the strain <span class="hlt">tensor</span>. The rotationally invariant form of the LSDA+U functional is employed and the double-counting correction is considered in the fully localized limit and around mean field. The electronic wave functions are expanded with either pseudoatomic orbitals (PAOs) or plane waves. In the PAO-basis case, the orthogonality <span class="hlt">stress</span> term is included. Our LSDA+U <span class="hlt">stress-tensor</span> formula is numerically tested with antiferromagnetic NiO and reproduces successfully the <span class="hlt">stress</span> values obtained from numerical derivatives of the total-energy values. As an application, we study elastic constants, bulk moduli, and sound velocities of NiO and MnO, obtaining results in good agreement with experimental data.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/27698143','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/27698143"><span>Simplified derivation of the gravitational wave <span class="hlt">stress</span> <span class="hlt">tensor</span> from the linearized Einstein field equations.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Balbus, Steven A</p> <p>2016-10-18</p> <p>A conserved <span class="hlt">stress</span> energy <span class="hlt">tensor</span> for weak field gravitational waves propagating in vacuum is derived directly from the linearized general relativistic wave equation alone, for an arbitrary gauge. In any harmonic gauge, the form of the <span class="hlt">tensor</span> leads directly to the classical expression for the outgoing wave energy. The method described here, however, is a much simpler, shorter, and more physically motivated approach than is the customary procedure, which involves a lengthy and cumbersome second-order (in wave-amplitude) calculation starting with the Einstein <span class="hlt">tensor</span>. Our method has the added advantage of exhibiting the direct coupling between the outgoing wave energy flux and the work done by the gravitational field on the sources. For nonharmonic gauges, the directly derived wave <span class="hlt">stress</span> <span class="hlt">tensor</span> has an apparent index asymmetry. This coordinate artifact may be straightforwardly removed, and the symmetrized (still gauge-invariant) <span class="hlt">tensor</span> then takes on its widely used form. Angular momentum conservation follows immediately. For any harmonic gauge, however, the <span class="hlt">stress</span> <span class="hlt">tensor</span> found is manifestly symmetric from the start, and its derivation depends, in its entirety, on the structure of the linearized wave equation.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016AnPhy.366...57I','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016AnPhy.366...57I"><span>Maxwell-Dirac <span class="hlt">stress</span>-energy <span class="hlt">tensor</span> in terms of Fierz bilinear currents</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Inglis, Shaun; Jarvis, Peter</p> <p>2016-03-01</p> <p>We analyse the <span class="hlt">stress</span>-energy <span class="hlt">tensor</span> for the self-coupled Maxwell-Dirac system in the bilinear current formalism, using two independent approaches. The first method used is that attributed to Belinfante: starting from the spinor form of the action, the well-known canonical <span class="hlt">stress</span>-energy <span class="hlt">tensor</span> is augmented, by extending the Noether symmetry current to include contributions from the Lorentz group, to a manifestly symmetric form. This form admits a transcription to bilinear current form. The second method used is the variational derivation based on the covariant coupling to general relativity. The starting point here at the outset is the transcription of the action using, as independent field variables, both the bilinear currents, together with a gauge invariant vector field (a proxy for the electromagnetic vector potential). A central feature of the two constructions is that they both involve the mapping of the Dirac contribution to the <span class="hlt">stress</span>-energy from the spinor fields to the equivalent set of bilinear <span class="hlt">tensor</span> currents, through the use of appropriate Fierz identities. Although this mapping is done at quite different stages, nonetheless we find that the two forms of the bilinear <span class="hlt">stress</span>-energy <span class="hlt">tensor</span> agree. Finally, as an application, we consider the reduction of the obtained <span class="hlt">stress</span>-energy <span class="hlt">tensor</span> in bilinear form, under the assumption of spherical symmetry.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://files.eric.ed.gov/fulltext/EJ155856.pdf','ERIC'); return false;" href="http://files.eric.ed.gov/fulltext/EJ155856.pdf"><span>Simple Derivation of the Maxwell <span class="hlt">Stress</span> <span class="hlt">Tensor</span> and Electrostrictive Effects in Crystals</span></a></p> <p><a target="_blank" href="http://www.eric.ed.gov/ERICWebPortal/search/extended.jsp?_pageLabel=advanced">ERIC Educational Resources Information Center</a></p> <p>Juretschke, H. J.</p> <p>1977-01-01</p> <p>Shows that local equilibrium and energy considerations in an elastic dielectric crystal lead to a simple derivation of the Maxwell <span class="hlt">stress</span> <span class="hlt">tensor</span> in anisotropic dielectric solids. The resulting equilibrium <span class="hlt">stress</span>-strain relations are applied to determine the deformations of a charged parallel plate capacitor. (MLH)</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016InJPh..90.1325L','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016InJPh..90.1325L"><span><span class="hlt">Quantum</span> cosmology with matter in scalar-<span class="hlt">tensor</span> theory</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Lee, S.; Lim, H.</p> <p>2016-11-01</p> <p>The cosmological application of the low energy effective action of string theory with perfect fluid type matter (satisfying p=γ ρ ) is reconsidered. First, its isotropic and anisotropic spacetime cosmological solutions are obtained for general γ . The scale factor duality is applied and checked for our model as well as in the presence of γ of which possible extension to nonvanishing γ is pioneered before. The asymptotic behavior of the solutions is investigated because of the complexity of the solutions. Second, as a quantization, we apply the canonical quantization and the corresponding Wheeler-De Witt equation is constructed for this scalar-<span class="hlt">tensor</span> theory. By solving the Wheeler-De Witt equation the wave function is found for general value of γ . On the basis of its wave function, the tunneling rate turns out to be just the ratio of norms of the wave function for pre- and post-big-bang phases. This result shows that the rate grows as γ gets value close to a specific value. This resolves the undetermined value for the behavior of the scale factors.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017JPhB...50g5502T','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017JPhB...50g5502T"><span>Spin correlation <span class="hlt">tensor</span> for measurement of <span class="hlt">quantum</span> entanglement in electron–electron scattering</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Tsurikov, D. E.; Samarin, S. N.; Williams, J. F.; Artamonov, O. M.</p> <p>2017-04-01</p> <p>We consider the problem of correct measurement of a <span class="hlt">quantum</span> entanglement in the two-body electron–electron scattering. An expression is derived for a spin correlation <span class="hlt">tensor</span> of a pure two-electron state. A geometric measure of a <span class="hlt">quantum</span> entanglement as the distance between two forms of this <span class="hlt">tensor</span> in entangled and separable cases is presented. Due to such definition, one does not need to look for the closest separable state to the analyzed state. We prove that introduced measure satisfies properties of a valid entanglement measure: nonnegativity, discriminance, normalization, non-growth under local operations and classical communication. This measure is calculated for a problem of electron–electron scattering. We prove that it does not depend on the azimuthal rotation angle of the second electron spin relative to the first electron spin before scattering. We specify how to find a spin correlation <span class="hlt">tensor</span> and the related measure of a <span class="hlt">quantum</span> entanglement in an experiment with electron–electron scattering. Finally, the introduced measure is extended to the mixed states.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/23531015','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/23531015"><span>Multidimensional supersymmetric <span class="hlt">quantum</span> mechanics: spurious states for the <span class="hlt">tensor</span> sector two Hamiltonian.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Chou, Chia-Chun; Kouri, Donald J</p> <p>2013-04-25</p> <p>We show that there exist spurious states for the sector two <span class="hlt">tensor</span> Hamiltonian in multidimensional supersymmetric <span class="hlt">quantum</span> mechanics. For one-dimensional supersymmetric <span class="hlt">quantum</span> mechanics on an infinite domain, the sector one and two Hamiltonians have identical spectra with the exception of the ground state of the sector one. For tensorial multidimensional supersymmetric <span class="hlt">quantum</span> mechanics, there exist normalizable spurious states for the sector two Hamiltonian with energy equal to the ground state energy of the sector one. These spurious states are annihilated by the adjoint charge operator, and hence, they do not correspond to physical states for the original Hamiltonian. The Hermitian property of the sector two Hamiltonian implies the orthogonality between spurious and physical states. In addition, we develop a method for construction of a specific form of the spurious states for any <span class="hlt">quantum</span> system and also generate several spurious states for a two-dimensional anharmonic oscillator system and for the hydrogen atom.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2015ZaMP...66.1143B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015ZaMP...66.1143B"><span>Green-Naghdi rate of the Kirchhoff <span class="hlt">stress</span> and deformation rate: the elasticity <span class="hlt">tensor</span></span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Bellini, Chiara; Federico, Salvatore</p> <p>2015-06-01</p> <p>The elasticity <span class="hlt">tensor</span> providing the power-conjugation of the Green-Naghdi rate of the Kirchhoff <span class="hlt">stress</span> and the deformation rate is required, e.g. by the commercially available Finite Element package ABAQUS/Standard for the material user subroutine UMAT, used to input material behaviours other than those included in the libraries of the package. This elasticity <span class="hlt">tensor</span> had been studied in the literature, but its symmetries have only been briefly discussed, and only its component form in Cartesian coordinates was known. In this work, we derived a covariant, component-free expression of this elasticity <span class="hlt">tensor</span> and thoroughly studied its symmetries. We found that, although symmetry on both pair of feet (indices) has been deemed to be desirable in the literature, the expression of the <span class="hlt">tensor</span> available to-date in fact possesses only symmetry on the first pair of feet (indices), whereas the second pair lacks symmetry, and therefore carries a skew-symmetric contribution. This contribution is unnecessary, as it is automatically filtered in the contraction of the elasticity <span class="hlt">tensor</span> with the symmetric deformation rate <span class="hlt">tensor</span>. In order to avoid carrying this unnecessary skew-symmetric contribution in the computations, we employ a <span class="hlt">tensor</span> identity that naturally symmetrises the second pair of feet of the elasticity <span class="hlt">tensor</span>. We demonstrated the validity and robustness of the implementation of the user-defined material based on this <span class="hlt">tensor</span> representation by simulating a benchmark problem consisting in biaxial tests of porcine and human atrial tissue, with material properties taken from previously performed experiments. We compared the results obtained by means of our user-defined material and those obtained through an equivalent built-in material, and obtained identical results.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/20020061791','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20020061791"><span>Elliptic Relaxation of a <span class="hlt">Tensor</span> Representation for the Redistribution Terms in a Reynolds <span class="hlt">Stress</span> Turbulence Model</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Carlson, J. R.; Gatski, T. B.</p> <p>2002-01-01</p> <p>A formulation to include the effects of wall proximity in a second-moment closure model that utilizes a <span class="hlt">tensor</span> representation for the redistribution terms in the Reynolds <span class="hlt">stress</span> equations is presented. The wall-proximity effects are modeled through an elliptic relaxation process of the <span class="hlt">tensor</span> expansion coefficients that properly accounts for both correlation length and time scales as the wall is approached. Direct numerical simulation data and Reynolds <span class="hlt">stress</span> solutions using a full differential approach are compared for the case of fully developed channel flow.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2015MPLA...3050127H','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015MPLA...3050127H"><span>Slow-roll inflation in loop <span class="hlt">quantum</span> cosmology of scalar-<span class="hlt">tensor</span> theories of gravity</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Han, Yu</p> <p>2015-07-01</p> <p>The slow-roll inflation of scalar-<span class="hlt">tensor</span> theories (STTs) of gravity in the context of loop <span class="hlt">quantum</span> cosmology (LQC) is investigated in this paper. After deriving the effective Hamiltonian, we obtain the semiclassical equations of motion for the background variables in both Jordan frame and Einstein frame of STTs. Then we apply these equations in the slow-roll limit and derive the LQC corrections to the scalar spectral index ns and the <span class="hlt">tensor</span>-to-scalar ratio r in the two frames of STTs. Finally, we take two special sectors of STTs as specific examples, namely the Starobinsky model and the non-minimally coupled scalar field model (with the coupling function ξϕ2R and the potential λ 4 ϕ4). We derive the detailed expressions of the LQC corrections to ns and r in terms of the e-folding number for these two models in both frames.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016ufm..conf..293D','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016ufm..conf..293D"><span>Notes on Translational and Rotational Properties of <span class="hlt">Tensor</span> Fields in Relativistic <span class="hlt">Quantum</span> Mechanics</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Dvoeglazov, V. V.</p> <p></p> <p>Recently, several discussions on the possible observability of 4-vector fields have been published in literature. Furthermore, several authors recently claimed existence of the helicity=0 fundamental field. We re-examine the theory of antisymmetric <span class="hlt">tensor</span> fields and 4-vector potentials. We study the massless limits. In fact, a theoretical motivation for this venture is the old papers of Ogievetskiĭ and Polubarinov, Hayashi, and Kalb and Ramond. Ogievetskiĭ and Polubarinov proposed the concept of the notoph, whose helicity properties are complementary to those of the photon. We analyze the <span class="hlt">quantum</span> field theory with taking into account mass dimensions of the notoph and the photon. It appears to be possible to describe both photon and notoph degrees of freedom on the basis of the modified Bargmann-Wigner formalism for the symmetric second-rank spinor. Next, we proceed to derive equations for the symmetric <span class="hlt">tensor</span> of the second rank on the basis of the Bargmann-Wigner formalism in a straightforward way. The symmetric multispinor of the fourth rank is used. Due to serious problems with the interpretation of the results obtained on using the standard procedure we generalize it and obtain the spin-2 relativistic equations, which are consistent with the general relativity. Thus, in fact we deduced the gravitational field equations from relativistic <span class="hlt">quantum</span> mechanics. The relations of this theory with the scalar-<span class="hlt">tensor</span> theories of gravitation and f(R) are discussed. Particular attention has been paid to the correct definitions of the energy-momentum <span class="hlt">tensor</span> and other Nöther currents in the electromagnetic theory, the relativistic theory of gravitation, the general relativity, and their generalizations. We estimate possible interactions, fermion-notoph, graviton-notoph, photon-notoph, and we conclude that they can probably be seen in experiments in the next few years.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19940007814','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19940007814"><span>Parameterization of subgrid-scale <span class="hlt">stress</span> by the velocity gradient <span class="hlt">tensor</span></span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Lund, Thomas S.; Novikov, E. A.</p> <p>1993-01-01</p> <p>The objective of this work is to construct and evaluate subgrid-scale models that depend on both the strain rate and the vorticity. This will be accomplished by first assuming that the subgrid-scale <span class="hlt">stress</span> is a function of the strain and rotation rate <span class="hlt">tensors</span>. Extensions of the Caley-Hamilton theorem can then be used to write the assumed functional dependence explicitly in the form of a <span class="hlt">tensor</span> polynomial involving products of the strain and rotation rates. Finally, use of this explicit expression as a subgrid-scale model will be evaluated using direct numerical simulation data for homogeneous, isotropic turbulence.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2012JAP...111a3504P','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2012JAP...111a3504P"><span><span class="hlt">Stress</span> <span class="hlt">tensor</span> dependence of the polarized Raman spectrum of tetragonal barium titanate</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Pezzotti, Giuseppe; Okai, Keisuke; Zhu, Wenliang</p> <p>2012-01-01</p> <p>The <span class="hlt">stress</span> <span class="hlt">tensor</span> dependence of the polarized Raman spectrum of the barium titanate (BaTiO3) tetragonal structure has been theoretically elucidated and the phonon deformation potential (PDP) constants of its A1(TO) and E(TO) vibrational modes measured by means of a spectroscopic analysis of single-crystalline samples under controlled <span class="hlt">stress</span> fields. Two types of <span class="hlt">stress</span> field were employed: (i) A uniaxial (compressive) <span class="hlt">stress</span> field generated with loading along different crystallographic axes and (ii) a biaxial (tensile) <span class="hlt">stress</span> field stored at the tip of a surface crack propagated across the a-plane of the crystal. This latter <span class="hlt">stress</span> field enabled us unfolding the full set of PDP values for the E(TO) vibrational mode. However, the highly graded (multiaxial) <span class="hlt">stress</span> field stored at the crack tip required both rationalizing the dependence of oblique phonons on crystal orientation and applying a spatial deconvolution routine based on the three-dimensional response of the Raman probe. According to a combination of experimental and computational procedures, we quantitatively uncoupled the effects of crystallographic orientation and spatial convolution from the locally collected Raman spectra. Uniaxial compression and biaxial tensile <span class="hlt">stress</span> calibrations led to consistent PDP values, thus allowing the establishment of a working algorithm for <span class="hlt">stress</span> analysis in the technologically important class of perovskitic material. Finally, as an application of the newly developed procedure, a <span class="hlt">tensor</span>-resolved <span class="hlt">stress</span> analysis was performed to evaluate the unknown (elastic) magnitude of the residual <span class="hlt">stress</span> components and the extent of the plastic deformation zone generated around a Vickers indentation print in BaTiO3 single crystal. The present findings open the way to <span class="hlt">tensor</span> resolved Raman analysis of the complex strain fields stored in advanced ferroelectric devices.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/23574214','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/23574214"><span>Efficient tree <span class="hlt">tensor</span> network states (TTNS) for <span class="hlt">quantum</span> chemistry: generalizations of the density matrix renormalization group algorithm.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Nakatani, Naoki; Chan, Garnet Kin-Lic</p> <p>2013-04-07</p> <p>We investigate tree <span class="hlt">tensor</span> network states for <span class="hlt">quantum</span> chemistry. Tree <span class="hlt">tensor</span> network states represent one of the simplest generalizations of matrix product states and the density matrix renormalization group. While matrix product states encode a one-dimensional entanglement structure, tree <span class="hlt">tensor</span> network states encode a tree entanglement structure, allowing for a more flexible description of general molecules. We describe an optimal tree <span class="hlt">tensor</span> network state algorithm for <span class="hlt">quantum</span> chemistry. We introduce the concept of half-renormalization which greatly improves the efficiency of the calculations. Using our efficient formulation we demonstrate the strengths and weaknesses of tree <span class="hlt">tensor</span> network states versus matrix product states. We carry out benchmark calculations both on tree systems (hydrogen trees and π-conjugated dendrimers) as well as non-tree molecules (hydrogen chains, nitrogen dimer, and chromium dimer). In general, tree <span class="hlt">tensor</span> network states require much fewer renormalized states to achieve the same accuracy as matrix product states. In non-tree molecules, whether this translates into a computational savings is system dependent, due to the higher prefactor and computational scaling associated with tree algorithms. In tree like molecules, tree network states are easily superior to matrix product states. As an illustration, our largest dendrimer calculation with tree <span class="hlt">tensor</span> network states correlates 110 electrons in 110 active orbitals.</p> </li> </ol> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_1");'>1</a></li> <li><a href="#" onclick='return showDiv("page_2");'>2</a></li> <li class="active"><span>3</span></li> <li><a href="#" onclick='return showDiv("page_4");'>4</a></li> <li><a href="#" onclick='return showDiv("page_5");'>5</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div><!-- col-sm-12 --> </div><!-- row --> </div><!-- page_3 --> <div id="page_4" class="hiddenDiv"> <div class="row"> <div class="col-sm-12"> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_2");'>2</a></li> <li><a href="#" onclick='return showDiv("page_3");'>3</a></li> <li class="active"><span>4</span></li> <li><a href="#" onclick='return showDiv("page_5");'>5</a></li> <li><a href="#" onclick='return showDiv("page_6");'>6</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div> </div> <div class="row"> <div class="col-sm-12"> <ol class="result-class" start="61"> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19870017907','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19870017907"><span>Altimetry data and the elastic <span class="hlt">stress</span> <span class="hlt">tensor</span> of subduction zones</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Caputo, Michele</p> <p>1987-01-01</p> <p>The maximum shear <span class="hlt">stress</span> (mss) field due to mass anomalies is estimated in the Apennines, the Kermadec-Tonga Trench, and the Rio Grande Rift areas and the results for each area are compared to observed seismicity. A maximum mss of 420 bar was calculated in the Kermadec-Tonga Trench region at a depth of 28 km. Two additional zones with more than 300 bar mss were also observed in the Kermadec-Tonga Trench study. Comparison of the calculated mss field with the observed seismicity in the Kermadec-Tonga showed two zones of well correlated activity. The Rio Grande Rift results showed a maximum mss of 700 bar occurring east of the rift and at a depth of 6 km. Recorded seismicity in the region was primarily constrained to a depth of approximately 5 km, correlating well to the results of the <span class="hlt">stress</span> calculations. Two areas of high mss are found in the Apennine region: 120 bar at a depth of 55 km, and 149 bar at the surface. Seismic events observed in the Apennine area compare favorably with the mss field calculated, exhibiting two zones of activity. The case of loading by seamounts and icecaps are also simulated. Results for this study show that the mss reaches a maximum of about 1/3 that of the applied surface <span class="hlt">stress</span> for both cases, and is located at a depth related to the diameter of the surface mass anomaly.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/975743','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/975743"><span>Calculations of the <span class="hlt">stress</span> <span class="hlt">tensor</span> under Symmetric cylindrical shock wave loading</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Chikhradze, N. M.; Lomidze, I.; Marquis, F. D. S.; Staudhammer, Karl P.; Japaridze, L. A.; Peikrishvili, A. B.</p> <p>2001-01-01</p> <p>The calculation of the components of the <span class="hlt">stress</span> <span class="hlt">tensor</span> under symmetric cylindrical shock wave loading, when the pressure impulse of cylindrical symmetry is being spread uniformly along the surface of an infinite cylindrical elastic body, have been carried out. The objective of these calculations is to assess with a sufficient approximation the <span class="hlt">stress</span>-deformed state in samples during low intensity axis-symmetric shock wave loading. The necessity of such an assessment is grounded on a wide utilization and practical applications of shock wave axis-symmetric loading used in the explosive processing of advanced materials. Tile main assumptions made at the initial stage of these calculations are: elasticity and isotropy of medium, constancy of the sound speed and Lame elasticity constants, and medium boundary conditions of cylindrical symmetry. Subsequently, the removal of some assumptions during the investigation process makes possible to take into account effects engendered by boundary conditions' asymmetry and changes in the sound speed and Lame constants These changes are caused by irreversible thermal transformations going on in the medium. Well known methods for solving differential equations, such as the Fourier method, functions of Bessel, Neumann, and Hankel, equations of Helmholtz, are used in these calculations. These calculations, assuming axial symmetry, are presented as a set of simple equations where the arguments are components of the <span class="hlt">stress</span> <span class="hlt">tensor</span> and the solution of this set, for this specific case, gives all the components of the <span class="hlt">stress</span> <span class="hlt">tensor</span>.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.dtic.mil/docs/citations/ADA495604','DTIC-ST'); return false;" href="http://www.dtic.mil/docs/citations/ADA495604"><span>Development and Evaluation of an Airborne Superconducting <span class="hlt">Quantum</span> Interference Device-Based Magnetic Gradiometer <span class="hlt">Tensor</span> System for Detection, Characterization and Mapping of Unexploded Ordnance</span></a></p> <p><a target="_blank" href="https://publicaccess.dtic.mil/psm/api/service/search/search">DTIC Science & Technology</a></p> <p></p> <p>2008-08-01</p> <p>FINAL REPORT Development and Evaluation of an Airborne Superconducting <span class="hlt">Quantum</span> Interference Device-Based Magnetic Gradiometer <span class="hlt">Tensor</span> System...Airborne Superconducting <span class="hlt">Quantum</span> Interference Device-Based Magnetic Gradiometer <span class="hlt">Tensor</span> System for Detection, Characterization and Mapping of Unexploded...Demonstration of the difference between a single component total field magnetometer and intrinsic gradiometer . (From Clarke, 1994). 4 Figure 3</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19850019114','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19850019114"><span>Altimetry data and the elastic <span class="hlt">stress</span> <span class="hlt">tensor</span> of subduction zones</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Caputo, M.</p> <p>1985-01-01</p> <p>The <span class="hlt">stress</span> field in the lithosphere caused by the distribution of density anomalies associated to the geoidal undulations observed by the GEOS-3 and SEASAT Earth satellites in the Tonga region was studied. Different models of the lithosphere were generated with different assumptions on the density distribution and geometry, all generating a geoid profile almost identical to the observed one. The first model is the Airy isostatic hypothesis which consists of a crust of density 2.85 laying on a lithosphere of density 3.35. The models obtained with different compensation depths give residual shortwavelength anomalies of the order of several tens of mgal and several tens of meters geoidal undulations. It indicates that there is no isostasy of the Airy type in the Tonga region because the observed geoid has very smooth undulation of about 25 m over a distance of 2000 km. The Pratt isostatic hypothesis is used in a model consisting of a crust of variable density laying on a lithosphere of higher density. This model gives smaller residual anomalies but still shows that there is no isostasy of the Pratt type in the Tonga region because the observed geoidal undulation are much smaller and smoother than the residual undulations associated to the Pratt model of isostasy.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/scitech/biblio/22489703','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/22489703"><span>Proton chemical shift <span class="hlt">tensors</span> determined by 3D ultrafast MAS double-<span class="hlt">quantum</span> NMR spectroscopy</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Zhang, Rongchun; Mroue, Kamal H.; Ramamoorthy, Ayyalusamy</p> <p>2015-10-14</p> <p>Proton NMR spectroscopy in the solid state has recently attracted much attention owing to the significant enhancement in spectral resolution afforded by the remarkable advances in ultrafast magic angle spinning (MAS) capabilities. In particular, proton chemical shift anisotropy (CSA) has become an important tool for obtaining specific insights into inter/intra-molecular hydrogen bonding. However, even at the highest currently feasible spinning frequencies (110–120 kHz), {sup 1}H MAS NMR spectra of rigid solids still suffer from poor resolution and severe peak overlap caused by the strong {sup 1}H–{sup 1}H homonuclear dipolar couplings and narrow {sup 1}H chemical shift (CS) ranges, which render it difficult to determine the CSA of specific proton sites in the standard CSA/single-<span class="hlt">quantum</span> (SQ) chemical shift correlation experiment. Herein, we propose a three-dimensional (3D) {sup 1}H double-<span class="hlt">quantum</span> (DQ) chemical shift/CSA/SQ chemical shift correlation experiment to extract the CS <span class="hlt">tensors</span> of proton sites whose signals are not well resolved along the single-<span class="hlt">quantum</span> chemical shift dimension. As extracted from the 3D spectrum, the F1/F3 (DQ/SQ) projection provides valuable information about {sup 1}H–{sup 1}H proximities, which might also reveal the hydrogen-bonding connectivities. In addition, the F2/F3 (CSA/SQ) correlation spectrum, which is similar to the regular 2D CSA/SQ correlation experiment, yields chemical shift anisotropic line shapes at different isotropic chemical shifts. More importantly, since the F2/F1 (CSA/DQ) spectrum correlates the CSA with the DQ signal induced by two neighboring proton sites, the CSA spectrum sliced at a specific DQ chemical shift position contains the CSA information of two neighboring spins indicated by the DQ chemical shift. If these two spins have different CS <span class="hlt">tensors</span>, both <span class="hlt">tensors</span> can be extracted by numerical fitting. We believe that this robust and elegant single-channel proton-based 3D experiment provides useful atomistic</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/26472372','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/26472372"><span>Proton chemical shift <span class="hlt">tensors</span> determined by 3D ultrafast MAS double-<span class="hlt">quantum</span> NMR spectroscopy.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Zhang, Rongchun; Mroue, Kamal H; Ramamoorthy, Ayyalusamy</p> <p>2015-10-14</p> <p>Proton NMR spectroscopy in the solid state has recently attracted much attention owing to the significant enhancement in spectral resolution afforded by the remarkable advances in ultrafast magic angle spinning (MAS) capabilities. In particular, proton chemical shift anisotropy (CSA) has become an important tool for obtaining specific insights into inter/intra-molecular hydrogen bonding. However, even at the highest currently feasible spinning frequencies (110-120 kHz), (1)H MAS NMR spectra of rigid solids still suffer from poor resolution and severe peak overlap caused by the strong (1)H-(1)H homonuclear dipolar couplings and narrow (1)H chemical shift (CS) ranges, which render it difficult to determine the CSA of specific proton sites in the standard CSA/single-<span class="hlt">quantum</span> (SQ) chemical shift correlation experiment. Herein, we propose a three-dimensional (3D) (1)H double-<span class="hlt">quantum</span> (DQ) chemical shift/CSA/SQ chemical shift correlation experiment to extract the CS <span class="hlt">tensors</span> of proton sites whose signals are not well resolved along the single-<span class="hlt">quantum</span> chemical shift dimension. As extracted from the 3D spectrum, the F1/F3 (DQ/SQ) projection provides valuable information about (1)H-(1)H proximities, which might also reveal the hydrogen-bonding connectivities. In addition, the F2/F3 (CSA/SQ) correlation spectrum, which is similar to the regular 2D CSA/SQ correlation experiment, yields chemical shift anisotropic line shapes at different isotropic chemical shifts. More importantly, since the F2/F1 (CSA/DQ) spectrum correlates the CSA with the DQ signal induced by two neighboring proton sites, the CSA spectrum sliced at a specific DQ chemical shift position contains the CSA information of two neighboring spins indicated by the DQ chemical shift. If these two spins have different CS <span class="hlt">tensors</span>, both <span class="hlt">tensors</span> can be extracted by numerical fitting. We believe that this robust and elegant single-channel proton-based 3D experiment provides useful atomistic-level structural and dynamical</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19960022265','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19960022265"><span>Reduced <span class="hlt">Stress</span> <span class="hlt">Tensor</span> and Dissipation and the Transport of Lamb Vector</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Wu, Jie-Zhi; Zhou, Ye; Wu, Jian-Ming</p> <p>1996-01-01</p> <p>We develop a methodology to ensure that the <span class="hlt">stress</span> <span class="hlt">tensor</span>, regardless of its number of independent components, can be reduced to an exactly equivalent one which has the same number of independent components as the surface force. It is applicable to the momentum balance if the shear viscosity is constant. A direct application of this method to the energy balance also leads to a reduction of the dissipation rate of kinetic energy. Following this procedure, significant saving in analysis and computation may be achieved. For turbulent flows, this strategy immediately implies that a given Reynolds <span class="hlt">stress</span> model can always be replaced by a reduced one before putting it into computation. Furthermore, we show how the modeling of Reynolds <span class="hlt">stress</span> <span class="hlt">tensor</span> can be reduced to that of the mean turbulent Lamb vector alone, which is much simpler. As a first step of this alternative modeling development, we derive the governing equations for the Lamb vector and its square. These equations form a basis of new second-order closure schemes and, we believe, should be favorably compared to that of traditional Reynolds <span class="hlt">stress</span> transport equation.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/25502054','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/25502054"><span>Resolving <span class="hlt">stress</span> <span class="hlt">tensor</span> components in space from polarized Raman spectra: polycrystalline alumina.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Pezzotti, Giuseppe; Zhu, Wenliang</p> <p>2015-01-28</p> <p>A method of Raman spectroscopic analysis has been proposed for evaluating tensorial <span class="hlt">stress</span> fields stored in alumina polycrystals with a corundum structure (α-Al2O3). Raman selection rules for all the vibrational modes of the structure were expanded into explicit functions of both 3 Euler angles in space and 4 Raman <span class="hlt">tensor</span> elements (RTE) of corundum. A theoretical treatment was then worked out according to the phonon deformation potential (PDP) formalism, which explicitly expressed the changes in force constants under <span class="hlt">stress</span> in matricial form. Close-form solutions could be obtained for the matrix eigenvalues as a function of 9 unknown variables, namely 6 independent <span class="hlt">stress</span> <span class="hlt">tensor</span> components and 3 Euler angles in space, the latter parameters being representatives of local crystal orientation. Successively, two separate sets of Raman calibration experiments were performed for the determination of both RTE and PDP constants of the corundum structure of alumina. Calibration experiments provided a quantitative frame to the newly developed Raman formalism. Polarized Raman spectra were systematically recorded in both single-crystalline and polycrystalline samples, with both A1g and Eg vibrational bands being characterized. Regarding polycrystalline samples, a validation of the proposed Raman method could be done through a comparison between Raman and fluorescence data collected at the same locations across an alumina/metal interface embedded in a steeply graded residual <span class="hlt">stress</span> field.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016GeoRL..43.8928M','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016GeoRL..43.8928M"><span>Method for estimating the <span class="hlt">stress</span> field from seismic moment <span class="hlt">tensor</span> data based on the flow rule in plasticity theory</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Matsumoto, S.</p> <p>2016-09-01</p> <p>The <span class="hlt">stress</span> field is a key factor controlling earthquake occurrence and crustal evolution. In this study, we propose an approach for determining the <span class="hlt">stress</span> field in a region using seismic moment <span class="hlt">tensors</span>, based on the classical equation in plasticity theory. Seismic activity is a phenomenon that relaxes crustal <span class="hlt">stress</span> and creates plastic strain in a medium because of faulting, which suggests that the medium could behave as a plastic body. Using the constitutive relation in plastic theory, the increment of the plastic strain <span class="hlt">tensor</span> is proportional to the deviatoric <span class="hlt">stress</span> <span class="hlt">tensor</span>. Simple mathematical manipulation enables the development of an inversion method for estimating the <span class="hlt">stress</span> field in a region. The method is tested on shallow earthquakes occurring on Kyushu Island, Japan.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/pages/biblio/1248965-full-elastic-strain-stress-tensor-measurements-from-individual-dislocation-cells-copper-through-si-vias','SCIGOV-DOEP'); return false;" href="https://www.osti.gov/pages/biblio/1248965-full-elastic-strain-stress-tensor-measurements-from-individual-dislocation-cells-copper-through-si-vias"><span>Full elastic strain and <span class="hlt">stress</span> <span class="hlt">tensor</span> measurements from individual dislocation cells in copper through-Si vias</span></a></p> <p><a target="_blank" href="http://www.osti.gov/pages">DOE PAGES</a></p> <p>Levine, Lyle E.; Okoro, Chukwudi A.; Xu, Ruqing</p> <p>2015-09-30</p> <p>We report non-destructive measurements of the full elastic strain and <span class="hlt">stress</span> <span class="hlt">tensors</span> from individual dislocation cells distributed along the full extent of a 50 mm-long polycrystalline copper via in Si is reported. Determining all of the components of these <span class="hlt">tensors</span> from sub-micrometre regions within deformed metals presents considerable challenges. The primary issues are ensuring that different diffraction peaks originate from the same sample volume and that accurate determination is made of the peak positions from plastically deformed samples. For these measurements, three widely separated reflections were examined from selected, individual grains along the via. The lattice spacings and peak positionsmore » were measured for multiple dislocation cell interiors within each grain and the cell-interior peaks were sorted out using the measured included angles. A comprehensive uncertainty analysis using a Monte Carlo uncertainty algorithm provided uncertainties for the elastic strain <span class="hlt">tensor</span> and <span class="hlt">stress</span> <span class="hlt">tensor</span> components.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/1248965','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/1248965"><span>Full elastic strain and <span class="hlt">stress</span> <span class="hlt">tensor</span> measurements from individual dislocation cells in copper through-Si vias</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Levine, Lyle E.; Okoro, Chukwudi A.; Xu, Ruqing</p> <p>2015-09-30</p> <p>We report non-destructive measurements of the full elastic strain and <span class="hlt">stress</span> <span class="hlt">tensors</span> from individual dislocation cells distributed along the full extent of a 50 mm-long polycrystalline copper via in Si is reported. Determining all of the components of these <span class="hlt">tensors</span> from sub-micrometre regions within deformed metals presents considerable challenges. The primary issues are ensuring that different diffraction peaks originate from the same sample volume and that accurate determination is made of the peak positions from plastically deformed samples. For these measurements, three widely separated reflections were examined from selected, individual grains along the via. The lattice spacings and peak positions were measured for multiple dislocation cell interiors within each grain and the cell-interior peaks were sorted out using the measured included angles. A comprehensive uncertainty analysis using a Monte Carlo uncertainty algorithm provided uncertainties for the elastic strain <span class="hlt">tensor</span> and <span class="hlt">stress</span> <span class="hlt">tensor</span> components.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=4645108','PMC'); return false;" href="https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=4645108"><span>Full elastic strain and <span class="hlt">stress</span> <span class="hlt">tensor</span> measurements from individual dislocation cells in copper through-Si vias</span></a></p> <p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pmc">PubMed Central</a></p> <p>Levine, Lyle E.; Okoro, Chukwudi; Xu, Ruqing</p> <p>2015-01-01</p> <p>Nondestructive measurements of the full elastic strain and <span class="hlt">stress</span> <span class="hlt">tensors</span> from individual dislocation cells distributed along the full extent of a 50 µm-long polycrystalline copper via in Si is reported. Determining all of the components of these <span class="hlt">tensors</span> from sub-micrometre regions within deformed metals presents considerable challenges. The primary issues are ensuring that different diffraction peaks originate from the same sample volume and that accurate determination is made of the peak positions from plastically deformed samples. For these measurements, three widely separated reflections were examined from selected, individual grains along the via. The lattice spacings and peak positions were measured for multiple dislocation cell interiors within each grain and the cell-interior peaks were sorted out using the measured included angles. A comprehensive uncertainty analysis using a Monte Carlo uncertainty algorithm provided uncertainties for the elastic strain <span class="hlt">tensor</span> and <span class="hlt">stress</span> <span class="hlt">tensor</span> components. PMID:26594371</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/26594371','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/26594371"><span>Full elastic strain and <span class="hlt">stress</span> <span class="hlt">tensor</span> measurements from individual dislocation cells in copper through-Si vias.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Levine, Lyle E; Okoro, Chukwudi; Xu, Ruqing</p> <p>2015-11-01</p> <p>Nondestructive measurements of the full elastic strain and <span class="hlt">stress</span> <span class="hlt">tensors</span> from individual dislocation cells distributed along the full extent of a 50 µm-long polycrystalline copper via in Si is reported. Determining all of the components of these <span class="hlt">tensors</span> from sub-micrometre regions within deformed metals presents considerable challenges. The primary issues are ensuring that different diffraction peaks originate from the same sample volume and that accurate determination is made of the peak positions from plastically deformed samples. For these measurements, three widely separated reflections were examined from selected, individual grains along the via. The lattice spacings and peak positions were measured for multiple dislocation cell interiors within each grain and the cell-interior peaks were sorted out using the measured included angles. A comprehensive uncertainty analysis using a Monte Carlo uncertainty algorithm provided uncertainties for the elastic strain <span class="hlt">tensor</span> and <span class="hlt">stress</span> <span class="hlt">tensor</span> components.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016PCE....95...19A','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016PCE....95...19A"><span>Moment <span class="hlt">tensors</span>, state of <span class="hlt">stress</span> and their relation to faulting processes in Gujarat, western India</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Aggarwal, Sandeep Kumar; Khan, Prosanta Kumar; Mohanty, Sarada Prasad; Roumelioti, Zafeiria</p> <p>2016-10-01</p> <p>Time domain moment <span class="hlt">tensor</span> analysis of 145 earthquakes (Mw 3.2 to 5.1), occurring during the period 2006-2014 in Gujarat region, has been performed. The events are mainly confined in the Kachchh area demarcated by the Island belt and Kachchh Mainland faults to its north and south, and two transverse faults to its east and west. Libraries of Green's functions were established using the 1D velocity model of Kachchh, Saurashtra and Mainland Gujarat. Green's functions and broadband displacement waveforms filtered at low frequency (0.5-0.8 Hz) were inverted to determine the moment <span class="hlt">tensor</span> solutions. The estimated solutions were rigorously tested through number of iterations at different source depths for finding reliable source locations. The identified heterogeneous nature of the <span class="hlt">stress</span> fields in the Kachchh area allowed us to divide this into four Zones 1-4. The <span class="hlt">stress</span> inversion results indicate that the Zone 1 is dominated with radial compression, Zone 2 with strike-slip compression, and Zones 3 and 4 with strike-slip extensions. The analysis further shows that the epicentral region of 2001 MW 7.7 Bhuj mainshock, located at the junction of Zones 2, 3 and 4, was associated with predominant compressional <span class="hlt">stress</span> and strike-slip motion along ∼ NNE-SSW striking fault on the western margin of the Wagad uplift. Other tectonically active parts of Gujarat (e.g. Jamnagar, Talala and Mainland) show earthquake activities are dominantly associated with strike-slip extension/compression faulting. <span class="hlt">Stress</span> inversion analysis shows that the maximum compressive <span class="hlt">stress</span> axes (σ1) are vertical for both the Jamnagar and Talala regions and horizontal for the Mainland Gujarat. These <span class="hlt">stress</span> regimes are distinctly different from those of the Kachchh region.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016JSAES..71..276A','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016JSAES..71..276A"><span>Preface to the special issue on "Regional moment <span class="hlt">tensors</span> and <span class="hlt">stress</span> field in South and Central America"</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Audemard, Franck; Zahradnik, Jiri; Assumpção, Marcelo</p> <p>2016-11-01</p> <p>This special issue follows from the Symposium "Regional Moment <span class="hlt">Tensor</span> Solutions: advances and new applications" held in Bogotá, Colombia, at the I Regional Assembly of the IASPEI's Latin American and Caribbean Seismological Commission (LACSC) in 2014. Seven papers are presented dealing with determination of moment <span class="hlt">tensors</span>, focal mechanisms and the <span class="hlt">stress</span> field in Central and South America. The study areas of each paper are indicated in the index Map of Fig. 1.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016PhRvD..93j4035B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016PhRvD..93j4035B"><span><span class="hlt">Quantum</span>-gravitational effects on gauge-invariant scalar and <span class="hlt">tensor</span> perturbations during inflation: The de Sitter case</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Brizuela, David; Kiefer, Claus; Krämer, Manuel</p> <p>2016-05-01</p> <p>We present detailed calculations for <span class="hlt">quantum</span>-gravitational corrections to the power spectra of gauge-invariant scalar and <span class="hlt">tensor</span> perturbations during inflation. This is done by performing a semiclassical Born-Oppenheimer type of approximation to the Wheeler-DeWitt equation, from which we obtain a Schrödinger equation with <span class="hlt">quantum</span>-gravitational correction terms. As a first step, we perform our calculation for a de Sitter universe and find that the correction terms lead to an enhancement of power on the largest scales.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2015JGRB..120.8422J','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015JGRB..120.8422J"><span>Geomechanical simulation of the <span class="hlt">stress</span> <span class="hlt">tensor</span> rotation caused by injection of cold water in a deep geothermal reservoir</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Jeanne, Pierre; Rutqvist, Jonny; Dobson, Patrick F.; Garcia, Julio; Walters, Mark; Hartline, Craig; Borgia, Andrea</p> <p>2015-12-01</p> <p>We present a three-dimensional thermohydromechanical numerical study of the evolution and distribution of the <span class="hlt">stress</span> <span class="hlt">tensor</span> within the northwest part of The Geysers geothermal reservoir (in California), including a detailed study of the region around one injection well from 2003 to 2012. Initially, after imposing a normal faulting <span class="hlt">stress</span> regime, we calculated local changes in the <span class="hlt">stress</span> regime around injection wells. Our results were compared with previously published studies in which the <span class="hlt">stress</span> state was inferred from inverting the focal plane mechanism of seismic events. Our main finding is that changes in <span class="hlt">stress</span> <span class="hlt">tensor</span> orientation are caused by injection-induced progressive cooling of the reservoir, as well as by the seasonal variations in injection rate. Because of the gravity flow and cooling around a liquid zone formed by the injection, the vertical <span class="hlt">stress</span> reduction is larger and propagates far below the injection well. At the same time, the horizontal <span class="hlt">stress</span> increases, mostly because of <span class="hlt">stress</span> redistribution below and above the cooling area. These two phenomena cause the rotation of the <span class="hlt">stress</span> <span class="hlt">tensor</span> and the appearance of a strike-slip regime above, inside, and below the cooling area. The cooling and the associated rotation of the <span class="hlt">stress</span> regime can play a significant role in the observed long-term deepening of the microseismicity below active injection wells.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2011PhRvD..84f6003G','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2011PhRvD..84f6003G"><span>Boundary <span class="hlt">stress</span> <span class="hlt">tensor</span> and asymptotically AdS3 non-Einstein spaces at the chiral point</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Giribet, Gaston; Goya, Andrés; Leston, Mauricio</p> <p>2011-09-01</p> <p>Chiral gravity admits asymptotically AdS3 solutions that are not locally equivalent to AdS3; meaning that solutions do exist which, while obeying the strong boundary conditions usually imposed in general relativity, happen not to be Einstein spaces. In topologically massive gravity (TMG), the existence of non-Einstein solutions is particularly connected to the question about the role played by complex saddle points in the Euclidean path integral. Consequently, studying (the existence of) nonlocally AdS3 solutions to chiral gravity is relevant to understanding the <span class="hlt">quantum</span> theory. Here, we discuss a special family of nonlocally AdS3 solutions to chiral gravity. In particular, we show that such solutions persist when one deforms the theory by adding the higher-curvature terms of the so-called new massive gravity. Moreover, the addition of higher-curvature terms to the gravity action introduces new nonlocally AdS3 solutions that have no analogues in TMG. Both stationary and time-dependent, axially symmetric solutions that asymptote AdS3 space without being locally equivalent to it appear. Defining the boundary <span class="hlt">stress</span> <span class="hlt">tensor</span> for the full theory, we show that these non-Einstein geometries have associated vanishing conserved charges.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/scitech/biblio/21035830','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/21035830"><span>Renormalized <span class="hlt">stress</span> <span class="hlt">tensor</span> in Kerr space-time: Numerical results for the Hartle-Hawking vacuum</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Duffy, Gavin; Ottewill, Adrian C.</p> <p>2008-01-15</p> <p>We show that the pathology which afflicts the Hartle-Hawking vacuum on the Kerr black hole space-time can be regarded as due to rigid rotation of the state with the horizon in the sense that, when the region outside the speed-of-light surface is removed by introducing a mirror, there is a state with the defining features of the Hartle-Hawking vacuum. In addition, we show that, when the field is in this state, the expectation value of the energy-momentum <span class="hlt">stress</span> <span class="hlt">tensor</span> measured by an observer close to the horizon and rigidly rotating with it corresponds to that of a thermal distribution at the Hawking temperature rigidly rotating with the horizon.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017ZaMP...68...17G','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017ZaMP...68...17G"><span>Local well-posedness to inhomogeneous Ericksen-Leslie system with general Leslie <span class="hlt">stress</span> <span class="hlt">tensor</span></span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Gong, Huajun; Li, Jinkai; Xu, Chen</p> <p>2017-02-01</p> <p>In this paper, we establish the local well-posedness of strong solutions to the Cauchy problem of the density-dependent liquid crystal system, with general Leslie <span class="hlt">stress</span> <span class="hlt">tensor</span>, in R^3. By using a biharmonic regularization argument, and making full use of the property of the intrinsic cancellation of the regularized system, we are able to overcome the difficulties caused by the high-order coupling terms, establish some appropriate a priori estimates, which are independent of the regularized parameter, and consequently obtain a strong solution to the original liquid crystal system, by letting the regularization parameter go to zero. The main advantage of the biharmonic regularization is that it does not destroy the property of the intrinsic cancellation of the original system.</p> </li> </ol> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_2");'>2</a></li> <li><a href="#" onclick='return showDiv("page_3");'>3</a></li> <li class="active"><span>4</span></li> <li><a href="#" onclick='return showDiv("page_5");'>5</a></li> <li><a href="#" onclick='return showDiv("page_6");'>6</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div><!-- col-sm-12 --> </div><!-- row --> </div><!-- page_4 --> <div id="page_5" class="hiddenDiv"> <div class="row"> <div class="col-sm-12"> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_3");'>3</a></li> <li><a href="#" onclick='return showDiv("page_4");'>4</a></li> <li class="active"><span>5</span></li> <li><a href="#" onclick='return showDiv("page_6");'>6</a></li> <li><a href="#" onclick='return showDiv("page_7");'>7</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div> </div> <div class="row"> <div class="col-sm-12"> <ol class="result-class" start="81"> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016EGUGA..18.3671K','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016EGUGA..18.3671K"><span>Crustal <span class="hlt">stress</span> field in the Greek region inferred from inversion of moment <span class="hlt">tensor</span> solutions</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Konstantinou, Konstantinos; Mouslopoulou, Vasiliki; Liang, Wen-Tzong; Heidbach, Oliver; Oncken, Onno; Suppe, John</p> <p>2016-04-01</p> <p>The Hellenic region is the seismically most active area in Europe, having experienced numerous large magnitude catastrophic earthquakes and associated devastating tsunamis. A means of mitigating these potential hazards is by better understanding the patterns of spatial and temporal deformation of the crust across the Hellenic orogenic system, over timescales that range from individual earthquakes to several tens of years. In this study for the first time we make collective use of the Global CMT (GCMT), Regional CMT (RCMT) and National Observatory of Athens (NOA) moment <span class="hlt">tensor</span> databases in order to extract focal mechanism solutions that will be used to infer crustal <span class="hlt">stresses</span> in the Greek region at an unprecedented resolution. We focus on the shallow seismicity within the upper plate (down to 42 km) and select solutions with good waveform fits and well-resolved hypocentral depths. In this way we obtained 1,614 focal mechanism solutions covering western Greece up to southern Albania, central and southern Greece, northern Aegean as well as the subduction trench west and east of Crete. These solutions are used as input to a regional-scale damped <span class="hlt">stress</span> inversion over a grid whose node spacing is 0.35 degrees for the purpose of recovering the three principal <span class="hlt">stress</span> axes and the <span class="hlt">stress</span> ratio R for each node. Several sensitivity tests are performed where parameters such as damping, hypocentral depth, magnitude range are varied, in order to ascertain the robustness of our results. The final <span class="hlt">stress</span> field model is then compared to the GPS-derived strain field revealing an excellent agreement between the two datasets. Additionally, maximum and minimum <span class="hlt">stress</span> axes orientations are correlated with the strike and dip of known faults in order to improve our understanding of future fault rupture and corresponding seismic hazard.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/26016539','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/26016539"><span><span class="hlt">Tensor</span> numerical methods in <span class="hlt">quantum</span> chemistry: from Hartree-Fock to excitation energies.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Khoromskaia, Venera; Khoromskij, Boris N</p> <p>2015-12-21</p> <p>We resume the recent successes of the grid-based <span class="hlt">tensor</span> numerical methods and discuss their prospects in real-space electronic structure calculations. These methods, based on the low-rank representation of the multidimensional functions and integral operators, first appeared as an accurate <span class="hlt">tensor</span> calculus for the 3D Hartree potential using 1D complexity operations, and have evolved to entirely grid-based <span class="hlt">tensor</span>-structured 3D Hartree-Fock eigenvalue solver. It benefits from <span class="hlt">tensor</span> calculation of the core Hamiltonian and two-electron integrals (TEI) in O(n log n) complexity using the rank-structured approximation of basis functions, electron densities and convolution integral operators all represented on 3D n × n × n Cartesian grids. The algorithm for calculating TEI <span class="hlt">tensor</span> in a form of the Cholesky decomposition is based on multiple factorizations using algebraic 1D "density fitting" scheme, which yield an almost irreducible number of product basis functions involved in the 3D convolution integrals, depending on a threshold ε > 0. The basis functions are not restricted to separable Gaussians, since the analytical integration is substituted by high-precision <span class="hlt">tensor</span>-structured numerical quadratures. The <span class="hlt">tensor</span> approaches to post-Hartree-Fock calculations for the MP2 energy correction and for the Bethe-Salpeter excitation energies, based on using low-rank factorizations and the reduced basis method, were recently introduced. Another direction is towards the <span class="hlt">tensor</span>-based Hartree-Fock numerical scheme for finite lattices, where one of the numerical challenges is the summation of electrostatic potentials of a large number of nuclei. The 3D grid-based <span class="hlt">tensor</span> method for calculation of a potential sum on a L × L × L lattice manifests the linear in L computational work, O(L), instead of the usual O(L(3) log L) scaling by the Ewald-type approaches.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016PhRvD..94l3527B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016PhRvD..94l3527B"><span><span class="hlt">Quantum</span>-gravitational effects on gauge-invariant scalar and <span class="hlt">tensor</span> perturbations during inflation: The slow-roll approximation</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Brizuela, David; Kiefer, Claus; Krämer, Manuel</p> <p>2016-12-01</p> <p>We continue our study on corrections from canonical <span class="hlt">quantum</span> gravity to the power spectra of gauge-invariant inflationary scalar and <span class="hlt">tensor</span> perturbations. A direct canonical quantization of a perturbed inflationary universe model is implemented, which leads to a Wheeler-DeWitt equation. For this equation, a semiclassical approximation is applied in order to obtain a Schrödinger equation with <span class="hlt">quantum</span>-gravitational correction terms, from which we calculate the corrections to the power spectra. We go beyond the de Sitter case discussed earlier and analyze our model in the first slow-roll approximation, considering terms linear in the slow-roll parameters. We find that the dominant correction term from the de Sitter case, which leads to an enhancement of power on the largest scales, gets modified by terms proportional to the slow-roll parameters. A correction to the <span class="hlt">tensor</span>-to-scalar ratio is also found at second order in the slow-roll parameters. Making use of the available experimental data, the magnitude of these <span class="hlt">quantum</span>-gravitational corrections is estimated. Finally, the effects for the temperature anisotropies in the cosmic microwave background are qualitatively obtained.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/11909293','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/11909293"><span>Body versus surface forces in continuum mechanics: is the Maxwell <span class="hlt">stress</span> <span class="hlt">tensor</span> a physically objective Cauchy <span class="hlt">stress</span>?</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Rinaldi, Carlos; Brenner, Howard</p> <p>2002-03-01</p> <p>The Maxwell <span class="hlt">stress</span> <span class="hlt">tensor</span> (MST) T(M) plays an important role in the dynamics of continua interacting with external fields, as in the commercially and scientifically important case of "ferrofluids." As a conceptual entity in quasistatic systems, the MST derives from the definition f(M)def=inverted Delta x T(M), where f(M)(x) is a physically objective volumetric external body-force density field at a point x of a continuum, derived from the solution of the pertinent governing equations. Beginning with the fact that T(M) is not uniquely defined via the preceding relationship from knowledge of f(M), we point out in this paper that the interpretation of T(M) as being a physical <span class="hlt">stress</span> is not only conceptually incorrect, but that in commonly occuring situations this interpretation will result in incorrect predictions of the physical response of the system. In short, by elementary examples, this paper emphasizes the need to maintain the classical physical distinction between the notions of body forces f and <span class="hlt">stresses</span> T. These examples include calculations of the torque on bodies, the work required to deform a fluid continuum, and the rate of interchange of energy between mechanical and other modes.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2007PhDT.......103A','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2007PhDT.......103A"><span>Formulation and simulation of the generalized ion viscous <span class="hlt">stress</span> <span class="hlt">tensor</span> in magnetized plasmas</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Addae-Kagyah, Michael K.</p> <p>2007-12-01</p> <p>Details of the generalized model of the parallel ion viscous <span class="hlt">stress</span> <span class="hlt">tensor</span>, pi∥, is presented in this work. Kinetic-based derivation of pi∥, employing a Chapman-Enskog-like (CEL) expansion of the plasma particle distribution function, is part of a broad research effort aimed at incorporating suitable kinetic physics into the physical modeling of tenuous, high-temperature (fusion-grade) plasmas. Often, this goal is achieved through the use of generalized, integral closures in the evolution equations of fluid quantities, which correspond to low-order velocity-space moments of the particle distribution functions. The primary analytical task in the formulation of pi∥ is the derivation of a drift kinetic equation (DKE) from the plasma kinetic equation (via appropriate gyro-averaging and ordering schemes). Next, the time-dependent DKE is solved for the kinetic distortion by reducing it to a system of coupled, linear equations, that results from an expansion in Legendre polynomials, and the correct exploitation of their orthogonality properties. The <span class="hlt">tensor</span>, pi∥ , is calculated in the final step as a second-order velocity-space moment of the kinetic distortion term in the CEL expansion. This is a steady-state version of pi∥, which is valid for arbitrary collision and transit frequencies. The upgraded theory reproduces Braginskii's pi ∥ in the regime of high collisionality, and agrees with Chang and Callen's results in the nearly collisionless regime. Subsequently, a time-dependent version of pi∥ (incorporating an exact form of linearized Coulomb collision operator) is formulated, as an enhancement to the steady-state model. Numerical simulations of three known physical phenomena in plasmas, incorporating finite effects of the steady-state, generalized pi∥, are executed in slab geometry, using the NIMROD simulation code. Specifically, ion acoustic wave propagation and dissipation, <span class="hlt">stress</span>-induced ion heating, and parallel ion momentum (or flow) flattening</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016Tectp.670..101B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016Tectp.670..101B"><span>The Beni-Ilmane (Algeria) seismic sequence of May 2010: Seismic sources and <span class="hlt">stress</span> <span class="hlt">tensor</span> calculations</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Beldjoudi, H.; Delouis, B.; Djellit, H.; Yelles-Chaouche, A.; Gharbi, S.; Abacha, I.</p> <p>2016-02-01</p> <p>A moderate earthquake with a moment magnitude of Mw 5.5 struck the Sub-Bibanique region of eastern Algeria on 14 May 2010, killing three people, injuring hundreds of others, and causing moderate damages in the epicentral area, mainly in the villages of Beni-Ilmane and Samma. The focal mechanism of the seismic source for the first shock, obtained by near-field waveform modelling, exhibits left-lateral strike-slip faulting with the first nodal plane oriented at N345°, and right-lateral strike-slip faulting with the second nodal plane oriented at N254°. A second earthquake that struck the region on 16 May 2010, with a moment magnitude of Mw 5.1, was located 9 km SW of the first earthquake. The focal mechanism obtained by waveform modelling showed reverse faulting with nodal planes oriented NE-SW (N25° and N250°). A third earthquake that struck the region on 23 May 2010, with a moment magnitude of Mw 5.2, was located 7 km S of the first shock. The obtained focal mechanism showed a left-lateral strike-slip plane oriented at N12° and a right-lateral strike-slip plane oriented at N257°. Field investigations combined with geological and seismotectonic analyses indicate that the three earthquake shocks were generated by activity on three distinct faults. The second and third shocks were generated on faults oriented WSW-ENE and NNE-SSW, respectively. The regional <span class="hlt">stress</span> <span class="hlt">tensor</span> calculated in the region gives an orientation of N340° for the maximum compressive <span class="hlt">stress</span> direction (σ1) which is close to the horizontal, with a <span class="hlt">stress</span> shape factor indicating either a compressional or a strike-slip regime.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2007PhRvB..75v4121L','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2007PhRvB..75v4121L"><span><span class="hlt">Stress</span>-free states of continuum dislocation fields: Rotations, grain boundaries, and the Nye dislocation density <span class="hlt">tensor</span></span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Limkumnerd, Surachate; Sethna, James P.</p> <p>2007-06-01</p> <p>We derive general relations between grain boundaries, rotational deformations, and <span class="hlt">stress</span>-free states for the mesoscale continuum Nye dislocation density <span class="hlt">tensor</span>. Dislocations generally are associated with long-range <span class="hlt">stress</span> fields. We provide the general form for dislocation density fields whose <span class="hlt">stress</span> fields vanish. We explain that a grain boundary (a dislocation wall satisfying Frank’s formula) has vanishing <span class="hlt">stress</span> in the continuum limit. We show that the general <span class="hlt">stress</span>-free state can be written explicitly as a (perhaps continuous) superposition of flat Frank walls. We show that the <span class="hlt">stress</span>-free states are also naturally interpreted as configurations generated by a general spatially dependent rotational deformation. Finally, we propose a least-squares definition for the spatially dependent rotation field of a general (<span class="hlt">stressful</span>) dislocation density field.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/26957166','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/26957166"><span>Analysis of structural correlations in a model binary 3D liquid through the eigenvalues and eigenvectors of the atomic <span class="hlt">stress</span> <span class="hlt">tensors</span>.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Levashov, V A</p> <p>2016-03-07</p> <p>It is possible to associate with every atom or molecule in a liquid its own atomic <span class="hlt">stress</span> <span class="hlt">tensor</span>. These atomic <span class="hlt">stress</span> <span class="hlt">tensors</span> can be used to describe liquids' structures and to investigate the connection between structural and dynamic properties. In particular, atomic <span class="hlt">stresses</span> allow to address atomic scale correlations relevant to the Green-Kubo expression for viscosity. Previously correlations between the atomic <span class="hlt">stresses</span> of different atoms were studied using the Cartesian representation of the <span class="hlt">stress</span> <span class="hlt">tensors</span> or the representation based on spherical harmonics. In this paper we address structural correlations in a 3D model binary liquid using the eigenvalues and eigenvectors of the atomic <span class="hlt">stress</span> <span class="hlt">tensors</span>. This approach allows to interpret correlations relevant to the Green-Kubo expression for viscosity in a simple geometric way. On decrease of temperature the changes in the relevant <span class="hlt">stress</span> correlation function between different atoms are significantly more pronounced than the changes in the pair density function. We demonstrate that this behaviour originates from the orientational correlations between the eigenvectors of the atomic <span class="hlt">stress</span> <span class="hlt">tensors</span>. We also found correlations between the eigenvalues of the same atomic <span class="hlt">stress</span> <span class="hlt">tensor</span>. For the studied system, with purely repulsive interactions between the particles, the eigenvalues of every atomic <span class="hlt">stress</span> <span class="hlt">tensor</span> are positive and they can be ordered: λ1 ≥ λ2 ≥ λ3 ≥ 0. We found that, for the particles of a given type, the probability distributions of the ratios (λ2/λ1) and (λ3/λ2) are essentially identical to each other in the liquids state. We also found that λ2 tends to be equal to the geometric average of λ1 and λ3. In our view, correlations between the eigenvalues may represent "the Poisson ratio effect" at the atomic scale.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/1981PThPh..65..338K','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/1981PThPh..65..338K"><span><span class="hlt">Quantum</span> Theory of Antisymmetric Higher Rank <span class="hlt">Tensor</span> Gauge Field in Higher Dimensional Space-Time</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Kimura, T.</p> <p>1981-01-01</p> <p>In a higher dimensional space-time, the Lagrangian formalism and the canonical operator formalism of covariant quantization of the antisymmetric <span class="hlt">tensor</span> gauge field of higher rank are formulated consistently by introducing BRS transformation and Lagrangian multiplier fields From the effective Lagrangian, the numbers of the physical components and the effective ghosts are counted correctly without referring to a special reference frame. The confinement of unphysical components is assured from the viewpoint of the ``quartet mechanism'' of Kugo and Ojima.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/27214268','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/27214268"><span>Direct Measurements of <span class="hlt">Quantum</span> Kinetic Energy <span class="hlt">Tensor</span> in Stable and Metastable Water near the Triple Point: An Experimental Benchmark.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Andreani, Carla; Romanelli, Giovanni; Senesi, Roberto</p> <p>2016-06-16</p> <p>This study presents the first direct and quantitative measurement of the nuclear momentum distribution anisotropy and the <span class="hlt">quantum</span> kinetic energy <span class="hlt">tensor</span> in stable and metastable (supercooled) water near its triple point, using deep inelastic neutron scattering (DINS). From the experimental spectra, accurate line shapes of the hydrogen momentum distributions are derived using an anisotropic Gaussian and a model-independent framework. The experimental results, benchmarked with those obtained for the solid phase, provide the state of the art directional values of the hydrogen mean kinetic energy in metastable water. The determinations of the direction kinetic energies in the supercooled phase, provide accurate and quantitative measurements of these dynamical observables in metastable and stable phases, that is, key insight in the physical mechanisms of the hydrogen <span class="hlt">quantum</span> state in both disordered and polycrystalline systems. The remarkable findings of this study establish novel insight into further expand the capacity and accuracy of DINS investigations of the nuclear <span class="hlt">quantum</span> effects in water and represent reference experimental values for theoretical investigations.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/scitech/biblio/22489713','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/22489713"><span>Piezo-optic <span class="hlt">tensor</span> of crystals from <span class="hlt">quantum</span>-mechanical calculations</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Erba, A. Dovesi, R.; Ruggiero, M. T.; Korter, T. M.</p> <p>2015-10-14</p> <p>An automated computational strategy is devised for the ab initio determination of the full fourth-rank piezo-optic <span class="hlt">tensor</span> of crystals belonging to any space group of symmetry. Elastic stiffness and compliance constants are obtained as numerical first derivatives of analytical energy gradients with respect to the strain and photo-elastic constants as numerical derivatives of analytical dielectric <span class="hlt">tensor</span> components, which are in turn computed through a Coupled-Perturbed-Hartree-Fock/Kohn-Sham approach, with respect to the strain. Both point and translation symmetries are exploited at all steps of the calculation, within the framework of periodic boundary conditions. The scheme is applied to the determination of the full set of ten symmetry-independent piezo-optic constants of calcium tungstate CaWO{sub 4}, which have recently been experimentally reconstructed. Present calculations unambiguously determine the absolute sign (positive) of the π{sub 61} constant, confirm the reliability of 6 out of 10 experimentally determined constants and provide new, more accurate values for the remaining 4 constants.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19950035694&hterms=Stress+effects&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D90%26Ntt%3DStress%2Beffects','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19950035694&hterms=Stress+effects&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D90%26Ntt%3DStress%2Beffects"><span>Coronal heating by the resonant absorption of Alfven waves: The effect of viscous <span class="hlt">stress</span> <span class="hlt">tensor</span></span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Ofman, L.; Davila, J. M.; Steinolfson, R. S.</p> <p>1994-01-01</p> <p>The time-dependent linearized magnetohydrodynamics (MHD) equations for a fully compressible, low-beta, viscoresistive plasma are solved numerically using an implicit integration scheme. The full viscosity <span class="hlt">stress</span> <span class="hlt">tensor</span> (Braginskii 1965) is included with the five parameters eta(sub i) i = 0 to 4. In agreement with previous studies, the numerical simulations demonstrate that the dissipation on inhomogeneities in the background Alfven speed occurs in a narrow resonant layer. For an active region in the solar corona the values of eta(sub i) are eta(sub o) = 0.65 g/cm/s, eta(sub 1) = 3.7 x 10(exp -12) g/cm/s, eta(sub 2) = 4 eta(sub 1), eta(sub 3) = 1.4 x 10(exp -6) g/cm/s, eta(sub 4) = 2 eta(sub 3), with n = 10(exp 10)/cu cm, T = 2 x 10(exp 6) K, and B = 100 G. When the Lundquist number S = 10(exp 4) and R(sub 1) much greater than S (where R(sub 1) is the dimensionless shear viscous number) the width of the resistive dissipation layer d(sub r) is 0.22a (where a is the density gradient length scale) and d(sub r) approximately S(exp -1/3). When S much greater than R(sub 1) the shear viscous dissipation layer width d(sub r) scales as R(sub 1)(exp -1/3). The shear viscous and the resistive dissipation occurs in an overlapping narrow region, and the total heating rate is independent of the value of the dissipation parameters in agreement with previous studies. Consequently, the maximum values of the perpendicular velocity and perpendicular magnetic field scale as R(sub 1)(exp -1/3). It is evident from the simulations that for solar parameters the heating due to the compressive viscosity (R(sub 0) = 560) is negligible compared to the resistive and the shear viscous (R(sub 1)) dissipation and it occurs in a broad layer of order a in width. In the solar corona with S approximately equals 10(exp 4) and R(sub 1) approximately equals 10(exp 14) (as calculated from the Braginskii expressions), the shear viscous resonant heating is of comparable magnitude to the resistive resonant</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/24116775','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/24116775"><span>Exact <span class="hlt">tensor</span> hypercontraction: a universal technique for the resolution of matrix elements of local finite-range N-body potentials in many-body <span class="hlt">quantum</span> problems.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Parrish, Robert M; Hohenstein, Edward G; Schunck, Nicolas F; Sherrill, C David; Martínez, Todd J</p> <p>2013-09-27</p> <p>Configuration-space matrix elements of N-body potentials arise naturally and ubiquitously in the Ritz-Galerkin solution of many-body <span class="hlt">quantum</span> problems. For the common specialization of local, finite-range potentials, we develop the exact <span class="hlt">tensor</span> hypercontraction method, which provides a quantized renormalization of the coordinate-space form of the N-body potential, allowing for a highly separable <span class="hlt">tensor</span> factorization of the configuration-space matrix elements. This representation allows for substantial computational savings in chemical, atomic, and nuclear physics simulations, particularly with respect to difficult "exchangelike" contractions.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2012AGUFM.T23D2706B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2012AGUFM.T23D2706B"><span>Determination of Hydraulically Activated Fractures and Field <span class="hlt">Stress</span> <span class="hlt">Tensors</span> in the Barnett Shale Using Microseismic Events Data</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Busetti, S.</p> <p>2012-12-01</p> <p>Seismic moment and <span class="hlt">stress</span> <span class="hlt">tensor</span> inversions are applied to microseismic events data to investigate the mechanical behavior of activated fractures during hydraulic fracturing in tight reservoirs. The goal is to understand the likelihood of different mechanisms for induced microseismicity, including low pressure fluid leak-off or <span class="hlt">stress</span> shadowing adjacent to bi-wing parent hydraulic fractures, and pressurized network flow with no parent fracture. The data includes 7,444 microseismic events generated from 18 sequential pumping stages in two adjacent horizontal wells in the Barnett Shale, recorded from two down-hole monitor wells. A tensile source model is used to derive parameters such as nodal plane orientations and slip vectors from the six component moment <span class="hlt">tensor</span> for each microseismic event. Three-dimensional <span class="hlt">stress</span> analysis techniques and a linearized <span class="hlt">stress</span> inversion scheme are used to calculate geomechanical parameters. Four scenarios are considered. The first case considers fractures seismically activated in the in-situ <span class="hlt">stress</span> field, which is determined from wellbore break-out data in the vertical wells. Fracture activation is assumed to occur by minor <span class="hlt">stress</span> perturbations with no <span class="hlt">stress</span> rotation. The second case also considers that the most unstable fractures in the wellbore state of <span class="hlt">stress</span> activated, but to determine the induced <span class="hlt">stress</span> state, <span class="hlt">stress</span> inversion on only the unstable fractures is used. The third case assumes that all of the nodal planes are mechanically valid but that the plane with the lowest misfit, the angle between the observed and predicted slip vector, is the correct one. In this case, the wellbore <span class="hlt">stress</span> state is ignored entirely and <span class="hlt">stress</span> inversion on all of the nodal planes is used to solve for the activation <span class="hlt">stress</span>. The fourth case expands case three by selecting the correct fault plane as the one with the highest instability in the inversion <span class="hlt">stress</span> state and a second inversion is used on only the unstable fractures. Preliminary</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/scitech/biblio/21024645','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/21024645"><span>Simulation of <span class="hlt">Quantum</span> Many-Body Systems with Strings of Operators and Monte Carlo <span class="hlt">Tensor</span> Contractions</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Schuch, Norbert; Wolf, Michael M.; Cirac, J. Ignacio; Verstraete, Frank</p> <p>2008-02-01</p> <p>We introduce string-bond states, a class of states obtained by placing strings of operators on a lattice, which encompasses the relevant states in <span class="hlt">quantum</span> information. For string-bond states, expectation values of local observables can be computed efficiently using Monte Carlo sampling, making them suitable for a variational algorithm which extends the density matrix renormalization group to higher dimensional and irregular systems. Numerical results demonstrate the applicability of these states to the simulation of many-body systems.0.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2015JVGR..305...19A','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015JVGR..305...19A"><span>Seismic activity and <span class="hlt">stress</span> <span class="hlt">tensor</span> inversion at Las Tres Vírgenes Volcanic and Geothermal Field (México)</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Antayhua-Vera, Yanet; Lermo-Samaniego, Javier; Quintanar-Robles, Luis; Campos-Enríquez, Oscar</p> <p>2015-10-01</p> <p>We analyze local earthquakes occurring between 2003 and 2012 at the Las Tres Vírgenes Volcanic and Geothermal Field (TVVGF) to establish their temporal and spatial distribution, and relationships with local and regional fault systems, water injection, acid stimulation and steam production tests. We obtained focal mechanisms and inverted data for the <span class="hlt">stress</span> <span class="hlt">tensor</span> to understand the local and regional <span class="hlt">stress</span> fields. We analyzed 423 local earthquakes with magnitudes between 0.1 and 2.9 Mc and hypocentral depths from 0.2 to 7.4 km b.s.l. The cutoff depth at ~ 7.4 km possibly delineates the brittle-ductile transition zone. We identified seven swarms (from 1 to 7). Swarms 1 (December 2009), 2 (May 2010), 3 (June-July 2010) and 7 (December 2012) are strongly correlated with injection processes; whereas swarms 5 (April 2012) and 6 (September 2012) are correlated with local tectonic faults. <span class="hlt">Stress</span> inversion showed NW-SE, E-W and NE-SW extensional orientations (Shmin), in agreement with the local tectonic <span class="hlt">stress</span> field; while NE-SW compressional orientations (SHmax) are correlated with the regional tectonic <span class="hlt">stress</span> field.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2014JGeo...82..118D','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2014JGeo...82..118D"><span>Seismic moment <span class="hlt">tensors</span> and regional <span class="hlt">stress</span> in the area of the December 2013-January 2014, Matese earthquake sequence (Italy)</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>D'Amico, Sebastiano; Cammarata, Laura; Cangemi, Marianna; Cavallaro, Danilo; Di Martino, Roberto Maria; Firetto Carlino, Marco</p> <p>2014-12-01</p> <p>The main goal of this study is to provide moment <span class="hlt">tensor</span> solutions for small and moderate earthquakes of the Matese seismic sequence in southern Italy for the period of December 2013-January 2014. We estimate the focal mechanisms of 31 earthquakes with local magnitudes related to the Matese earthquake seismic sequence (December 2013-January 2014) in Southern-Central Italy which are recorded by the broadband stations of the Italian National Seismic Network and the Mediterranean Very Broadband Seismographic Network (MedNet) run by the Istituto Nazionale di Geofisica e Vulcanologia (INGV). The solutions show that normal faulting is the prevailing style of seismic deformation in agreement with the local faults mapped out in the area. Comparisons with already published solutions and with seismological and geological information available allowed us to properly interpret the moment <span class="hlt">tensor</span> solutions in the frame of the seismic sequence evolution and also to furnish additional information about less energetic seismic phases. Focal data were inverted to obtain the seismogenic <span class="hlt">stress</span> in the study area. The results are compatible with the major tectonic domain of the area.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2015CoPhC.190...33K','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015CoPhC.190...33K"><span>All-electron formalism for total energy strain derivatives and <span class="hlt">stress</span> <span class="hlt">tensor</span> components for numeric atom-centered orbitals</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Knuth, Franz; Carbogno, Christian; Atalla, Viktor; Blum, Volker; Scheffler, Matthias</p> <p>2015-05-01</p> <p>We derive and implement the strain derivatives of the total energy of solids, i.e., the analytic <span class="hlt">stress</span> <span class="hlt">tensor</span> components, in an all-electron, numeric atom-centered orbital based density-functional formalism. We account for contributions that arise in the semi-local approximation (LDA/GGA) as well as in the generalized Kohn-Sham case, in which a fraction of exact exchange (hybrid functionals) is included. In this work, we discuss the details of the implementation including the numerical corrections for sparse integrations grids which allow to produce accurate results. We validate the implementation for a variety of test cases by comparing to strain derivatives performed via finite differences. Additionally, we include the detailed definition of the overlapping atom-centered integration formalism used in this work to obtain total energies and their derivatives.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/20568847','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/20568847"><span>General formulation of pressure and <span class="hlt">stress</span> <span class="hlt">tensor</span> for arbitrary many-body interaction potentials under periodic boundary conditions.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Thompson, Aidan P; Plimpton, Steven J; Mattson, William</p> <p>2009-10-21</p> <p>Three distinct forms are derived for the force virial contribution to the pressure and <span class="hlt">stress</span> <span class="hlt">tensor</span> of a collection of atoms interacting under periodic boundary conditions. All three forms are written in terms of forces acting on atoms, and so are valid for arbitrary many-body interatomic potentials. All three forms are mathematically equivalent. In the special case of atoms interacting with pair potentials, they reduce to previously published forms. (i) The atom-cell form is similar to the standard expression for the virial for a finite nonperiodic system, but with an explicit correction for interactions with periodic images. (ii) The atom form is particularly suited to implementation in modern molecular dynamics simulation codes using spatial decomposition parallel algorithms. (iii) The group form of the virial allows the contributions to the virial to be assigned to individual atoms.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016JSAES..71..309A','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016JSAES..71..309A"><span>Present-day <span class="hlt">stress</span> <span class="hlt">tensors</span> along the southern Caribbean plate boundary zone from inversion of focal mechanism solutions: A successful trial</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Audemard M., Franck A.; Castilla, Raymi</p> <p>2016-11-01</p> <p>This paper presents a compilation of 16 present-day <span class="hlt">stress</span> <span class="hlt">tensors</span> along the southern Caribbean plate boundary zone (PBZ), and particularly in western and along northern Venezuela. As a trial, these new <span class="hlt">stress</span> <span class="hlt">tensors</span> along PBZ have been calculated from inversion of 125 focal mechanism solutions (FMS) by applying the Angelier & Mechler's dihedral method, which were originally gathered by the first author and published in 2005. These new <span class="hlt">tensors</span> are compared to those 59 <span class="hlt">tensors</span> inverted from fault-slip data measured only in Plio-Quaternary sedimentary rocks, compiled in Audemard et al. (2005), which were originally calculated by several researchers through the inversion methods developed by Angelier and Mechler or Etchecopar et al. The two sets of <span class="hlt">stress</span> <span class="hlt">tensors</span>, one derived from geological data and the other one from seismological data, compare very well throughout the PBZ in terms of both <span class="hlt">stress</span> orientation and shape of the <span class="hlt">stress</span> <span class="hlt">tensor</span>. This region is characterized by a compressive strike-slip (transpressional senso lato), occasionally compressional, regime from the southern Mérida Andes on the southwest to the gulf of Paria in the east. Significant changes in direction of the maximum horizontal <span class="hlt">stress</span> (σH = σ1) can be established along it though. The σ1 direction varies progressively from nearly east-west in the southern Andes (SW Venezuela) to between NW-SE and NNW-SSE in northwestern Venezuela; this direction remaining constant across northern Venezuela, from Colombia to Trinidad. In addition, the σV defined by inversion of focal mechanisms or by the shape of the <span class="hlt">stress</span> ellipsoid derived from the Etchecopar et al.'s method better characterize whether the <span class="hlt">stress</span> regime is transpressional or compressional, or even very rarely trantensional at local scale. The orientation and space variation of this regional <span class="hlt">stress</span> field in western Venezuela results from the addition of the two major neighbouring interplate maximum horizontal <span class="hlt">stress</span> orientations (</p> </li> </ol> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_3");'>3</a></li> <li><a href="#" onclick='return showDiv("page_4");'>4</a></li> <li class="active"><span>5</span></li> <li><a href="#" onclick='return showDiv("page_6");'>6</a></li> <li><a href="#" onclick='return showDiv("page_7");'>7</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div><!-- col-sm-12 --> </div><!-- row --> </div><!-- page_5 --> <div id="page_6" class="hiddenDiv"> <div class="row"> <div class="col-sm-12"> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_4");'>4</a></li> <li><a href="#" onclick='return showDiv("page_5");'>5</a></li> <li class="active"><span>6</span></li> <li><a href="#" onclick='return showDiv("page_7");'>7</a></li> <li><a href="#" onclick='return showDiv("page_8");'>8</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div> </div> <div class="row"> <div class="col-sm-12"> <ol class="result-class" start="101"> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.dtic.mil/docs/citations/ADA158219','DTIC-ST'); return false;" href="http://www.dtic.mil/docs/citations/ADA158219"><span>Errors Due to Counting Statistics in the Triaxial Strain (<span class="hlt">Stress</span>) <span class="hlt">Tensor</span> Determined by Diffraction.</span></a></p> <p><a target="_blank" href="https://publicaccess.dtic.mil/psm/api/service/search/search">DTIC Science & Technology</a></p> <p></p> <p>2014-09-26</p> <p>Distribution of this docimnt Reproduction in whole or in part in unlimited is permitted for any purpose of the United States Government L" __j a m...1973). 3) S. Taira, T. Abe and T. Ehiro, X-ray Study of Surface Residual <span class="hlt">Stress</span> Produced in Fatigue Process of Annealed Metals, Bull J.S.M.E., 12:53</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/25757374','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/25757374"><span>Microstructural abnormalities in children with post-traumatic <span class="hlt">stress</span> disorder: a diffusion <span class="hlt">tensor</span> imaging study at 3.0T.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Lei, Du; Li, Lingjiang; Li, Lei; Suo, Xueling; Huang, Xiaoqi; Lui, Su; Li, Jing; Bi, Feng; Kemp, Graham J; Gong, Qiyong</p> <p>2015-03-11</p> <p>Posttraumatic <span class="hlt">stress</span> disorder (PTSD) is a severe anxiety disorder characterized by re-experiencing, avoidance and hyperarousal. Brain microstructure abnormalities in PTSD, especially in children, are not yet well characterized. The aim of this study was to use MR diffusion <span class="hlt">tensor</span> imaging (DTI) to identify brain microstructure alterations in children with PTSD compared to non-PTSD controls who experienced the same time-limited trauma. We studied 27 children with PTSD and 24 age- and gender-matched traumatized controls without PTSD, who all experienced the 2008 Sichuan major earthquake. DTI data were acquired and analyzed in terms of fractional anisotropy (FA), mean diffusivity (MD), radial diffusivity (RD) and axial diffusivity (AD). Children with PTSD showed an abnormal pattern, not only of FA, but also of the diffusivity measures MD, AD and RD. Most of the abnormal brain regions belonged to two important networks: the default-mode network, including precuneus and angular gyrus, and the salience network, including insula, putamen and thalamus. This DTI study identifies microstructural abnormalities of children with PTSD after a major earthquake, our results are consistent with the suggestion that pediatric PTSD is accompanied by a connectivity disequilibrium between the salience and default-mode networks, a finding of potential pathophysiological significance.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2013JSeis..17..207O','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2013JSeis..17..207O"><span>The Constantine (Algeria) seismic sequence of 27 October 1985: a new rupture model from aftershock relocation, focal mechanisms, and <span class="hlt">stress</span> <span class="hlt">tensors</span></span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Ousadou, F.; Dorbath, L.; Dorbath, C.; Bounif, M. A.; Benhallou, H.</p> <p>2013-04-01</p> <p>The October 27, 1985 Constantine earthquake of magnitude MS 5.9 (NEIC) although moderate is the strongest earthquake recorded in the eastern Tellian Atlas (northeast Algeria) since the beginning of instrumental seismology. The main shock locations given by different institutions are scattered and up to 10 km away northwest from the NE-SW 30 km long elongated aftershocks cloud localized by a dedicated temporary portable network. The focal mechanism indicates left-lateral strike-slip on an almost vertical fault with a small reverse component on the northwest dipping plane. This paper presents relocations of the main shock and aftershocks using TomoDD. One hundred thirty-eight individual focal mechanisms have been built allowing the determination of the <span class="hlt">stress</span> <span class="hlt">tensor</span> at different scales. A rupture model has been suggested, which explains the different observations of aftershock distribution and <span class="hlt">stress</span> <span class="hlt">tensor</span> rotation.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016EGUGA..18.7028K','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016EGUGA..18.7028K"><span>HYPODD Relocations and <span class="hlt">Stress</span> <span class="hlt">Tensor</span> Inversion Analyses of Local Earthquake Clusters in the Sea of Marmara</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Korkusuz Öztürk, Yasemin; Meral Özel, Nurcan</p> <p>2016-04-01</p> <p>Extensional focal mechanism solutions are mostly observed even in the Central Marmara by this comprehensive research although the main Marmara Fault that is the western branch of the NAF, is dominated by a right lateral strike-slip regime. Marmara Region, a seismically very active area, is located at the western section of the North Anatolian Fault Zone (NAFZ). The 1912 Mürefte and 1999 Izmit earthquakes are the last devastating events of the western and eastern sections of this region, respectively. The region between the locations of these earthquakes, is prone to a large earthquake. Therefore, the analysis of the Sea of Marmara is significant. The main objective of this research is to determine earthquake hypocenters and focal mechanism solutions accurately, hence we obtain recent states of <span class="hlt">stresses</span> for this region. Accordingly, this research aims to define branches of fault structures and its geometrical orientations in the Sea of Marmara. In this study, a cluster of events in the Central Marmara is analyzed using hypocenter program as a usual location technique. In addition, these events and other clustered events (Korkusuz Öztürk et al., 2015) are relocated using HYPODD relocation procedure. Even though NAF is mostly dominated by a right lateral strike slip fault, we found out many extensional source mechanisms. Also, from the comparison of relocation results of hypocenter and HYPODD programs, it is found out that most of the relocations have the same orientations and dipping angles of the segments of the main Marmara Fault are not clear. As a result, since we observe many normal faulting mechanisms in the Sea of Marmara, we expect to observe some deviations in orientations of vertical orientations of the fault segments comparing a dip-slip model. Therefore, this research will continue to clearly identify fault dip angles of main fault segments in Marmara Sea. Further, our sensitive relocation and <span class="hlt">stress</span> analyses will make an important contribution to a</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=4852678','PMC'); return false;" href="https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=4852678"><span>White Matter Changes in Posttraumatic <span class="hlt">Stress</span> Disorder Following Mild Traumatic Brain Injury: A Prospective Longitudinal Diffusion <span class="hlt">Tensor</span> Imaging Study</span></a></p> <p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pmc">PubMed Central</a></p> <p>Li, Li; Sun, Gang; Liu, Kai; Li, Min; Li, Bo; Qian, Shao-Wen; Yu, Li-Li</p> <p>2016-01-01</p> <p>Background: The ability to predict posttraumatic <span class="hlt">stress</span> disorder (PTSD) is a critical issue in the management of patients with mild traumatic brain injury (mTBI), as early medical and rehabilitative interventions may reduce the risks of long-term cognitive changes. The aim of the present study was to investigate how diffusion <span class="hlt">tensor</span> imaging (DTI) metrics changed in the transition from acute to chronic phases in patients with mTBI and whether the alteration relates to the development of PTSD. Methods: Forty-three patients with mTBI and 22 healthy volunteers were investigated. The patients were divided into two groups: successful recovery (SR, n = 22) and poor recovery (PR, n = 21), based on neurocognitive evaluation at 1 or 6 months after injury. All patients underwent magnetic resonance imaging investigation at acute (within 3 days), subacute (10–20 days), and chronic (1–6 months) phases after injury. Group differences of fractional anisotropy (FA) and mean diffusivity (MD) were analyzed using tract-based spatial statistics (TBSS). The accuracy of DTI metrics for classifying PTSD was estimated using Bayesian discrimination analysis. Results: TBSS showed white matter (WM) abnormalities in various brain regions. In the acute phase, FA values were higher for PR and SR patients than controls (all P < 0.05). In subacute phase, PR patients have higher mean MD than SR and controls (all P < 0.05). In the chronic phase, lower FA and higher MD were observed in PR compared with both SR and control groups (all P < 0.05). PR and SR groups could be discriminated with a sensitivity of 73%, specificity of 78%, and accuracy of 75.56%, in terms of MD value in subacute phase. Conclusions: Patients with mTBI have multiple abnormalities in various WM regions. DTI metrics change over time and provide a potential indicator at subacute stage for PTSD following mTBI. PMID:27098796</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2015PhFl...27a5102H','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015PhFl...27a5102H"><span>Anisotropy of the Reynolds <span class="hlt">stress</span> <span class="hlt">tensor</span> in the wakes of wind turbine arrays in Cartesian arrangements with counter-rotating rotors</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Hamilton, Nicholas; Cal, Raúl Bayoán</p> <p>2015-01-01</p> <p>A 4 × 3 wind turbine array in a Cartesian arrangement was constructed in a wind tunnel setting with four configurations based on the rotational sense of the rotor blades. The fourth row of devices is considered to be in the fully developed turbine canopy for a Cartesian arrangement. Measurements of the flow field were made with stereo particle-image velocimetry immediately upstream and downstream of the selected model turbines. Rotational sense of the turbine blades is evident in the mean spanwise velocity W and the Reynolds shear <span class="hlt">stress</span> - v w ¯ . The flux of kinetic energy is shown to be of greater magnitude following turbines in arrays where direction of rotation of the blades varies. Invariants of the normalized Reynolds <span class="hlt">stress</span> anisotropy <span class="hlt">tensor</span> (η and ξ) are plotted in the Lumley triangle and indicate that distinct characters of turbulence exist in regions of the wake following the nacelle and the rotor blade tips. Eigendecomposition of the <span class="hlt">tensor</span> yields principle components and corresponding coordinate system transformations. Characteristic spheroids representing the balance of components in the normalized anisotropy <span class="hlt">tensor</span> are composed with the eigenvalues yielding shapes predicted by the Lumley triangle. Rotation of the coordinate system defined by the eigenvectors demonstrates trends in the streamwise coordinate following the rotors, especially trailing the top-tip of the rotor and below the hub. Direction of rotation of rotor blades is shown by the orientation of characteristic spheroids according to principle axes. In the inflows of exit row turbines, the normalized Reynolds <span class="hlt">stress</span> anisotropy <span class="hlt">tensor</span> shows cumulative effects of the upstream turbines, tending toward prolate shapes for uniform rotational sense, oblate spheroids for streamwise organization of rotational senses, and a mixture of characteristic shapes when the rotation varies by row. Comparison between the invariants of the Reynolds <span class="hlt">stress</span> anisotropy <span class="hlt">tensor</span> and terms from the mean</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2010AGUFM.V31E..06G','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2010AGUFM.V31E..06G"><span>Investigating the pre- and post-eruptive <span class="hlt">stress</span> regime at Redoubt volcano, Alaska, from 2008-1010 using seismic anisotropy and <span class="hlt">stress-tensor</span> inversions</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Gardine, M.; Roman, D. C.</p> <p>2010-12-01</p> <p>Redoubt volcano, located on the west side of Cook Inlet approximately 170 km southwest of Anchorage, Alaska, began erupting in March 2009. The eruption, which consisted of at least 17 explosive events over a three-week time period followed by three months of dome-building, significantly impacted both aviation and oil production operations in the area. Pre-eruptive seismicity was generally limited to deep (>20 km) long-period (DLP) earthquakes starting in late 2008, transitioning to bursts of strong, shallow volcanic tremor for nearly three months prior to the eruption. The near-complete absence of precursory volcano-tectonic (VT) earthquakes is unusual for eruptions of this type and complicates understanding of the dynamics of the Redoubt magmatic system. However, the strong volcanic tremor preceding the eruption suggests that magma was ascending and the system was pressurizing for months prior to the first explosion - a situation during which VT earthquakes typically occur. The study of subtle changes in <span class="hlt">stress</span> conditions at Redoubt may elucidate the reasons for the observed near-complete lack of precursory VT seismicity. Using first-motion data from waveforms recorded by seismic stations operated in the vicinity of Redoubt by the Alaska Volcano Observatory (AVO) and the Alaska Earthquake Information Center (AEIC), we computed double-couple fault-plane solutions for approximately 200 VT earthquakes occurring in the months prior to and immediately following the first eruption in March 2009. The analysis of the fault-plane solutions using spatial and temporal <span class="hlt">stress-tensor</span> inversions combined with cumulative misfit analysis will help to constrain if, when, and where localized precursory changes in <span class="hlt">stress</span> occurred. In addition, we performed an analysis of shear-wave splitting using data from deep slab events located by AEIC within a 70 km radius for one year prior to and one year following the eruption, which resulted in approximately 500 high-quality measurements on</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017PhRvL.118k0504Y','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017PhRvL.118k0504Y"><span>Loop Optimization for <span class="hlt">Tensor</span> Network Renormalization</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Yang, Shuo; Gu, Zheng-Cheng; Wen, Xiao-Gang</p> <p>2017-03-01</p> <p>We introduce a <span class="hlt">tensor</span> renormalization group scheme for coarse graining a two-dimensional <span class="hlt">tensor</span> network that can be successfully applied to both classical and <span class="hlt">quantum</span> systems on and off criticality. The key innovation in our scheme is to deform a 2D <span class="hlt">tensor</span> network into small loops and then optimize the <span class="hlt">tensors</span> on each loop. In this way, we remove short-range entanglement at each iteration step and significantly improve the accuracy and stability of the renormalization flow. We demonstrate our algorithm in the classical Ising model and a frustrated 2D <span class="hlt">quantum</span> model.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2015JSP...160.1389B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015JSP...160.1389B"><span><span class="hlt">Tensor</span> Network Contractions for #SAT</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Biamonte, Jacob D.; Morton, Jason; Turner, Jacob</p> <p>2015-09-01</p> <p>The computational cost of counting the number of solutions satisfying a Boolean formula, which is a problem instance of #SAT, has proven subtle to quantify. Even when finding individual satisfying solutions is computationally easy (e.g. 2-SAT, which is in ), determining the number of solutions can be #-hard. Recently, computational methods simulating <span class="hlt">quantum</span> systems experienced advancements due to the development of <span class="hlt">tensor</span> network algorithms and associated <span class="hlt">quantum</span> physics-inspired techniques. By these methods, we give an algorithm using an axiomatic <span class="hlt">tensor</span> contraction language for n-variable #SAT instances with complexity where c is the number of COPY-<span class="hlt">tensors</span>, g is the number of gates, and d is the maximal degree of any COPY-<span class="hlt">tensor</span>. Thus, n-variable counting problems can be solved efficiently when their <span class="hlt">tensor</span> network expression has at most COPY-<span class="hlt">tensors</span> and polynomial fan-out. This framework also admits an intuitive proof of a variant of the Tovey conjecture (the r,1-SAT instance of the Dubois-Tovey theorem). This study increases the theory, expressiveness and application of <span class="hlt">tensor</span> based algorithmic tools and provides an alternative insight on these problems which have a long history in statistical physics and computer science.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2013EGUGA..15.2310D','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2013EGUGA..15.2310D"><span>Tectonic <span class="hlt">stress</span> inversion of large multi-phase fracture data sets: application of Win-<span class="hlt">Tensor</span> to reveal the brittle tectonic history of the Lufilan Arc, DRC</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Delvaux, Damien; Kipata, Louis; Sintubin, Manuel</p> <p>2013-04-01</p> <p>Large fault-slip data sets from multiphase orogenic regions present a particular challenge in paleostress reconstructions. The Lufilian Arc is an arcuate fold-and-thrust belt that formed during the late Pan-African times as the result of combined N-S and E-W amalgamation of Gondwana in SE-DRCongo and N-Zambia. We studied more than 22 sites in the Lufilian Arc, and its foreland and correlated the results obtained with existing result in the Ubende belt of W-Tanzania. Most studied sites are characterized by multiphase brittle deformation in which the observed brittle structures are the result of progressive saturation of the host rock by neoformed fractures and the reactivation of early formed fractures. They correspond to large mining exploitations with multiple large and continuous outcrops that allow obtaining datasets sufficiently large to be of statistical significance and often corresponding to several successive brittle events. In this context, the reconstruction of tectonic <span class="hlt">stress</span> necessitates an initial field-base separation of data, completed by a dynamic separation of the original data set into subsets. In the largest sites, several parts of the deposits have been measured independently and are considered as sub-sites that are be processed separately in an initial stage. The procedure used for interactive fault-slip data separation and <span class="hlt">stress</span> inversion will be illustrated by field examples (Luiswishi and Manono mining sites). This principle has been applied to all result in the reconstruction of the brittle tectonic history of the region, starting with two major phases of orogenic compression, followed by late orogenic extension and extensional collapse. A regional tectonic inversion during the early Mesozoic, as a result of far- field <span class="hlt">stresses</span> mark the transition towards rift-related extension. More details in Kipata, Delvaux et al.(2013), Geologica Belgica 16/1-2: 001-017 Win-<span class="hlt">Tensor</span> can be downloaded at: http://users.skynet.be/damien.delvaux/<span class="hlt">Tensor/tensor</span>-index.html</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2002IJNAM..26..925J','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2002IJNAM..26..925J"><span><span class="hlt">Tensor</span> visualizations in computational geomechanics</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Jeremi, Boris; Scheuermann, Gerik; Frey, Jan; Yang, Zhaohui; Hamann, Bernd; Joy, Kenneth I.; Hagen, Hans</p> <p>2002-08-01</p> <p>We present a novel technique for visualizing <span class="hlt">tensors</span> in three dimensional (3D) space. Of particular interest is the visualization of <span class="hlt">stress</span> <span class="hlt">tensors</span> resulting from 3D numerical simulations in computational geomechanics. To this end we present three different approaches to visualizing <span class="hlt">tensors</span> in 3D space, namely hedgehogs, hyperstreamlines and hyperstreamsurfaces. We also present a number of examples related to <span class="hlt">stress</span> distributions in 3D solids subjected to single and load couples. In addition, we present <span class="hlt">stress</span> visualizations resulting from single-pile and pile-group computations. The main objective of this work is to investigate various techniques for visualizing general Cartesian <span class="hlt">tensors</span> of rank 2 and it's application to geomechanics problems.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016JCoPh.308..322F','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016JCoPh.308..322F"><span>Mixed weak-perturbative solution method for Maxwell's equations of diffusion with Müller's partial <span class="hlt">stress</span> <span class="hlt">tensor</span> in the low velocity limit</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Faliagas, A. C.</p> <p>2016-03-01</p> <p>Maxwell's theory of multicomponent diffusion and subsequent extensions are based on systems of mass and momentum conservation equations. The partial <span class="hlt">stress</span> <span class="hlt">tensor</span>, which is involved in these equations, is expressed in terms of the gradients of velocity fields by statistical and continuum mechanical methods. We propose a method for the solution of Maxwell's equations of diffusion coupled with Müller's expression for the partial <span class="hlt">stress</span> <span class="hlt">tensor</span>. The proposed method consists in a singular perturbation process, followed by a weak (finite element) analysis of the resulting PDE systems. The singularity involved in the obtained equations was treated by a special technique, by which lower-order systems were supplemented by proper combinations of higher-order equations. The method proved particularly efficient for the solution of the Maxwell-Müller system, eventually reducing the number of unknown fields to that of the classical Navier-Stokes/Fick system. It was applied to the classical Stefan tube problem and the Hagen-Poiseuille flow in a hollow-fiber membrane tube. Numerical results for these problems are presented, and compared with the Navier-Stokes/Fick approximation. It is shown that the 0-th order term of the Maxwell-Müller equations differs from a properly formulated Navier-Stokes/Fick system, by a numerically insignificant amount. Numerical results for 1st-order terms indicate a good agreement of the classical approximation (with properly formulated Navier-Stokes and Fick's equations) with the Maxwell-Müller system, in the studied cases.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/scitech/biblio/1230898','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/1230898"><span>MATLAB <span class="hlt">Tensor</span> Toolbox</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Kolda, Tamara G.; Bader, Brett W.</p> <p>2006-08-03</p> <p>This software provides a collection of MATLAB classes for <span class="hlt">tensor</span> manipulations that can be used for fast algorithm prototyping. The <span class="hlt">tensor</span> class extends the functionality of MATLAB's multidimensional arrays by supporting additional operations such as <span class="hlt">tensor</span> multiplication. We have also added support for sparse <span class="hlt">tensor</span>, <span class="hlt">tensors</span> in Kruskal or Tucker format, and <span class="hlt">tensors</span> stored as matrices (both dense and sparse).</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/28358','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/28358"><span>Coordinates of the <span class="hlt">quantum</span> plane as q-<span class="hlt">tensor</span> operators in U{sub q} (su(2) * su(2))</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Biedenharn, L.C.; Lohe, M.A.</p> <p>1995-01-13</p> <p>The relation between the set of transformations M{sub q}(2) of the <span class="hlt">quantum</span> plane and the <span class="hlt">quantum</span> universal enveloping algebra U{sub q}(u(2)) is investigated by constructing representations of the factor algebra U{sub q} (u(2) * u(2)). The non-commuting coordinates of M{sub q}(2), on which U{sub q}(2) * U{sub q}(2) acts, are realized as q-spinors with respect to each U{sub q}(u(2)) algebra. The representation matrices of U{sub q}(2) are constructed as polynomials in these spinor components. This construction allows a derivation of the commutation relations of the noncommuting coordinates of M{sub q}(2) directly from properties of U{sub q}(u(2)). The generalization of these results to U{sub q}(u(n)) and M{sub q}(n) is also discussed.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://pubs.er.usgs.gov/publication/70025929','USGSPUBS'); return false;" href="http://pubs.er.usgs.gov/publication/70025929"><span>Multiple seismogenic processes for high-frequency earthquakes at Katmai National Park, Alaska: Evidence from <span class="hlt">stress</span> <span class="hlt">tensor</span> inversions of fault-plane solutions</span></a></p> <p><a target="_blank" href="http://pubs.er.usgs.gov/pubs/index.jsp?view=adv">USGS Publications Warehouse</a></p> <p>Moran, S.C.</p> <p>2003-01-01</p> <p>The volcanological significance of seismicity within Katmai National Park has been debated since the first seismograph was installed in 1963, in part because Katmai seismicity consists almost entirely of high-frequency earthquakes that can be caused by a wide range of processes. I investigate this issue by determining 140 well-constrained first-motion fault-plane solutions for shallow (depth < 9 km) earthquakes occuring between 1995 and 2001 and inverting these solutions for the <span class="hlt">stress</span> <span class="hlt">tensor</span> in different regions within the park. Earthquakes removed by several kilometers from the volcanic axis occur in a <span class="hlt">stress</span> field characterized by horizontally oriented ??1 and ??3 axes, with ??1 rotated slightly (12??) relative to the NUVELIA subduction vector, indicating that these earthquakes are occurring in response to regional tectonic forces. On the other hand, <span class="hlt">stress</span> <span class="hlt">tensors</span> for earthquake clusters beneath several Katmai cluster volcanoes have vertically oriented ??1 axes, indicating that these events are occuring in response to local, not regional, processes. At Martin-Mageik, vertically oriented ??1 is most consistent with failure under edifice loading conditions in conjunction with localized pore pressure increases associated with hydrothermal circulation cells. At Trident-Novarupta, it is consistent with a number of possible models, including occurence along fractures formed during the 1912 eruption that now serve as horizontal conduits for migrating fluids and/or volatiles from nearby degassing and cooling magma bodies. At Mount Katmai, it is most consistent with continued seismicity along ring-fracture systems created in the 1912 eruption, perhaps enhanced by circulating hydrothermal fluids and/or seepage from the caldera-filling lake.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016GeoJI.204..236W','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016GeoJI.204..236W"><span>Probabilistic waveform inversion for 22 earthquake moment <span class="hlt">tensors</span> in Hungary: new constraints on the tectonic <span class="hlt">stress</span> pattern inside the Pannonian basin</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Wéber, Zoltán</p> <p>2016-01-01</p> <p>We have successfully estimated the full moment <span class="hlt">tensors</span> of 22 local earthquakes with local magnitude ranging from 1.2 to 4.8 that occurred in the Hungarian part of the Pannonian basin between 1995 and 2014. We used a probabilistic waveform inversion procedure that takes into account the effects of the random noise contained in the seismograms, the uncertainty of the hypocentre determined from arrival times and the inaccurate knowledge of the velocity structure, while estimating the error affecting the derived focal parameters. The applied probabilistic approach maps the posterior probability density functions (PPDFs) for both the hypocentral coordinates and the moment <span class="hlt">tensor</span> components. The final estimates are given by the maximum likelihood points of the PPDFs, while solution uncertainties are presented by histogram plots. The estimated uncertainties in the moment <span class="hlt">tensor</span> components are plotted on the focal sphere in such a way, that the significance of the double couple (DC), the compensated linear vector dipole (CLVD) and the isotropic (ISO) parts of the source can be assessed. We have shown that the applied waveform inversion method is equally suitable to recover the source mechanism for low-magnitude events using short-period local waveforms as well as for moderate-size earthquakes using long-period seismograms. The non-DC components of the retrieved focal mechanisms are statistically insignificant for all the analysed earthquakes. The negligible amount of the ISO component implies the tectonic nature of the investigated events. The moment <span class="hlt">tensor</span> solutions reported by other agencies for five of the ML > 4 earthquakes studied in this paper are very similar to those calculated by the applied waveform inversion algorithm. We have found only strike-slip and thrust faulting events, giving further support to the hypothesis that the Pannonian basin is currently experiencing a compressional regime of deformation. The orientations of the obtained focal mechanisms are in</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/scitech/biblio/1178516','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/1178516"><span>CAST: Contraction Algorithm for Symmetric <span class="hlt">Tensors</span></span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Rajbhandari, Samyam; NIkam, Akshay; Lai, Pai-Wei; Stock, Kevin; Krishnamoorthy, Sriram; Sadayappan, Ponnuswamy</p> <p>2014-09-22</p> <p><span class="hlt">Tensor</span> contractions represent the most compute-intensive core kernels in ab initio computational <span class="hlt">quantum</span> chemistry and nuclear physics. Symmetries in these <span class="hlt">tensor</span> contractions makes them difficult to load balance and scale to large distributed systems. In this paper, we develop an efficient and scalable algorithm to contract symmetric <span class="hlt">tensors</span>. We introduce a novel approach that avoids data redistribution in contracting symmetric <span class="hlt">tensors</span> while also avoiding redundant storage and maintaining load balance. We present experimental results on two parallel supercomputers for several symmetric contractions that appear in the CCSD <span class="hlt">quantum</span> chemistry method. We also present a novel approach to <span class="hlt">tensor</span> redistribution that can take advantage of parallel hyperplanes when the initial distribution has replicated dimensions, and use collective broadcast when the final distribution has replicated dimensions, making the algorithm very efficient.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016PhRvA..94d2324B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016PhRvA..94d2324B"><span><span class="hlt">Tensor</span> eigenvalues and entanglement of symmetric states</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Bohnet-Waldraff, F.; Braun, D.; Giraud, O.</p> <p>2016-10-01</p> <p><span class="hlt">Tensor</span> eigenvalues and eigenvectors have been introduced in the recent mathematical literature as a generalization of the usual matrix eigenvalues and eigenvectors. We apply this formalism to a <span class="hlt">tensor</span> that describes a multipartite symmetric state or a spin state, and we investigate to what extent the corresponding <span class="hlt">tensor</span> eigenvalues contain information about the multipartite entanglement (or, equivalently, the <span class="hlt">quantumness</span>) of the state. This extends previous results connecting entanglement to spectral properties related to the state. We show that if the smallest <span class="hlt">tensor</span> eigenvalue is negative, the state is detected as entangled. While for spin-1 states the positivity of the smallest <span class="hlt">tensor</span> eigenvalue is equivalent to separability, we show that for higher values of the angular momentum there is a correlation between entanglement and the value of the smallest <span class="hlt">tensor</span> eigenvalue.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017PhRvB..95d5117E','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017PhRvB..95d5117E"><span>Algorithms for <span class="hlt">tensor</span> network renormalization</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Evenbly, G.</p> <p>2017-01-01</p> <p>We discuss in detail algorithms for implementing <span class="hlt">tensor</span> network renormalization (TNR) for the study of classical statistical and <span class="hlt">quantum</span> many-body systems. First, we recall established techniques for how the partition function of a 2 D classical many-body system or the Euclidean path integral of a 1 D <span class="hlt">quantum</span> system can be represented as a network of <span class="hlt">tensors</span>, before describing how TNR can be implemented to efficiently contract the network via a sequence of coarse-graining transformations. The efficacy of the TNR approach is then benchmarked for the 2 D classical statistical and 1 D <span class="hlt">quantum</span> Ising models; in particular the ability of TNR to maintain a high level of accuracy over sustained coarse-graining transformations, even at a critical point, is demonstrated.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016PhRvD..93f4044B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016PhRvD..93f4044B"><span><span class="hlt">Quantum</span> focusing conjecture</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Bousso, Raphael; Fisher, Zachary; Leichenauer, Stefan; Wall, Aron C.</p> <p>2016-03-01</p> <p>We propose a universal inequality that unifies the Bousso bound with the classical focusing theorem. Given a surface σ that need not lie on a horizon, we define a finite generalized entropy Sgen as the area of σ in Planck units, plus the von Neumann entropy of its exterior. Given a null congruence N orthogonal to σ , the rate of change of Sgen per unit area defines a <span class="hlt">quantum</span> expansion. We conjecture that the <span class="hlt">quantum</span> expansion cannot increase along N . This extends the notion of universal focusing to cases where <span class="hlt">quantum</span> matter may violate the null energy condition. Integrating the conjecture yields a precise version of the Strominger-Thompson <span class="hlt">quantum</span> Bousso bound. Applied to locally parallel light-rays, the conjecture implies a novel inequality, the <span class="hlt">quantum</span> null energy condition, a lower bound on the <span class="hlt">stress</span> <span class="hlt">tensor</span> in terms of the second derivative of the von Neumann entropy. We sketch a proof of the latter relation in <span class="hlt">quantum</span> field theory.</p> </li> </ol> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_4");'>4</a></li> <li><a href="#" onclick='return showDiv("page_5");'>5</a></li> <li class="active"><span>6</span></li> <li><a href="#" onclick='return showDiv("page_7");'>7</a></li> <li><a href="#" onclick='return showDiv("page_8");'>8</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div><!-- col-sm-12 --> </div><!-- row --> </div><!-- page_6 --> <div id="page_7" class="hiddenDiv"> <div class="row"> <div class="col-sm-12"> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_5");'>5</a></li> <li><a href="#" onclick='return showDiv("page_6");'>6</a></li> <li class="active"><span>7</span></li> <li><a href="#" onclick='return showDiv("page_8");'>8</a></li> <li><a href="#" onclick='return showDiv("page_9");'>9</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div> </div> <div class="row"> <div class="col-sm-12"> <ol class="result-class" start="121"> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/scitech/biblio/1253357','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/1253357"><span><span class="hlt">Tensor</span> Algebra Library for NVidia Graphics Processing Units</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Liakh, Dmitry</p> <p>2015-03-16</p> <p>This is a general purpose math library implementing basic <span class="hlt">tensor</span> algebra operations on NVidia GPU accelerators. This software is a <span class="hlt">tensor</span> algebra library that can perform basic <span class="hlt">tensor</span> algebra operations, including <span class="hlt">tensor</span> contractions, <span class="hlt">tensor</span> products, <span class="hlt">tensor</span> additions, etc., on NVidia GPU accelerators, asynchronously with respect to the CPU host. It supports a simultaneous use of multiple NVidia GPUs. Each asynchronous API function returns a handle which can later be used for querying the completion of the corresponding <span class="hlt">tensor</span> algebra operation on a specific GPU. The <span class="hlt">tensors</span> participating in a particular <span class="hlt">tensor</span> operation are assumed to be stored in local RAM of a node or GPU RAM. The main research area where this library can be utilized is the <span class="hlt">quantum</span> many-body theory (e.g., in electronic structure theory).</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2013AGUFM.V43D..05H','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2013AGUFM.V43D..05H"><span>Moment- and <span class="hlt">Stress-Tensor</span>-Inversion of volcanic earthquakes: Constraining driving forces of the 2010 eruptions at Eyjajfallajökull (Iceland)</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Hensch, M.; Brandsdottir, B.; Cesca, S.; Lund, B.</p> <p>2013-12-01</p> <p>The Eyjafjallajökull stratovolcano is located at the western border of the Eastern Volcanic Zone (EVZ) in South Iceland, west of Mýrdalsjökull (Katla). Since the settlement in Iceland, three eruptions have been documented in Eyjafjallajökull before 2010, in 920, 1612 and 1821-1823. Following three episodes of persistent microearthquake activity in the 1990s, seismicity increased again in spring 2009 under the northeastern flank of Eyjafjallajökull. The activity raised throughout the year and culminated in an intense earthquake swarm in February-March 2010. Simultaneous inflation observed by GPS and InSAR data confirmed magmatic accumulation within the volcano which heralded the subsequent eruptions. In early March, the permanent seismic network around the volcano was augmented by additional stations to enhance hypocentral earthquake locations and to improve the liability of focal solutions. Earthquake locations revealed more than one accumulation zone at shallow (3-5 km) depth beneath the northeastern flank of the volcano throughout March 2010. The seismic clusters migrated eastwards during the week prior to the Fimmvörduháls flank eruption on 21. March. The 14. April summit eruption was preceded by a seismic cluster beneath the central part of the volcano. Focal mechanisms derived from P-wave polarity analysis indicate E-W striking reverse faulting for the February-March earthquake swarm, same as for an intrusion event in 1994. Normal faulting events were observed beneath the summit crater prior to the second eruption, indicating that magma was on its way to the surface. The scope of this study is to constrain driving forces of the intrusive activity beneath Eyjafjallajökull in detail by inverting focal mechanism data towards the <span class="hlt">stress</span> <span class="hlt">tensor</span>. This analysis reveals a significant change of the direction of maximum <span class="hlt">stress</span> between the intrusion phase during the weeks before the eruptions and the final magma ascent prior to the summit eruption. Unstable T</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2012PhRvL.109e5501H','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2012PhRvL.109e5501H"><span><span class="hlt">Quantum</span> Electronic <span class="hlt">Stress</span>: Density-Functional-Theory Formulation and Physical Manifestation</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Hu, Hao; Liu, Miao; Wang, Z. F.; Zhu, Junyi; Wu, Dangxin; Ding, Hepeng; Liu, Zheng; Liu, Feng</p> <p>2012-08-01</p> <p>The concept of <span class="hlt">quantum</span> electronic <span class="hlt">stress</span> (QES) is introduced and formulated within density functional theory to elucidate extrinsic electronic effects on the <span class="hlt">stress</span> state of solids and thin films in the absence of lattice strain. A formal expression of QES (σQE) is derived in relation to deformation potential of electronic states (Ξ) and variation of electron density (Δn), σQE=ΞΔn as a <span class="hlt">quantum</span> analog of classical Hooke’s law. Two distinct QES manifestations are demonstrated quantitatively by density functional theory calculations: (1) in the form of bulk <span class="hlt">stress</span> induced by charge carriers and (2) in the form of surface <span class="hlt">stress</span> induced by <span class="hlt">quantum</span> confinement. Implications of QES in some physical phenomena are discussed to underlie its importance.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017JHEP...03..048C','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017JHEP...03..048C"><span>ahcal{N} = 4 super-Yang-Mills in LHC superspace part II: non-chiral correlation functions of the <span class="hlt">stress-tensor</span> multiplet</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Chicherin, Dmitry; Sokatchev, Emery</p> <p>2017-03-01</p> <p>We study the multipoint super-correlation functions of the full non-chiral <span class="hlt">stress-tensor</span> multiplet in N = 4 super-Yang-Mills theory in the Born approximation. We derive effective supergraph Feynman rules for them. Surprisingly, the Feynman rules for the non-chiral correlators are obtained from those for the chiral correlators by a simple Grassmann shift of the space-time variables. We rely on the formulation of the theory in Lorentz harmonic chiral (LHC) superspace elaborated in the twin paper arXiv:1601.06803. In this approach only the chiral half of the supersymmetry is manifest. The other half is realized by nonlinear and nonlocal transformations of the LHC superfields. However, at Born level only the simple linear part of the transformations is relevant. It corresponds to effectively working in the self-dual sector of the theory. Our method is also applicable to a wider class of supermultiplets like all the half-BPS operators and the Konishi multiplet.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/15011574','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/15011574"><span>Compressive and Tensile <span class="hlt">Stress</span> in CdSe Semiconductor <span class="hlt">Quantum</span> Dots</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Meulenberg, R W; Jennings, T; Strouse, G F</p> <p>2004-06-02</p> <p>Compressive and tensile <span class="hlt">stress</span> in colloidal CdSe <span class="hlt">quantum</span> dots (QDs) is examined using resonance Raman spectroscopy. We find that the dispersion of the longitudinal optical phonon mode with size does not follow theoretical calculations based on phonon confinement models. To account for these deviations, the presence of compressive or tensile <span class="hlt">stress</span> in the QDs was proposed. We find that CdSe QDs prepared via a single source precursor (SSP) method exhibit compressive <span class="hlt">stress</span>, while CdSe QDs prepared via high temperature lyothermal methods exhibit tensile <span class="hlt">stress</span>. Evidence is provided that the SSP CdSe QDs <span class="hlt">stress</span> is directly related to a surface effect.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=20000012445&hterms=topology&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D40%26Ntt%3Dtopology','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=20000012445&hterms=topology&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D40%26Ntt%3Dtopology"><span>The Topology of Symmetric <span class="hlt">Tensor</span> Fields</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Levin, Yingmei; Batra, Rajesh; Hesselink, Lambertus; Levy, Yuval</p> <p>1997-01-01</p> <p>Combinatorial topology, also known as "rubber sheet geometry", has extensive applications in geometry and analysis, many of which result from connections with the theory of differential equations. A link between topology and differential equations is vector fields. Recent developments in scientific visualization have shown that vector fields also play an important role in the analysis of second-order <span class="hlt">tensor</span> fields. A second-order <span class="hlt">tensor</span> field can be transformed into its eigensystem, namely, eigenvalues and their associated eigenvectors without loss of information content. Eigenvectors behave in a similar fashion to ordinary vectors with even simpler topological structures due to their sign indeterminacy. Incorporating information about eigenvectors and eigenvalues in a display technique known as hyperstreamlines reveals the structure of a <span class="hlt">tensor</span> field. The simplify and often complex <span class="hlt">tensor</span> field and to capture its important features, the <span class="hlt">tensor</span> is decomposed into an isotopic <span class="hlt">tensor</span> and a deviator. A <span class="hlt">tensor</span> field and its deviator share the same set of eigenvectors, and therefore they have a similar topological structure. A a deviator determines the properties of a <span class="hlt">tensor</span> field, while the isotopic part provides a uniform bias. Degenerate points are basic constituents of <span class="hlt">tensor</span> fields. In 2-D <span class="hlt">tensor</span> fields, there are only two types of degenerate points; while in 3-D, the degenerate points can be characterized in a Q'-R' plane. Compressible and incompressible flows share similar topological feature due to the similarity of their deviators. In the case of the deformation <span class="hlt">tensor</span>, the singularities of its deviator represent the area of vortex core in the field. In turbulent flows, the similarities and differences of the topology of the deformation and the Reynolds <span class="hlt">stress</span> <span class="hlt">tensors</span> reveal that the basic addie-viscosity assuptions have their validity in turbulence modeling under certain conditions.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2003EAEJA.....5440B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2003EAEJA.....5440B"><span>Seismic Activity Related to the 2002-2003 Mt. Etna Volcano Eruption (Italy): Fault Plane Solutions and <span class="hlt">Stress</span> <span class="hlt">Tensor</span> Computation</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Barberi, G.; Cammarata, L.; Cocina, O.; Maiolino, V.; Musumeci, C.; Privitera, E.</p> <p>2003-04-01</p> <p>Late on the night of October 26, 2002, a bi-lateral eruption started on both the eastern and the southeastern flanks of Mt. Etna. The opening of the eruptive fracture system on the NE sector and the reactivation of the 2001 fracture system, on the S sector, were accompanied by a strong seismic swarm recorded between October 26 and 28 and by sharp increase of volcanic tremor amplitude. After this initial phase, on October 29 another seismogenetic zone became active in the SE sector of the volcano. At present (January 2003) the eruption is still in evolution. During the whole period a total of 862 earthquakes (Md≫1) was recorded by the local permanent seismic network run by INGV - Sezione di Catania. The maximum magnitude observed was Md=4.4. We focus our attention on 55 earthquakes with magnitude Md≫ 3.0. The dataset consists of accurate digital pickings of P- and S-phases including first-motion polarities. Firstly earthquakes were located using a 1D velocity model (Hirn et alii, 1991), then events were relocated by using two different 3D velocity models (Aloisi et alii, 2002; Patane et alii, 2002). Results indicate that most of earthquakes are located to the east of the Summit Craters and to northeast of them. Fault plane solutions (FPS) obtained show prevalent strike-slip rupture mechanisms. The suitable FPSs were considered for the application of Gephart and Forsyth`s algorithm in order to evaluate seismic <span class="hlt">stress</span> field characteristics. Taking into account the preliminary results we propose a kinematic model of the eastern flank eastward movement in response of the intrusion processes in the central part of the volcano. References Aloisi M., Cocina O., Neri G., Orecchio B., Privitera E. (2002). Seismic tomography of the crust underneath the Etna volcano, Sicily. Physics of the Earth and Planetary Interiors 4154, pp. 1-17 Hirn A., Nercessian A., Sapin M., Ferrucci F., Wittlinger G. (1991). Seismic heterogeneity of Mt. Etna: structure and activity. Geophys. J</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/scitech/biblio/21266316','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/21266316"><span>Averaged null energy condition in loop <span class="hlt">quantum</span> cosmology</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Li Lifang; Zhu Jianyang</p> <p>2009-02-15</p> <p>Wormholes and time machines are objects of great interest in general relativity. However, to support them it needs exotic matters which are impossible at the classical level. Semiclassical gravity introduces the <span class="hlt">quantum</span> effects into the <span class="hlt">stress</span>-energy <span class="hlt">tensor</span> and constructs many self-consistent wormholes. But they are not traversable due to the averaged null energy condition. Loop <span class="hlt">quantum</span> gravity (LQG) significantly modifies the Einstein equation in the deep <span class="hlt">quantum</span> region. If we write the modified Einstein equation in the form of the standard one but with an effective <span class="hlt">stress</span>-energy <span class="hlt">tensor</span>, it is convenient to analyze the geometry in LQG through the energy condition. Loop <span class="hlt">quantum</span> cosmology (LQC), an application of LQG, has an effective <span class="hlt">stress</span>-energy <span class="hlt">tensor</span> which violates some kinds of local energy conditions. So it is natural that the inflation emerges in LQC. In this paper, we investigate the averaged null energy condition in LQC in the framework of the effective Hamiltonian, and we find that the effective <span class="hlt">stress</span>-energy <span class="hlt">tensor</span> in LQC violates the averaged null energy condition in the massless scalar field coupled model.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/1985PhRvB..32.3780N','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/1985PhRvB..32.3780N"><span><span class="hlt">Quantum</span>-mechanical theory of <span class="hlt">stress</span> and force</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Nielsen, O. H.; Martin, Richard M.</p> <p>1985-09-01</p> <p>The <span class="hlt">stress</span> theorem presented previously by the present authors is derived in detail and is related to the virial and force theorems. <span class="hlt">Stress</span> fields are considered in two alternative forms, both of which give the same macroscopic <span class="hlt">stress</span> and forces on nuclei when integrated over appropriate surfaces. A crucial concept is interactions that ``cross'' surfaces. Explicit forms of the <span class="hlt">stress</span> field within the local-density approximation are given, together with a generalization of the approximate Liberman form for pressure. Reciprocal-space expressions and ab initio calculations are considered in detail in an accompanying paper.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016SIGMA..12..094G','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016SIGMA..12..094G"><span>Invitation to Random <span class="hlt">Tensors</span></span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Gurau, Razvan</p> <p>2016-09-01</p> <p>This article is preface to the SIGMA special issue ''<span class="hlt">Tensor</span> Models, Formalism and Applications'', http://www.emis.de/journals/SIGMA/<span class="hlt">Tensor</span>_Models.html. The issue is a collection of eight excellent, up to date reviews on random <span class="hlt">tensor</span> models. The reviews combine pedagogical introductions meant for a general audience with presentations of the most recent developments in the field. This preface aims to give a condensed panoramic overview of random <span class="hlt">tensors</span> as the natural generalization of random matrices to higher dimensions.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2015ApPhL.107g2106G','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015ApPhL.107g2106G"><span><span class="hlt">Stress</span>-directed compositional patterning of SiGe substrates for lateral <span class="hlt">quantum</span> barrier manipulation</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Ghosh, Swapnadip; Kaiser, Daniel; Bonilla, Jose; Sinno, Talid; Han, Sang M.</p> <p>2015-08-01</p> <p>While vertical stacking of <span class="hlt">quantum</span> well and dot structures is well established in heteroepitaxial semiconductor materials, manipulation of <span class="hlt">quantum</span> barriers in the lateral directions poses a significant engineering challenge. Here, we demonstrate lateral <span class="hlt">quantum</span> barrier manipulation in a crystalline SiGe alloy using structured mechanical fields to drive compositional redistribution. To apply <span class="hlt">stress</span>, we make use of a nano-indenter array that is pressed against a Si0.8Ge0.2 wafer in a custom-made mechanical press. The entire assembly is then annealed at high temperatures, during which the larger Ge atoms are selectively driven away from areas of compressive <span class="hlt">stress</span>. Compositional analysis of the SiGe substrates reveals that this approach leads to a transfer of the indenter array pattern to the near-surface elemental composition, resulting in near 100% Si regions underneath each indenter that are separated from each other by the surrounding Si0.8Ge0.2 bulk. The "<span class="hlt">stress</span> transfer" process is studied in detail using multiscale computer simulations that demonstrate its robustness across a wide range of applied <span class="hlt">stresses</span> and annealing temperatures. While the "Si nanodot" structures formed here are not intrinsically useful as <span class="hlt">quantum</span> structures, it is anticipated that the <span class="hlt">stress</span> transfer process may be modified by judicious control of the SiGe film thickness and indenter array pattern to form more technologically useful structures.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/scitech/biblio/22489112','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/22489112"><span><span class="hlt">Stress</span>-directed compositional patterning of SiGe substrates for lateral <span class="hlt">quantum</span> barrier manipulation</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Ghosh, Swapnadip; Kaiser, Daniel; Sinno, Talid E-mail: meister@unm.edu; Bonilla, Jose; Han, Sang M. E-mail: meister@unm.edu</p> <p>2015-08-17</p> <p>While vertical stacking of <span class="hlt">quantum</span> well and dot structures is well established in heteroepitaxial semiconductor materials, manipulation of <span class="hlt">quantum</span> barriers in the lateral directions poses a significant engineering challenge. Here, we demonstrate lateral <span class="hlt">quantum</span> barrier manipulation in a crystalline SiGe alloy using structured mechanical fields to drive compositional redistribution. To apply <span class="hlt">stress</span>, we make use of a nano-indenter array that is pressed against a Si{sub 0.8}Ge{sub 0.2} wafer in a custom-made mechanical press. The entire assembly is then annealed at high temperatures, during which the larger Ge atoms are selectively driven away from areas of compressive <span class="hlt">stress</span>. Compositional analysis of the SiGe substrates reveals that this approach leads to a transfer of the indenter array pattern to the near-surface elemental composition, resulting in near 100% Si regions underneath each indenter that are separated from each other by the surrounding Si{sub 0.8}Ge{sub 0.2} bulk. The “<span class="hlt">stress</span> transfer” process is studied in detail using multiscale computer simulations that demonstrate its robustness across a wide range of applied <span class="hlt">stresses</span> and annealing temperatures. While the “Si nanodot” structures formed here are not intrinsically useful as <span class="hlt">quantum</span> structures, it is anticipated that the <span class="hlt">stress</span> transfer process may be modified by judicious control of the SiGe film thickness and indenter array pattern to form more technologically useful structures.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/25772261','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/25772261"><span>Cadmium sulfide <span class="hlt">quantum</span> dots induce oxidative <span class="hlt">stress</span> and behavioral impairments in the marine clam Scrobicularia plana.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Buffet, Pierre-Emmanuel; Zalouk-Vergnoux, Aurore; Poirier, Laurence; Lopes, Christelle; Risso-de-Faverney, Christine; Guibbolini, Marielle; Gilliland, Douglas; Perrein-Ettajani, Hanane; Valsami-Jones, Eugenia; Mouneyrac, Catherine</p> <p>2015-07-01</p> <p>Cadmium sulfide (CdS) <span class="hlt">quantum</span> dots have a number of current applications in electronics and solar cells and significant future potential in medicine. The aim of the present study was to examine the toxic effects of CdS <span class="hlt">quantum</span> dots on the marine clam Scrobicularia plana exposed for 14 d to these nanomaterials (10 µg Cd L(-1) ) in natural seawater and to compare them with soluble Cd. Measurement of labile Cd released from CdS <span class="hlt">quantum</span> dots showed that 52% of CdS <span class="hlt">quantum</span> dots remained in the nanoparticulate form. Clams accumulated the same levels of Cd regardless of the form in which it was delivered (soluble Cd vs CdS <span class="hlt">quantum</span> dots). However, significant changes in biochemical responses were observed in clams exposed to CdS <span class="hlt">quantum</span> dots compared with soluble Cd. Increased activities of catalase and glutathione-S-transferase were significantly higher in clams exposed in seawater to Cd as the nanoparticulate versus the soluble form, suggesting a specific nano effect. The behavior of S. plana in sediment showed impairments of foot movements only in the case of exposure to CdS <span class="hlt">quantum</span> dots. The results show that oxidative <span class="hlt">stress</span> and behavior biomarkers are sensitive predictors of CdS <span class="hlt">quantum</span> dots toxicity in S. plana. Such responses, appearing well before changes might occur at the population level, demonstrate the usefulness of this model species and type of biomarker in the assessment of nanoparticle contamination in estuarine ecosystems.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/scitech/biblio/21528549','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/21528549"><span><span class="hlt">Tensor</span> network decompositions in the presence of a global symmetry</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Singh, Sukhwinder; Pfeifer, Robert N. C.; Vidal, Guifre</p> <p>2010-11-15</p> <p><span class="hlt">Tensor</span> network decompositions offer an efficient description of certain many-body states of a lattice system and are the basis of a wealth of numerical simulation algorithms. We discuss how to incorporate a global symmetry, given by a compact, completely reducible group G, in <span class="hlt">tensor</span> network decompositions and algorithms. This is achieved by considering <span class="hlt">tensors</span> that are invariant under the action of the group G. Each symmetric <span class="hlt">tensor</span> decomposes into two types of <span class="hlt">tensors</span>: degeneracy <span class="hlt">tensors</span>, containing all the degrees of freedom, and structural <span class="hlt">tensors</span>, which only depend on the symmetry group. In numerical calculations, the use of symmetric <span class="hlt">tensors</span> ensures the preservation of the symmetry, allows selection of a specific symmetry sector, and significantly reduces computational costs. On the other hand, the resulting <span class="hlt">tensor</span> network can be interpreted as a superposition of exponentially many spin networks. Spin networks are used extensively in loop <span class="hlt">quantum</span> gravity, where they represent states of <span class="hlt">quantum</span> geometry. Our work highlights their importance in the context of <span class="hlt">tensor</span> network algorithms as well, thus setting the stage for cross-fertilization between these two areas of research.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2011CQGra..28x5011J','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2011CQGra..28x5011J"><span>Initial value constraints with <span class="hlt">tensor</span> matter</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Jacobson, Ted</p> <p>2011-12-01</p> <p>In generally covariant metric gravity theories with <span class="hlt">tensor</span> matter fields, the initial value constraint equations, unlike in general relativity, are in general not just the 0μ components of the metric field equation. This happens because higher derivatives can occur in the matter <span class="hlt">stress</span> <span class="hlt">tensor</span>. A universal form for these constraints is derived here from a generalized Bianchi identity that includes matter fields. As an application, the constraints for Einstein-aether theory are found.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2012AGUFM.S51B2409R','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2012AGUFM.S51B2409R"><span>High-Precision Locations and the <span class="hlt">Stress</span> Field from Instrumental Seismicity, Moment <span class="hlt">Tensors</span>, and Short-Period Mechanisms through the Mina Deflection, Central Walker Lane</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Ruhl, C. J.; Smith, K. D.</p> <p>2012-12-01</p> <p>The Mina Deflection (MD) region of the central Walker Lane of eastern California and western Nevada, is a complex zone of northeast-trending normal, and primarily left-lateral strike-slip to oblique-slip faulting that separates the Southern Walker Lane (SWL) from a series of east-tilted normal fault blocks in the Central Walker Lane (CWL) (Faulds and Henry, 2008; Surpless, 2008). The MD accommodates the transfer of right-lateral strike-slip motion from northwest-striking faults in the SWL to a series of left-stepping northwest-striking right-lateral strike-slip faults in the CWL, east of the Wassuk Range near Hawthorne, NV. The ~50 km wide ~80 km long right-step is a distinct transition in regional physiography that has been attributed to strain accommodation through pre-Cenozoic lithospheric structures. Several slip transfer mechanisms have been proposed within the MD, from clockwise rotation of high-angle fault blocks (Wesnousky, 2005), to low-angle displacement within the Silver Peak-Lone Mountain complex (Oldow et al., 2001), and curved fault arrays associated with localized basins and tectonic depressions (Ferranti et al., 2009). The region has been a regular source of M4+ events, the most recent being an extended sequence that included twenty-seven M 3.5+ earthquakes (largest event M 4.6) south of Hawthorne in 2011. These earthquakes (< 5 km depth) define shallow W-dipping (dip ~56°) and NW-dipping (dip ~70°) normal faulting constrained by moment <span class="hlt">tensor</span> (MT) solutions and earthquake relocations. Temporary stations deployed in the source area provide good control. A distributed sequence in 2004, between Queen Valley and Mono Lake, primarily associated with the Huntoon Valley fault, included three M 5+ left-lateral strike-slip faulting events. A 1997 sequence in northern Fish Lake Valley (east of the White Mountains), with mainshock Mw 5.3 (Ichinose et al., 2003), also showed high-angle northeast-striking left-lateral strike-slip motion. Historical events</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19930068626&hterms=second+field&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DTitle%26N%3D0%26No%3D20%26Ntt%3Dsecond%2Bfield','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19930068626&hterms=second+field&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DTitle%26N%3D0%26No%3D20%26Ntt%3Dsecond%2Bfield"><span>Visualization of second order <span class="hlt">tensor</span> fields and matrix data</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Delmarcelle, Thierry; Hesselink, Lambertus</p> <p>1992-01-01</p> <p>We present a study of the visualization of 3-D second order <span class="hlt">tensor</span> fields and matrix data. The general problem of visualizing unsymmetric real or complex Hermitian second order <span class="hlt">tensor</span> fields can be reduced to the simultaneous visualization of a real and symmetric second order <span class="hlt">tensor</span> field and a real vector field. As opposed to the discrete iconic techniques commonly used in multivariate data visualization, the emphasis is on exploiting the mathematical properties of <span class="hlt">tensor</span> fields in order to facilitate their visualization and to produce a continuous representation of the data. We focus on interactively sensing and exploring real and symmetric second order <span class="hlt">tensor</span> data by generalizing the vector notion of streamline to the <span class="hlt">tensor</span> concept of hyperstreamline. We <span class="hlt">stress</span> the importance of a structural analysis of the data field analogous to the techniques of vector field topology extraction in order to obtain a unique and objective representation of second order <span class="hlt">tensor</span> fields.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/scitech/biblio/1178515','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/1178515"><span>A Communication-Optimal Framework for Contracting Distributed <span class="hlt">Tensors</span></span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Rajbhandari, Samyam; NIkam, Akshay; Lai, Pai-Wei; Stock, Kevin; Krishnamoorthy, Sriram; Sadayappan, Ponnuswamy</p> <p>2014-11-16</p> <p><span class="hlt">Tensor</span> contractions are extremely compute intensive generalized matrix multiplication operations encountered in many computational science fields, such as <span class="hlt">quantum</span> chemistry and nuclear physics. Unlike distributed matrix multiplication, which has been extensively studied, limited work has been done in understanding distributed <span class="hlt">tensor</span> contractions. In this paper, we characterize distributed <span class="hlt">tensor</span> contraction algorithms on torus networks. We develop a framework with three fundamental communication operators to generate communication-efficient contraction algorithms for arbitrary <span class="hlt">tensor</span> contractions. We show that for a given amount of memory per processor, our framework is communication optimal for all <span class="hlt">tensor</span> contractions. We demonstrate performance and scalability of our framework on up to 262,144 cores of BG/Q supercomputer using five <span class="hlt">tensor</span> contraction examples.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016PhRvA..93a3855S','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016PhRvA..93a3855S"><span>Kinetic-energy-momentum <span class="hlt">tensor</span> in electrodynamics</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Sheppard, Cheyenne J.; Kemp, Brandon A.</p> <p>2016-01-01</p> <p>We show that the Einstein-Laub formulation of electrodynamics is invalid since it yields a <span class="hlt">stress</span>-energy-momentum (SEM) <span class="hlt">tensor</span> that is not frame invariant. Two leading hypotheses for the kinetic formulation of electrodynamics (Chu and Einstein-Laub) are studied by use of the relativistic principle of virtual power, mathematical modeling, Lagrangian methods, and SEM transformations. The relativistic principle of virtual power is used to demonstrate the field dynamics associated with energy relations within a relativistic framework. Lorentz transformations of the respective SEM <span class="hlt">tensors</span> demonstrate the relativistic frameworks for each studied formulation. Mathematical modeling of stationary and moving media is used to illustrate the differences and discrepancies of specific proposed kinetic formulations, where energy relations and conservation theorems are employed. Lagrangian methods are utilized to derive the field kinetic Maxwell's equations, which are studied with respect to SEM <span class="hlt">tensor</span> transforms. Within each analysis, the Einstein-Laub formulation violates special relativity, which invalidates the Einstein-Laub SEM <span class="hlt">tensor</span>.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/scitech/biblio/6835444','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/6835444"><span>Comments on conformal Killing vector fields and <span class="hlt">quantum</span> field theory</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Brown, M.R.; Ottewill, A.C.; Siklos, S.T.C.</p> <p>1982-10-15</p> <p>We give a comprehensive analysis of those vacuums for flat and conformally flat space-times which can be defined by timelike, hypersurface-orthogonal, conformal Killing vector fields. We obtain formulas for the difference in <span class="hlt">stress</span>-energy density between any two such states and display the correspondence with the renormalized <span class="hlt">stress</span> <span class="hlt">tensors</span>. A brief discussion is given of the relevance of these results to <span class="hlt">quantum</span>-mechanical measurements made by noninertial observers moving through flat space.</p> </li> </ol> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_5");'>5</a></li> <li><a href="#" onclick='return showDiv("page_6");'>6</a></li> <li class="active"><span>7</span></li> <li><a href="#" onclick='return showDiv("page_8");'>8</a></li> <li><a href="#" onclick='return showDiv("page_9");'>9</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div><!-- col-sm-12 --> </div><!-- row --> </div><!-- page_7 --> <div id="page_8" class="hiddenDiv"> <div class="row"> <div class="col-sm-12"> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_6");'>6</a></li> <li><a href="#" onclick='return showDiv("page_7");'>7</a></li> <li class="active"><span>8</span></li> <li><a href="#" onclick='return showDiv("page_9");'>9</a></li> <li><a href="#" onclick='return showDiv("page_10");'>10</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div> </div> <div class="row"> <div class="col-sm-12"> <ol class="result-class" start="141"> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017SCPMA..6026811W','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017SCPMA..6026811W"><span>Pulse laser induced graphite-to-diamond phase transition: the role of <span class="hlt">quantum</span> electronic <span class="hlt">stress</span></span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Wang, ZhengFei; Liu, Feng</p> <p>2017-02-01</p> <p>First-principles calculations show that the pulse laser induced graphite-to-diamond phase transition is related to the lattice <span class="hlt">stress</span> generated by the excited carriers, termed as "<span class="hlt">quantum</span> electronic <span class="hlt">stress</span> (QES)". We found that the excited carriers in graphite generate a large anisotropic QES that increases linearly with the increasing carrier density. Using the QES as a guiding parameter, structural relaxation spontaneously transforms the graphite phase into the diamond phase, as the QES is reduced and minimized. Our results suggest that the concept of QES can be generally applied as a good measure to characterize the pulse laser induced phase transitions, in analogy to pressure induced phase transitions.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016PhLB..760..244C','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016PhLB..760..244C"><span><span class="hlt">Quantum</span> dress for a naked singularity</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Casals, Marc; Fabbri, Alessandro; Martínez, Cristián; Zanelli, Jorge</p> <p>2016-09-01</p> <p>We investigate semiclassical backreaction on a conical naked singularity space-time with a negative cosmological constant in (2 + 1)-dimensions. In particular, we calculate the renormalized <span class="hlt">quantum</span> <span class="hlt">stress</span>-energy <span class="hlt">tensor</span> for a conformally coupled scalar field on such naked singularity space-time. We then obtain the backreacted metric via the semiclassical Einstein equations. We show that, in the regime where the semiclassical approximation can be trusted, backreaction dresses the naked singularity with an event horizon, thus enforcing (weak) cosmic censorship.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/1992PhRvD..46.4421B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/1992PhRvD..46.4421B"><span><span class="hlt">Quantum</span> field theory in spaces with closed timelike curves</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Boulware, David G.</p> <p>1992-11-01</p> <p>Gott spacetime has closed timelike curves, but no locally anomalous <span class="hlt">stress</span> energy. A complete orthonormal set of eigenfunctions of the wave operator is found in the special case of a spacetime in which the total deficit angle is 2π. A scalar <span class="hlt">quantum</span> field theory is constructed using these eigenfunctions. The resultant interacting <span class="hlt">quantum</span> field theory is not unitary because the field operators can create real, on-shell, particles in the noncausal region. These particles propagate for finite proper time accumulating an arbitrary phase before being annihilated at the same spacetime point as that at which they were created. As a result, the effective potential within the noncausal region is complex, and probability is not conserved. The <span class="hlt">stress</span> <span class="hlt">tensor</span> of the scalar field is evaluated in the neighborhood of the Cauchy horizon; in the case of a sufficiently small Compton wavelength of the field, the <span class="hlt">stress</span> <span class="hlt">tensor</span> is regular and cannot prevent the formation of the Cauchy horizon.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/scitech/biblio/22479609','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/22479609"><span>Positivity of linear maps under <span class="hlt">tensor</span> powers</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Müller-Hermes, Alexander Wolf, Michael M.; Reeb, David</p> <p>2016-01-15</p> <p>We investigate linear maps between matrix algebras that remain positive under <span class="hlt">tensor</span> powers, i.e., under <span class="hlt">tensoring</span> with n copies of themselves. Completely positive and completely co-positive maps are trivial examples of this kind. We show that for every n ∈ ℕ, there exist non-trivial maps with this property and that for two-dimensional Hilbert spaces there is no non-trivial map for which this holds for all n. For higher dimensions, we reduce the existence question of such non-trivial “<span class="hlt">tensor</span>-stable positive maps” to a one-parameter family of maps and show that an affirmative answer would imply the existence of non-positive partial transpose bound entanglement. As an application, we show that any <span class="hlt">tensor</span>-stable positive map that is not completely positive yields an upper bound on the <span class="hlt">quantum</span> channel capacity, which for the transposition map gives the well-known cb-norm bound. We, furthermore, show that the latter is an upper bound even for the local operations and classical communications-assisted <span class="hlt">quantum</span> capacity, and that moreover it is a strong converse rate for this task.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2015JPhCS.640a2040K','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015JPhCS.640a2040K"><span>Uni10: an open-source library for <span class="hlt">tensor</span> network algorithms</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Kao, Ying-Jer; Hsieh, Yun-Da; Chen, Pochung</p> <p>2015-09-01</p> <p>We present an object-oriented open-source library for developing <span class="hlt">tensor</span> network algorithms written in C++ called Uni10. With Uni10, users can build a symmetric <span class="hlt">tensor</span> from a collection of bonds, while the bonds are constructed from a list of <span class="hlt">quantum</span> numbers associated with different <span class="hlt">quantum</span> states. It is easy to label and permute the indices of the <span class="hlt">tensors</span> and access a block associated with a particular <span class="hlt">quantum</span> number. Furthermore a network class is used to describe arbitrary <span class="hlt">tensor</span> network structure and to perform network contractions efficiently. We give an overview of the basic structure of the library and the hierarchy of the classes. We present examples of the construction of a spin-1 Heisenberg Hamiltonian and the implementation of the <span class="hlt">tensor</span> renormalization group algorithm to illustrate the basic usage of the library. The library described here is particularly well suited to explore and fast prototype novel <span class="hlt">tensor</span> network algorithms and to implement highly efficient codes for existing algorithms.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/25844072','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/25844072"><span>Tree <span class="hlt">Tensor</span> Network State with Variable <span class="hlt">Tensor</span> Order: An Efficient Multireference Method for Strongly Correlated Systems.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Murg, V; Verstraete, F; Schneider, R; Nagy, P R; Legeza, Ö</p> <p>2015-03-10</p> <p>We study the tree-<span class="hlt">tensor</span>-network-state (TTNS) method with variable <span class="hlt">tensor</span> orders for <span class="hlt">quantum</span> chemistry. TTNS is a variational method to efficiently approximate complete active space (CAS) configuration interaction (CI) wave functions in a <span class="hlt">tensor</span> product form. TTNS can be considered as a higher order generalization of the matrix product state (MPS) method. The MPS wave function is formulated as products of matrices in a multiparticle basis spanning a truncated Hilbert space of the original CAS-CI problem. These matrices belong to active orbitals organized in a one-dimensional array, while <span class="hlt">tensors</span> in TTNS are defined upon a tree-like arrangement of the same orbitals. The tree-structure is advantageous since the distance between two arbitrary orbitals in the tree scales only logarithmically with the number of orbitals N, whereas the scaling is linear in the MPS array. It is found to be beneficial from the computational costs point of view to keep strongly correlated orbitals in close vicinity in both arrangements; therefore, the TTNS ansatz is better suited for multireference problems with numerous highly correlated orbitals. To exploit the advantages of TTNS a novel algorithm is designed to optimize the tree <span class="hlt">tensor</span> network topology based on <span class="hlt">quantum</span> information theory and entanglement. The superior performance of the TTNS method is illustrated on the ionic-neutral avoided crossing of LiF. It is also shown that the avoided crossing of LiF can be localized using only ground state properties, namely one-orbital entanglement.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2010RpMP...65...29S','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2010RpMP...65...29S"><span>Schrödinger and related equations as hamiltonian systems, manifolds of second-order <span class="hlt">tensors</span> and new ideas of nonlinearity in <span class="hlt">quantum</span> mechanics</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Sławianowski, J. J.; Kovalchuk, V.</p> <p>2010-01-01</p> <p>Considered is the Schrödinger equation in a finite-dimensional space as an equation of mathematical physics derivable from the variational principle and treatable in terms of the Lagrange-Hamilton formalism. It provides an interesting example of "mechanics" with singular Lagrangians, effectively treatable within the framework of Dirac formalism. We discuss also some modified "Schrödinger" equations involving second-order time derivatives and introduce a kind of nondirect, nonperturbative, geometrically-motivated nonlinearity based on making the scalar product a dynamical quantity. There are some reasons to expect that this might be a new way of describing open dynamical systems and explaining some <span class="hlt">quantum</span> "paradoxes".</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017JMPSo..99...93A','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017JMPSo..99...93A"><span>The atomistic representation of first strain-gradient elastic <span class="hlt">tensors</span></span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Admal, Nikhil Chandra; Marian, Jaime; Po, Giacomo</p> <p>2017-02-01</p> <p>We derive the atomistic representations of the elastic <span class="hlt">tensors</span> appearing in the linearized theory of first strain-gradient elasticity for an arbitrary multi-lattice. In addition to the classical second-Piola) <span class="hlt">stress</span> and elastic moduli <span class="hlt">tensors</span>, these include the rank-three double-<span class="hlt">stress</span> <span class="hlt">tensor</span>, the rank-five <span class="hlt">tensor</span> of mixed elastic moduli, and the rank-six <span class="hlt">tensor</span> of strain-gradient elastic moduli. The atomistic representations are closed-form analytical expressions in terms of the first and second derivatives of the interatomic potential with respect to interatomic distances, and dyadic products of relative atomic positions. Moreover, all expressions are local, in the sense that they depend only on the atomic neighborhood of a lattice site. Our results emanate from the condition of energetic equivalence between continuum and atomistic representations of a crystal, when the kinematics of the latter is governed by the Cauchy-Born rule. Using the derived expressions, we prove that the odd-order <span class="hlt">tensors</span> vanish if the lattice basis admits central-symmetry. The analytical expressions are implemented as a KIM compliant algorithm to compute the strain gradient elastic <span class="hlt">tensors</span> for various materials. Numerical results are presented to compare representative interatomic potentials used in the literature for cubic crystals, including simple lattices (fcc Al and Cu and bcc Fe and W) and multi-lattices (diamond-cubic Si). We observe that central potentials exhibit generalized Cauchy relations for the rank-six <span class="hlt">tensor</span> of strain-gradient elastic moduli. In addition, this <span class="hlt">tensor</span> is found to be indefinite for many potentials. We discuss the relationship between indefiniteness and material stability. Finally, the atomistic representations are specialized to central potentials in simple lattices. These expressions are used with analytical potentials to study the sensitivity of the elastic <span class="hlt">tensors</span> to the choice of the cutoff radius.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016PCE....95....2S','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016PCE....95....2S"><span>A ten year Moment <span class="hlt">Tensor</span> database for Western Greece</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Serpetsidaki, Anna; Sokos, Efthimios; Tselentis, G.-Akis</p> <p>2016-10-01</p> <p>Moment <span class="hlt">Tensors</span> (MTs) provide important information for seismotectonic, <span class="hlt">stress</span> distribution and source studies. It is also important as a real time or near real time information in shakemaps, tsunami warning, and <span class="hlt">stress</span> transfer. Therefore a reliable and rapid MT computation is a routine task for modern seismic networks with broadband sensors and real-time digital telemetry. In this paper we present the database of Moment <span class="hlt">Tensor</span> solutions computed during the last ten years in Western Greece by the University of Patras, Seismological Laboratory (UPSL). The data from UPSL broad band network were used together with the ISOLA Moment <span class="hlt">Tensor</span> inversion package for routine MT calculation. The procedures followed and the comparison of UPSL derived solutions with the ones provided by other agencies for Western Greece region are presented as well. The Moment <span class="hlt">Tensor</span> database includes solutions for events in the magnitude range 2.8-6.8 and provides a unique insight into the faulting characteristics of Western Greece. Moreover it paves the way for detailed studies of <span class="hlt">stress</span> <span class="hlt">tensor</span> and <span class="hlt">stress</span> transfer. The weak events' Moment <span class="hlt">Tensor</span> included in UPSL's database are important for the comprehension of local seismotectonics and reveal the role of minor faults, which may be critical in seismic hazard estimation.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/scitech/biblio/1311348','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/1311348"><span><span class="hlt">Quantum</span> Efficiency Loss after PID <span class="hlt">Stress</span>: Wavelength Dependence on Cell Surface and Cell Edge</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Oh, Jaewon; Bowden, Stuart; TamizhMani, GovindaSamy; Hacke, Peter</p> <p>2015-06-14</p> <p>It is known that the potential induced degradation (PID) <span class="hlt">stress</span> of conventional p-base solar cells affects power, shunt resistance, junction recombination, and <span class="hlt">quantum</span> efficiency (QE). One of the primary solutions to address the PID issue is a modification of chemical and physical properties of antireflection coating (ARC) on the cell surface. Depending on the edge isolation method used during cell processing, the ARC layer near the edges may be uniformly or non-uniformly damaged. Therefore, the pathway for sodium migration from glass to the cell junction could be either through all of the ARC surface if surface and edge ARC have low quality or through the cell edge if surface ARC has high quality but edge ARC is defective due to certain edge isolation process. In this study, two PID susceptible cells from two different manufacturers have been investigated. The QE measurements of these cells before and after PID <span class="hlt">stress</span> were performed at both surface and edge. We observed the wavelength dependent QE loss only in the first manufacturer's cell but not in the second manufacturer's cell. The first manufacturer's cell appeared to have low quality ARC whereas the second manufacturer's cell appeared to have high quality ARC with defective edge. To rapidly screen a large number of cells for PID <span class="hlt">stress</span> testing, a new but simple test setup that does not require laminated cell coupon has been developed and is used in this investigation.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/26079203','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/26079203"><span>Complex responses to Si <span class="hlt">quantum</span> dots accumulation in carp liver tissue: Beyond oxidative <span class="hlt">stress</span>.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Serban, Andreea Iren; Stanca, Loredana; Sima, Cornelia; Staicu, Andrea Cristina; Zarnescu, Otilia; Dinischiotu, Anca</p> <p>2015-09-05</p> <p>The use of <span class="hlt">quantum</span> dots (QDs) in biomedical applications is limited due to their inherent toxicity caused by the heavy metal core of the particles. Consequently, silicon-based QDs are expected to display diminished toxicity. We investigated the in vivo effects induced by Si/SiO2 QDs intraperitoneally injected in crucian carp liver. The QDs contained a crystalline Si core encased in a SiO2 shell, with a size between 2.75 and 11.25nm and possess intrinsic fluorescence (Ex 325nm/Em ∼690nm). Tissue fluorescence microscopy analysis revealed the presence of QDs in the liver for at least 2weeks after injection. Although protein and lipid oxidative <span class="hlt">stress</span> markers showed the onset of oxidative <span class="hlt">stress</span>, the hepatic tissue exhibited significant antioxidant adaptations (increase of antioxidant enzymes, recovery of glutathione levels), sustained by the activation of Hsp30 and Hsp70 chaperoning proteins. The increased activity of cyclooxigenase-2 (COX-2) and matrix metalloproteinases (MMPs) support the idea that Si/SiO2 QDs have a potential to induce inflammatory response, a scenario also indicated by the profile of Hsp60 and Hsp90 heat shock proteins. MMPs profile and the recovery of oxidative <span class="hlt">stress</span> markers suggested a tissue remodelation phase after 3weeks from QDs administration.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/scitech/biblio/22403071','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/22403071"><span>Conformal killing <span class="hlt">tensors</span> and covariant Hamiltonian dynamics</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Cariglia, M.; Gibbons, G. W.; Holten, J.-W. van; Horvathy, P. A.; Zhang, P.-M.</p> <p>2014-12-15</p> <p>A covariant algorithm for deriving the conserved quantities for natural Hamiltonian systems is combined with the non-relativistic framework of Eisenhart, and of Duval, in which the classical trajectories arise as geodesics in a higher dimensional space-time, realized by Brinkmann manifolds. Conserved quantities which are polynomial in the momenta can be built using time-dependent conformal Killing <span class="hlt">tensors</span> with flux. The latter are associated with terms proportional to the Hamiltonian in the lower dimensional theory and with spectrum generating algebras for higher dimensional quantities of order 1 and 2 in the momenta. Illustrations of the general theory include the Runge-Lenz vector for planetary motion with a time-dependent gravitational constant G(t), motion in a time-dependent electromagnetic field of a certain form, <span class="hlt">quantum</span> dots, the Hénon-Heiles and Holt systems, respectively, providing us with Killing <span class="hlt">tensors</span> of rank that ranges from one to six.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2013JHEP...04..054W','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2013JHEP...04..054W"><span><span class="hlt">Tensor</span> modes on the string theory landscape</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Westphal, Alexander</p> <p>2013-04-01</p> <p>We attempt an estimate for the distribution of the <span class="hlt">tensor</span> mode fraction r over the landscape of vacua in string theory. The dynamics of eternal inflation and <span class="hlt">quantum</span> tunneling lead to a kind of democracy on the landscape, providing no bias towards large-field or small-field inflation regardless of the class of measure. The <span class="hlt">tensor</span> mode fraction then follows the number frequency distributions of inflationary mechanisms of string theory over the landscape. We show that an estimate of the relative number frequencies for small-field vs large-field inflation, while unattainable on the whole landscape, may be within reach as a regional answer for warped Calabi-Yau flux compactifications of type IIB string theory.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016PhRvL.117u0402K','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016PhRvL.117u0402K"><span>Fermionic Orbital Optimization in <span class="hlt">Tensor</span> Network States</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Krumnow, C.; Veis, L.; Legeza, Ö.; Eisert, J.</p> <p>2016-11-01</p> <p><span class="hlt">Tensor</span> network states and specifically matrix-product states have proven to be a powerful tool for simulating ground states of strongly correlated spin models. Recently, they have also been applied to interacting fermionic problems, specifically in the context of <span class="hlt">quantum</span> chemistry. A new freedom arising in such nonlocal fermionic systems is the choice of orbitals, it being far from clear what choice of fermionic orbitals to make. In this Letter, we propose a way to overcome this challenge. We suggest a method intertwining the optimization over matrix product states with suitable fermionic Gaussian mode transformations. The described algorithm generalizes basis changes in the spirit of the Hartree-Fock method to matrix-product states, and provides a black box tool for basis optimization in <span class="hlt">tensor</span> network methods.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=4078720','PMC'); return false;" href="https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=4078720"><span>Diffusion <span class="hlt">Tensor</span> Image Registration Using Hybrid Connectivity and <span class="hlt">Tensor</span> Features</span></a></p> <p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pmc">PubMed Central</a></p> <p>Wang, Qian; Yap, Pew-Thian; Wu, Guorong; Shen, Dinggang</p> <p>2014-01-01</p> <p>Most existing diffusion <span class="hlt">tensor</span> imaging (DTI) registration methods estimate structural correspondences based on voxelwise matching of <span class="hlt">tensors</span>. The rich connectivity information that is given by DTI, however, is often neglected. In this article, we propose to integrate complementary information given by connectivity features and <span class="hlt">tensor</span> features for improved registration accuracy. To utilize connectivity information, we place multiple anchors representing different brain anatomies in the image space, and define the connectivity features for each voxel as the geodesic distances from all anchors to the voxel under consideration. The geodesic distance, which is computed in relation to the <span class="hlt">tensor</span> field, encapsulates information of brain connectivity. We also extract <span class="hlt">tensor</span> features for every voxel to reflect the local statistics of <span class="hlt">tensors</span> in its neighborhood. We then combine both connectivity features and <span class="hlt">tensor</span> features for registration of <span class="hlt">tensor</span> images. From the images, landmarks are selected automatically and their correspondences are determined based on their connectivity and <span class="hlt">tensor</span> feature vectors. The deformation field that deforms one <span class="hlt">tensor</span> image to the other is iteratively estimated and optimized according to the landmarks and their associated correspondences. Experimental results show that, by using connectivity features and <span class="hlt">tensor</span> features simultaneously, registration accuracy is increased substantially compared with the cases using either type of features alone. PMID:24293159</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/1992qfts.rept.....B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/1992qfts.rept.....B"><span><span class="hlt">Quantum</span> field theory in spaces with closed time-like curves</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Boulware, D. G.</p> <p></p> <p>Gott spacetime has closed timelike curves, but no locally anomalous <span class="hlt">stress</span>-energy. A complete orthonormal set of eigenfunctions of the wave operator is found in the special case of a spacetime in which the total deficit angle is 27(pi). A scalar <span class="hlt">quantum</span> field theory is constructed using these eigenfunctions. The resultant interacting <span class="hlt">quantum</span> field theory is not unitary because the field operators can create real, on-shell, particles in the acausal region. These particles propagate for finite proper time accumulating an arbitrary phase before being annihilated at the same spacetime point as that at which they were created. As a result, the effective potential within the acausal region is complex, and probability is not conserved. The <span class="hlt">stress</span> <span class="hlt">tensor</span> of the scalar field is evaluated in the neighborhood of the Cauchy horizon; in the case of a sufficiently small Compton wavelength of the field, the <span class="hlt">stress</span> <span class="hlt">tensor</span> is regular and cannot prevent the formation of the Cauchy horizon.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19820039510&hterms=gradiometer&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D40%26Ntt%3Dgradiometer','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19820039510&hterms=gradiometer&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D40%26Ntt%3Dgradiometer"><span>Superconducting <span class="hlt">tensor</span> gravity gradiometer</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Paik, H. J.</p> <p>1981-01-01</p> <p>The employment of superconductivity and other material properties at cryogenic temperatures to fabricate sensitive, low-drift, gravity gradiometer is described. The device yields a reduction of noise of four orders of magnitude over room temperature gradiometers, and direct summation and subtraction of signals from accelerometers in varying orientations are possible with superconducting circuitry. Additional circuits permit determination of the linear and angular acceleration vectors independent of the measurement of the gravity gradient <span class="hlt">tensor</span>. A dewar flask capable of maintaining helium in a liquid state for a year's duration is under development by NASA, and a superconducting <span class="hlt">tensor</span> gravity gradiometer for the NASA Geodynamics Program is intended for a LEO polar trajectory to measure the harmonic expansion coefficients of the earth's gravity field up to order 300.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016APS..MARC44011D','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016APS..MARC44011D"><span><span class="hlt">Tensor</span> network characterization of superconducting circuits</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Duclos-Cianci, Guillaume; Poulin, David; Najafi-Yazdi, Alireza</p> <p></p> <p>Superconducting circuits are promising candidates in the development of reliable <span class="hlt">quantum</span> computing devices. In principle, one can obtain the Hamiltonian of a generic superconducting circuit and solve for its eigenvalues to obtain its energy spectrum. In practice, however, the computational cost of calculating eigenvalues of a complex device with many degrees of freedom can become prohibitively expensive. In the present work, we investigate the application of <span class="hlt">tensor</span> network algorithms to enable efficient and accurate characterization of superconducting circuits comprised of many components. Suitable validation test cases are performed to study the accuracy, computational efficiency and limitations of the proposed approach.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017CoPhC.213..130D','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017CoPhC.213..130D"><span>E6<span class="hlt">Tensors</span>: A Mathematica package for E6 <span class="hlt">Tensors</span></span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Deppisch, Thomas</p> <p>2017-04-01</p> <p>We present the Mathematica package E6<span class="hlt">Tensors</span>, a tool for explicit <span class="hlt">tensor</span> calculations in E6 gauge theories. In addition to matrix expressions for the group generators of E6, it provides structure constants, various higher rank <span class="hlt">tensors</span> and expressions for the representations 27, 78, 351 and 351‧. This paper comes along with a short manual including physically relevant examples. I further give a complete list of gauge invariant, renormalisable terms for superpotentials and Lagrangians.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016JAESc.127..231N','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016JAESc.127..231N"><span>The regional moment <span class="hlt">tensor</span> of the 5 May 2014 Chiang Rai earthquake (Mw = 6.5), Northern Thailand, with its aftershocks and its implication to the <span class="hlt">stress</span> and the instability of the Phayao Fault Zone</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Noisagool, Sutthipong; Boonchaisuk, Songkhun; Pornsopin, Patinya; Siripunvaraporn, Weerachai</p> <p>2016-09-01</p> <p>On 5 May 2014, the largest earthquake in Thailand modern history occurred in Northern Thailand with over a thousand aftershocks. Most of the epicenters are located within the transition area of the Mae Lao segment (north) and Pan segment (central) of the Phayao Fault Zone (PFZ). Good quality data from all events (ML > 4) are only available for the seismic stations closer to the epicenters (<500 km). The regional moment <span class="hlt">tensor</span> (RMT) inversion was applied to derive a sequence of thirty focal mechanisms, moment magnitudes and source depths generated along the PFZ. Our studies reveal that 24 events are strike - slip with normal (transtensional), four are strike - slip with thrust (transpressional), and two are reverse. The main shock has an Mw of 6.5, slightly larger than previously estimated (ML 6.3) while Mw of the aftershocks is mostly lower than ML. This suggests that a regional magnitude calibration is necessary. The hypocenter depths of most events are around 11 km, not as shallow as estimated earlier. In addition, a <span class="hlt">stress</span> inversion was applied to these 30 focal mechanisms to determine the <span class="hlt">stresses</span> of the region, the Mohr's diagram, and the principal fault planes. The retrieved maximum <span class="hlt">stress</span> direction (N18E) is in agreement with other studies. One of the derived principal fault plane with a strike of N48E is in good agreement with that of the Mae Lao segment. Both estimated shape ratio and plunges led us to conclude that this area has a uniaxial horizontal compression in NNE-SSW with small WNW-ESE extension, similar to the interpretation of Tingay et al. (2010). Based on the Mohr's diagram of fault plane solutions, we provide geophysical evidence which reveals that the high shear <span class="hlt">stress</span> Mae Lao segment is likely to slip first producing the main shock on 5 May 2014. The energy transfer between the segments has then led to many aftershocks with mixed mechanisms. At the end, we re-visited the analysis of the former largest earthquake in Northern Thailand in the</p> </li> </ol> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_6");'>6</a></li> <li><a href="#" onclick='return showDiv("page_7");'>7</a></li> <li class="active"><span>8</span></li> <li><a href="#" onclick='return showDiv("page_9");'>9</a></li> <li><a href="#" onclick='return showDiv("page_10");'>10</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div><!-- col-sm-12 --> </div><!-- row --> </div><!-- page_8 --> <div id="page_9" class="hiddenDiv"> <div class="row"> <div class="col-sm-12"> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_7");'>7</a></li> <li><a href="#" onclick='return showDiv("page_8");'>8</a></li> <li class="active"><span>9</span></li> <li><a href="#" onclick='return showDiv("page_10");'>10</a></li> <li><a href="#" onclick='return showDiv("page_11");'>11</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div> </div> <div class="row"> <div class="col-sm-12"> <ol class="result-class" start="161"> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2006AGUFMIN31A1320C','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2006AGUFMIN31A1320C"><span>Visualization of Time-Varying Strain Green <span class="hlt">Tensors</span></span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Callaghan, S. A.; Maechling, P.</p> <p>2006-12-01</p> <p>Geophysical <span class="hlt">tensor</span> data calculated by earthquake wave propagation simulation codes is used to investigate <span class="hlt">stresses</span> and strains near the earth's surface. To assist scientists with the interpretation of <span class="hlt">tensor</span> data sets, we have developed distributed processing and visualization techniques for visualizing time-varying, volumetric <span class="hlt">tensor</span> data. We have applied our techniques to strain Green <span class="hlt">tensor</span> data calculated for the SCEC/CME CyberShake project in order to explore basin effects in Southern California. One step in the CyberShake project workflow is to generate strain Green <span class="hlt">tensors</span> for a volume to allow physics-based seismic hazard analysis. These volumes are typically 400 x 400 x 40 km with grid points every 200 m, with 1800 timesteps, yielding multiple terabytes of <span class="hlt">tensor</span> data in many small files. To graphically display the six-component <span class="hlt">tensors</span>, we use ellipsoids with the major axes aligned with the three eigenvectors, scaled according to the normalized eigenvalues, and colored based on the magnitude of the eigenvalues. This allows for visualization of the <span class="hlt">tensor</span> magnitudes, which span a range of over 105, while keeping the ellipsoids a constant size. This software was implemented using the Mesa implementation of OpenGL using the C language. In order to allow interactive visualization of the data, rendering is performed on a parallel computational cluster and real- time images are sent to the user via network sockets. To enable meaningful investigation of the data, a scale for the ellipsoid colors is included. Additionally, a georeferenced surface image is added to provide a point of reference for the user and allow analysis of <span class="hlt">tensor</span> behavior with other georeferenced data, enabling validation of the CyberShake software and examination of varying ground motions due to basin effects.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017CQGra..34d5002F','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017CQGra..34d5002F"><span>Labeling spherically symmetric spacetimes with the Ricci <span class="hlt">tensor</span></span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Ferrando, Joan Josep; Sáez, Juan Antonio</p> <p>2017-02-01</p> <p>We complete the intrinsic characterization of spherically symmetric solutions partially accomplished in a previous paper (Ferrando and Sáez 2010 Class. <span class="hlt">Quantum</span> Grav. 27 205024). In this approach we consider every compatible algebraic type of the Ricci <span class="hlt">tensor</span>, and we analyze specifically the conformally flat case for perfect fluid and Einstein–Maxwell solutions. As a direct application we obtain the ideal labeling (exclusively involving explicit concomitants of the metric <span class="hlt">tensor</span>) of the Schwarzschild interior metric and the Vaidya solution. The Stephani universes and some significative subfamilies are also characterized.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/scitech/biblio/21448534','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/21448534"><span>Competition between the <span class="hlt">tensor</span> light shift and nonlinear Zeeman effect</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Chalupczak, W.; Wojciechowski, A.; Pustelny, S.; Gawlik, W.</p> <p>2010-08-15</p> <p>Many precision measurements (e.g., in spectroscopy, atomic clocks, <span class="hlt">quantum</span>-information processing, etc.) suffer from systematic errors introduced by the light shift. In our experimental configuration, however, the <span class="hlt">tensor</span> light shift plays a positive role enabling the observation of spectral features otherwise masked by the cancellation of the transition amplitudes and creating resonances at a frequency unperturbed either by laser power or beam inhomogeneity. These phenomena occur thanks to the special relation between the nonlinear Zeeman and light shift effects. The interplay between these two perturbations is systematically studied and the cancellation of the nonlinear Zeeman effect by the <span class="hlt">tensor</span> light shift is demonstrated.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2012AIPC.1424..176K','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2012AIPC.1424..176K"><span>Extended <span class="hlt">tensor</span> products and generalization of the notion of entanglement</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Khrennikov, Andrei; Rosinger, Elemer E.</p> <p>2012-03-01</p> <p>Motivated by the novel applications of the mathematical formalism of <span class="hlt">quantum</span> theory and its generalizations in cognitive science, psychology, social and political sciences, and economics, we extend the notion of the <span class="hlt">tensor</span> product and entanglement. We also study the relation between conventional entanglement of complex qubits and our generalized entanglement. Our construction can also be used to describe entanglement in the framework of non-Archimedean physics. It is also possible to construct <span class="hlt">tensor</span> products of non-Archimedean (e.g., p-adic) and complex Hilbert spaces.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/24074963','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/24074963"><span>Reduced white matter integrity in the cingulum and anterior corona radiata in posttraumatic <span class="hlt">stress</span> disorder in male combat veterans: a diffusion <span class="hlt">tensor</span> imaging study.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Sanjuan, Pilar Margaret; Thoma, Robert; Claus, Eric Daniel; Mays, Nicci; Caprihan, Arvind</p> <p>2013-12-30</p> <p>Posttraumatic <span class="hlt">stress</span> (PTSD) and alcohol use (AUD) disorders are associated with abnormal anterior cingulate cortex/ventromedial prefrontal cortex, thalamus, and amygdala function, yet microstructural white matter (WM) differences in executive-limbic tracts are likely also involved. Investigating WM in limbic-thalamo-cortical tracts, this study hypothesized (1) fractional anisotropy (FA) in dorsal cingulum, parahippocampal cingulum, and anterior corona radiata (ACR) would be lower in individuals with comorbid PTSD/AUD compared to in individuals with AUD-only and (2) that FA would be related to both AUD and PTSD severity. 22 combat veterans with comorbid PTSD/AUD or AUD-only completed DTI scans. ANCOVAs indicated lower FA in right (F(df=1,19)=9.091, P=0.0071) and left (F(df=1,19)=10.375, P=0.0045) dorsal cingulum and right ACR (F(df=1,19)=18.914, P=0.0003) for individuals with comorbid PTSD/AUD vs. individuals with AUD-only, even controlling for alcohol use. Multiple linear regressions revealed that FA in the right ACR was inversely related to PTSD severity (r=-0.683, P=0.004). FA was not significantly related to alcohol severity. Reduced WM integrity in limbic-thalamo-cortical tracts is implicated in PTSD, even in the presence of comorbid AUD. These findings suggest that diminished WM integrity in tracts important for top-down control may be an important anomaly in PTSD and/or comorbid PTSD/AUD.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2013PhRvD..87d7702F','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2013PhRvD..87d7702F"><span>Torque anomaly in <span class="hlt">quantum</span> field theory</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Fulling, S. A.; Mera, F. D.; Trendafilova, C. S.</p> <p>2013-02-01</p> <p>The expectation values of energy density and pressure of a <span class="hlt">quantum</span> field inside a wedge-shaped region appear to violate the expected relationship between torque and total energy as a function of angle. In particular, this is true of the well-known Deutsch-Candelas <span class="hlt">stress</span> <span class="hlt">tensor</span> for the electromagnetic field, whose definition requires no regularization except possibly at the vertex. Unlike a similar anomaly in the pressure exerted by a reflecting boundary against a perpendicular wall, this problem cannot be dismissed as an artifact of an ad hoc regularization.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/scitech/biblio/22479541','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/22479541"><span><span class="hlt">Quantum</span> reverse hypercontractivity</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Cubitt, Toby; Kastoryano, Michael; Montanaro, Ashley; Temme, Kristan</p> <p>2015-10-15</p> <p>We develop reverse versions of hypercontractive inequalities for <span class="hlt">quantum</span> channels. By generalizing classical techniques, we prove a reverse hypercontractive inequality for <span class="hlt">tensor</span> products of qubit depolarizing channels. We apply this to obtain a rapid mixing result for depolarizing noise applied to large subspaces and to prove bounds on a <span class="hlt">quantum</span> generalization of non-interactive correlation distillation.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2009PhRvB..80o5131G','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2009PhRvB..80o5131G"><span><span class="hlt">Tensor</span>-entanglement-filtering renormalization approach and symmetry-protected topological order</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Gu, Zheng-Cheng; Wen, Xiao-Gang</p> <p>2009-10-01</p> <p>We study the renormalization group flow of the Lagrangian for statistical and <span class="hlt">quantum</span> systems by representing their path integral in terms of a <span class="hlt">tensor</span> network. Using a <span class="hlt">tensor</span>-entanglement-filtering renormalization approach that removes local entanglement and produces a coarse-grained lattice, we show that the resulting renormalization flow of the <span class="hlt">tensors</span> in the <span class="hlt">tensor</span> network has a nice fixed-point structure. The isolated fixed-point <span class="hlt">tensors</span> Tinv plus the symmetry group Gsym of the <span class="hlt">tensors</span> (i.e., the symmetry group of the Lagrangian) characterize various phases of the system. Such a characterization can describe both the symmetry breaking phases and topological phases, as illustrated by two-dimensional (2D) statistical Ising model, 2D statistical loop-gas model, and 1+1D <span class="hlt">quantum</span> spin-1/2 and spin-1 models. In particular, using such a (Gsym,Tinv) characterization, we show that the Haldane phase for a spin-1 chain is a phase protected by the time-reversal, parity, and translation symmetries. Thus the Haldane phase is a symmetry-protected topological phase. The (Gsym,Tinv) characterization is more general than the characterizations based on the boundary spins and string order parameters. The <span class="hlt">tensor</span> renormalization approach also allows us to study continuous phase transitions between symmetry breaking phases and/or topological phases. The scaling dimensions and the central charges for the critical points that describe those continuous phase transitions can be calculated from the fixed-point <span class="hlt">tensors</span> at those critical points.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/scitech/biblio/22307946','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/22307946"><span><span class="hlt">Stress</span> influenced trapping processes in Si based multi-<span class="hlt">quantum</span> well structures and heavy ions implanted Si</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Ciurea, Magdalena Lidia Lazanu, Sorina</p> <p>2014-10-06</p> <p>Multi-<span class="hlt">quantum</span> well structures and Si wafers implanted with heavy iodine and bismuth ions are studied in order to evaluate the influence of <span class="hlt">stress</span> on the parameters of trapping centers. The experimental method of thermostimullatedcurrents without applied bias is used, and the trapping centers are filled by illumination. By modeling the discharge curves, we found in multilayered structures the parameters of both 'normal' traps and '<span class="hlt">stress</span>-induced' ones, the last having a Gaussian-shaped temperature dependence of the cross section. The <span class="hlt">stress</span> field due to the presence of stopped heavy ions implanted into Si was modeled by a permanent electric field. The increase of the strain from the neighborhood of I ions to the neighborhood of Bi ions produces the broadening of some energy levels and also a temperature dependence of the cross sections for all levels.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/974890','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/974890"><span>MATLAB <span class="hlt">tensor</span> classes for fast algorithm prototyping.</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Bader, Brett William; Kolda, Tamara Gibson</p> <p>2004-10-01</p> <p><span class="hlt">Tensors</span> (also known as mutidimensional arrays or N-way arrays) are used in a variety of applications ranging from chemometrics to psychometrics. We describe four MATLAB classes for <span class="hlt">tensor</span> manipulations that can be used for fast algorithm prototyping. The <span class="hlt">tensor</span> class extends the functionality of MATLAB's multidimensional arrays by supporting additional operations such as <span class="hlt">tensor</span> multiplication. The <span class="hlt">tensor</span> as matrix class supports the 'matricization' of a <span class="hlt">tensor</span>, i.e., the conversion of a <span class="hlt">tensor</span> to a matrix (and vice versa), a commonly used operation in many algorithms. Two additional classes represent <span class="hlt">tensors</span> stored in decomposed formats: cp <span class="hlt">tensor</span> and tucker <span class="hlt">tensor</span>. We descibe all of these classes and then demonstrate their use by showing how to implement several <span class="hlt">tensor</span> algorithms that have appeared in the literature.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2005SPIE.5757..258I','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2005SPIE.5757..258I"><span><span class="hlt">Tensor</span> SVD and distributed control</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Iyer, Ram V.</p> <p>2005-05-01</p> <p>The (approximate) diagonalization of symmetric matrices has been studied in the past in the context of distributed control of an array of collocated smart actuators and sensors. For distributed control using a two dimensional array of actuators and sensors, it is more natural to describe the system transfer function as a complex <span class="hlt">tensor</span> rather than a complex matrix. In this paper, we study the problem of approximately diagonalizing a transfer function <span class="hlt">tensor</span> via the <span class="hlt">tensor</span> singular value decomposition (TSVD) for a locally spatially invariant system, and study its application along with the technique of recursive orthogonal transforms to achieve distributed control for a smart structure.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/1995PhRvD..52.2850G','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/1995PhRvD..52.2850G"><span><span class="hlt">Tensor</span> interactions and τ decays</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Godina Nava, J. J.; López Castro, G.</p> <p>1995-09-01</p> <p>We study the effects of charged <span class="hlt">tensor</span> weak currents on the strangeness-changing decays of the τ lepton. First, we use the available information on the K+e3 form factors to obtain B(τ--->K-π0ντ)~10-4 when the Kπ system is produced in an antisymmetric <span class="hlt">tensor</span> configuration. Then we propose a mechanism for the direct production of the K*2(1430) in τ decays. Using the current upper limit on this decay we set a bound on the symmetric <span class="hlt">tensor</span> interactions.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=4560518','PMC'); return false;" href="https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=4560518"><span>Apoptosis and necrosis induced by novel realgar <span class="hlt">quantum</span> dots in human endometrial cancer cells via endoplasmic reticulum <span class="hlt">stress</span> signaling pathway</span></a></p> <p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pmc">PubMed Central</a></p> <p>Wang, Huan; Liu, Zhengyun; Gou, Ying; Qin, Yu; Xu, Yaze; Liu, Jie; Wu, Jin-Zhu</p> <p>2015-01-01</p> <p>Realgar (AS4S4) has been used in traditional medicines for malignancy, but the poor water solubility is still a major hindrance to its clinical use. Realgar <span class="hlt">quantum</span> dots (RQDs) were therefore synthesized with improved water solubility and bioavailability. Human endometrial cancer JEC cells were exposed to various concentrations of RQDs to evaluate their anticancer effects and to explore mechanisms by the MTT assay, transmission electron microscopy (TEM), flow cytometry, real-time reverse transcriptase polymerase chain reaction (RT-PCR) and Western blot analysis. Results revealed that the highest photoluminescence <span class="hlt">quantum</span> yield of the prepared RQDs was up to approximately 70%, with the average size of 5.48 nm. RQDs induced antipro-liferative activity against JEC cells in a concentration-dependent manner. In light microscopy and TEM examinations, RQDs induced vacuolization and endoplasmic reticulum (ER) dilation in JEC cells in a concentration-dependent manner. ER <span class="hlt">stress</span> by RQDs were further confirmed by increased expression of GADD153 and GRP78 at both mRNA and protein levels. ER <span class="hlt">stress</span> further led to JEC cell apoptosis and necrosis, as evidenced by flow cytometry and mitochondrial membrane potential detection. Our findings demonstrated that the newly synthesized RQDs were effective against human endometrial cancer cells. The underlying mechanism appears to be, at least partly, due to ER <span class="hlt">stress</span> leading to apoptotic cell death and necrosis. PMID:26357474</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/26357474','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/26357474"><span>Apoptosis and necrosis induced by novel realgar <span class="hlt">quantum</span> dots in human endometrial cancer cells via endoplasmic reticulum <span class="hlt">stress</span> signaling pathway.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Wang, Huan; Liu, Zhengyun; Gou, Ying; Qin, Yu; Xu, Yaze; Liu, Jie; Wu, Jin-Zhu</p> <p>2015-01-01</p> <p>Realgar (AS4S4) has been used in traditional medicines for malignancy, but the poor water solubility is still a major hindrance to its clinical use. Realgar <span class="hlt">quantum</span> dots (RQDs) were therefore synthesized with improved water solubility and bioavailability. Human endometrial cancer JEC cells were exposed to various concentrations of RQDs to evaluate their anticancer effects and to explore mechanisms by the MTT assay, transmission electron microscopy (TEM), flow cytometry, real-time reverse transcriptase polymerase chain reaction (RT-PCR) and Western blot analysis. Results revealed that the highest photoluminescence <span class="hlt">quantum</span> yield of the prepared RQDs was up to approximately 70%, with the average size of 5.48 nm. RQDs induced antipro-liferative activity against JEC cells in a concentration-dependent manner. In light microscopy and TEM examinations, RQDs induced vacuolization and endoplasmic reticulum (ER) dilation in JEC cells in a concentration-dependent manner. ER <span class="hlt">stress</span> by RQDs were further confirmed by increased expression of GADD153 and GRP78 at both mRNA and protein levels. ER <span class="hlt">stress</span> further led to JEC cell apoptosis and necrosis, as evidenced by flow cytometry and mitochondrial membrane potential detection. Our findings demonstrated that the newly synthesized RQDs were effective against human endometrial cancer cells. The underlying mechanism appears to be, at least partly, due to ER <span class="hlt">stress</span> leading to apoptotic cell death and necrosis.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017JMPSo.100...62T','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017JMPSo.100...62T"><span>Nonlocal elasticity <span class="hlt">tensors</span> in dislocation and disclination cores</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Taupin, V.; Gbemou, K.; Fressengeas, C.; Capolungo, L.</p> <p>2017-03-01</p> <p>Nonlocal elastic constitutive laws are introduced for crystals containing defects such as dislocations and disclinations. In addition to pointwise elastic moduli <span class="hlt">tensors</span> adequately reflecting the elastic response of defect-free regions by relating <span class="hlt">stresses</span> to strains and couple-<span class="hlt">stresses</span> to curvatures, elastic cross-moduli <span class="hlt">tensors</span> relating strains to couple-<span class="hlt">stresses</span> and curvatures to <span class="hlt">stresses</span> within convolution integrals are derived from a nonlocal analysis of strains and curvatures in the defects cores. Sufficient conditions are derived for positive-definiteness of the resulting free energy, and stability of elastic solutions is ensured. The elastic <span class="hlt">stress</span>/couple <span class="hlt">stress</span> fields associated with prescribed dislocation/disclination density distributions and solving the momentum and moment of momentum balance equations in periodic media are determined by using a Fast Fourier Transform spectral method. The convoluted cross-moduli bring the following results: (i) Nonlocal <span class="hlt">stresses</span> and couple <span class="hlt">stresses</span> oppose their local counterparts in the defects core regions, playing the role of restoring forces and possibly ensuring spatio-temporal stability of the simulated defects, (ii) The couple <span class="hlt">stress</span> fields are strongly affected by nonlocality. Such effects favor the stability of the simulated grain boundaries and allow investigating their elastic interactions with extrinsic defects, (iii) Driving forces inducing grain growth or refinement derive from the self-<span class="hlt">stress</span> and couple <span class="hlt">stress</span> fields of grain boundaries in nanocrystalline configurations.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/pages/biblio/1338722-nonlocal-elasticity-tensors-dislocation-disclination-cores','SCIGOV-DOEP'); return false;" href="https://www.osti.gov/pages/biblio/1338722-nonlocal-elasticity-tensors-dislocation-disclination-cores"><span>Nonlocal elasticity <span class="hlt">tensors</span> in dislocation and disclination cores</span></a></p> <p><a target="_blank" href="http://www.osti.gov/pages">DOE PAGES</a></p> <p>Taupin, V.; Gbemou, K.; Fressengeas, C.; ...</p> <p>2017-01-07</p> <p>We introduced nonlocal elastic constitutive laws for crystals containing defects such as dislocations and disclinations. Additionally, the pointwise elastic moduli <span class="hlt">tensors</span> adequately reflect the elastic response of defect-free regions by relating <span class="hlt">stresses</span> to strains and couple-<span class="hlt">stresses</span> to curvatures, elastic cross-moduli <span class="hlt">tensors</span> relating strains to couple-<span class="hlt">stresses</span> and curvatures to <span class="hlt">stresses</span> within convolution integrals are derived from a nonlocal analysis of strains and curvatures in the defects cores. Sufficient conditions are derived for positive-definiteness of the resulting free energy, and stability of elastic solutions is ensured. The elastic <span class="hlt">stress</span>/couple <span class="hlt">stress</span> fields associated with prescribed dislocation/disclination density distributions and solving the momentum andmore » moment of momentum balance equations in periodic media are determined by using a Fast Fourier Transform spectral method. Here, the convoluted cross-moduli bring the following results: (i) Nonlocal <span class="hlt">stresses</span> and couple <span class="hlt">stresses</span> oppose their local counterparts in the defects core regions, playing the role of restoring forces and possibly ensuring spatio-temporal stability of the simulated defects, (ii) The couple <span class="hlt">stress</span> fields are strongly affected by nonlocality. Such effects favor the stability of the simulated grain boundaries and allow investigating their elastic interactions with extrinsic defects, (iii) Driving forces inducing grain growth or refinement derive from the self-<span class="hlt">stress</span> and couple <span class="hlt">stress</span> fields of grain boundaries in nanocrystalline configurations.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://pubs.er.usgs.gov/publication/70017285','USGSPUBS'); return false;" href="http://pubs.er.usgs.gov/publication/70017285"><span>Moment <span class="hlt">tensors</span> of ten witwatersrand mine tremors</span></a></p> <p><a target="_blank" href="http://pubs.er.usgs.gov/pubs/index.jsp?view=adv">USGS Publications Warehouse</a></p> <p>McGarr, A.</p> <p>1992-01-01</p> <p>Ground motions, recorded both underground and on the surface in two of the South African Gold mining districts, were inverted to determine complete moment <span class="hlt">tensors</span> for 10 mining-induced tremors in the magnitude range 1.9 to 3.3. The resulting moment <span class="hlt">tensors</span> fall into two separate categories. Seven of the events involve substantial coseismic volumetric reduction-??V together with normal faulting entailing shear deformation ??AD, where the summation is over fault planes of area A and average slip D. For these events the ratio-??V/??AD ranges from 0.58 to 0.92, with an average value of 0.71. For the remaining three events ??V is not significantly different from zero; these events are largely double-couple sources involving normal faulting. Surprisingly, the two types of source mechanism appear to be very distinct in that there is not a continuous distribution of the source mix from ??V=0 to-??V?????AD. Presumably, the coseismic closure indicates substantial interaction between a mine stope and adjacent shear failure in the surrounding rock, under the influence of an ambient <span class="hlt">stress</span> for which the maximum principal <span class="hlt">stress</span> is oriented vertically. ?? 1992 Birkha??user Verlag.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19950012873','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19950012873"><span>Visualizing second order <span class="hlt">tensor</span> fields with hyperstreamlines</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Delmarcelle, Thierry; Hesselink, Lambertus</p> <p>1993-01-01</p> <p>Hyperstreamlines are a generalization to second order <span class="hlt">tensor</span> fields of the conventional streamlines used in vector field visualization. As opposed to point icons commonly used in visualizing <span class="hlt">tensor</span> fields, hyperstreamlines form a continuous representation of the complete <span class="hlt">tensor</span> information along a three-dimensional path. This technique is useful in visulaizing both symmetric and unsymmetric three-dimensional <span class="hlt">tensor</span> data. Several examples of <span class="hlt">tensor</span> field visualization in solid materials and fluid flows are provided.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017APS..APR.M6009E','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017APS..APR.M6009E"><span>Emergent Gravity from Vanishing Energy-Momentum <span class="hlt">Tensor</span></span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Erlich, Joshua</p> <p>2017-01-01</p> <p>We propose a constraint of vanishing energy-momentum <span class="hlt">tensor</span> for <span class="hlt">quantum</span> gravity. We are led to a metric-independent effective theory similar to the Dirac-Born-Infeld theory with vanishing gauge fields, modulated by a scalar potential. In the limit of a large number of fields, we explicitly demonstrate the existence of a composite massless spin-2 graviton in the spectrum that couples to matter as in Einstein gravity. We comment on the cosmological constant problem, the generalization to theories of fermions and gauge fields, and the relation to other approaches to <span class="hlt">quantum</span> gravity. This work was supported by the NSF under Grant PHY-1519644.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2013PhRvD..87l1502D','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2013PhRvD..87l1502D"><span><span class="hlt">Quantum</span> hyperbolic geometry in loop <span class="hlt">quantum</span> gravity with cosmological constant</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Dupuis, Maïté; Girelli, Florian</p> <p>2013-06-01</p> <p>Loop <span class="hlt">quantum</span> gravity (LQG) is an attempt to describe the <span class="hlt">quantum</span> gravity regime. Introducing a nonzero cosmological constant Λ in this context has been a standing problem. Other approaches, such as Chern-Simons gravity, suggest that <span class="hlt">quantum</span> groups can be used to introduce Λ into the game. Not much is known when defining LQG with a <span class="hlt">quantum</span> group. <span class="hlt">Tensor</span> operators can be used to construct observables in any type of discrete <span class="hlt">quantum</span> gauge theory with a classical/<span class="hlt">quantum</span> gauge group. We illustrate this by constructing explicitly geometric observables for LQG defined with a <span class="hlt">quantum</span> group and show for the first time that they encode a quantized hyperbolic geometry. This is a novel argument pointing out the usefulness of <span class="hlt">quantum</span> groups as encoding a nonzero cosmological constant. We conclude by discussing how <span class="hlt">tensor</span> operators provide the right formalism to unlock the LQG formulation with a nonzero cosmological constant.</p> </li> </ol> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_7");'>7</a></li> <li><a href="#" onclick='return showDiv("page_8");'>8</a></li> <li class="active"><span>9</span></li> <li><a href="#" onclick='return showDiv("page_10");'>10</a></li> <li><a href="#" onclick='return showDiv("page_11");'>11</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div><!-- col-sm-12 --> </div><!-- row --> </div><!-- page_9 --> <div id="page_10" class="hiddenDiv"> <div class="row"> <div class="col-sm-12"> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_8");'>8</a></li> <li><a href="#" onclick='return showDiv("page_9");'>9</a></li> <li class="active"><span>10</span></li> <li><a href="#" onclick='return showDiv("page_11");'>11</a></li> <li><a href="#" onclick='return showDiv("page_12");'>12</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div> </div> <div class="row"> <div class="col-sm-12"> <ol class="result-class" start="181"> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/scitech/biblio/1237827','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/1237827"><span>A Framework for Load Balancing of <span class="hlt">Tensor</span> Contraction Expressions via Dynamic Task Partitioning</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Lai, Pai-Wei; Stock, Kevin; Rajbhandari, Samyam; Krishnamoorthy, Sriram; Sadayappan, Ponnuswamy</p> <p>2013-11-17</p> <p>In this paper, we introduce the Dynamic Load-balanced <span class="hlt">Tensor</span> Contractions (DLTC), a domain-specific library for efficient task parallel execution of <span class="hlt">tensor</span> contraction expressions, a class of computation encountered in <span class="hlt">quantum</span> chemistry and physics. Our framework decomposes each contraction into smaller unit of tasks, represented by an abstraction referred to as iterators. We exploit an extra level of parallelism by having tasks across independent contractions executed concurrently through a dynamic load balancing run- time. We demonstrate the improved performance, scalability, and flexibility for the computation of <span class="hlt">tensor</span> contraction expressions on parallel computers using examples from coupled cluster methods.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19980003843','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19980003843"><span>Development of the <span class="hlt">Tensoral</span> Computer Language</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Ferziger, Joel; Dresselhaus, Eliot</p> <p>1996-01-01</p> <p>The research scientist or engineer wishing to perform large scale simulations or to extract useful information from existing databases is required to have expertise in the details of the particular database, the numerical methods and the computer architecture to be used. This poses a significant practical barrier to the use of simulation data. The goal of this research was to develop a high-level computer language called <span class="hlt">Tensoral</span>, designed to remove this barrier. The <span class="hlt">Tensoral</span> language provides a framework in which efficient generic data manipulations can be easily coded and implemented. First of all, <span class="hlt">Tensoral</span> is general. The fundamental objects in <span class="hlt">Tensoral</span> represent <span class="hlt">tensor</span> fields and the operators that act on them. The numerical implementation of these <span class="hlt">tensors</span> and operators is completely and flexibly programmable. New mathematical constructs and operators can be easily added to the <span class="hlt">Tensoral</span> system. <span class="hlt">Tensoral</span> is compatible with existing languages. <span class="hlt">Tensoral</span> <span class="hlt">tensor</span> operations co-exist in a natural way with a host language, which may be any sufficiently powerful computer language such as Fortran, C, or Vectoral. <span class="hlt">Tensoral</span> is very-high-level. <span class="hlt">Tensor</span> operations in <span class="hlt">Tensoral</span> typically act on entire databases (i.e., arrays) at one time and may, therefore, correspond to many lines of code in a conventional language. <span class="hlt">Tensoral</span> is efficient. <span class="hlt">Tensoral</span> is a compiled language. Database manipulations are simplified optimized and scheduled by the compiler eventually resulting in efficient machine code to implement them.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/28230538','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/28230538"><span>Interrogating surface state of isolated and agglomerated PbS <span class="hlt">quantum</span> dots with solvent-induced <span class="hlt">stress</span>.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Sher, Pin-Hao; Wang, Juen-Kai</p> <p>2017-04-21</p> <p>Applications of <span class="hlt">quantum</span> dots (QDs) are often obstructed by the associated surface electronic states that quench photoluminescence (PL) and hinder charge transport. Preventing this is still largely being stymied owing to the lack of means to regulate their presence. Dispersing PbS QDs in toluene, we show that varying the solvent temperature offers a way of modulating their surface electronic state. A comprehensive energy-transfer model explains all the anomalous temperature-dependent behavior of the absorption and PL, explicitly revealing the PL quenching dynamics of isolated QDs due to the induced surface state by imposing solvent <span class="hlt">stress</span> on their surface ligands. This study demonstrates that the local <span class="hlt">stress</span> induced by a solvent can serve as a 'switch' for the surface electronic states of QDs, which is enabled by the well-studied thermo-physical properties of a liquid solvent.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017Nanot..28p5703S','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017Nanot..28p5703S"><span>Interrogating surface state of isolated and agglomerated PbS <span class="hlt">quantum</span> dots with solvent-induced <span class="hlt">stress</span></span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Sher, Pin-Hao; Wang, Juen-Kai</p> <p>2017-04-01</p> <p>Applications of <span class="hlt">quantum</span> dots (QDs) are often obstructed by the associated surface electronic states that quench photoluminescence (PL) and hinder charge transport. Preventing this is still largely being stymied owing to the lack of means to regulate their presence. Dispersing PbS QDs in toluene, we show that varying the solvent temperature offers a way of modulating their surface electronic state. A comprehensive energy-transfer model explains all the anomalous temperature-dependent behavior of the absorption and PL, explicitly revealing the PL quenching dynamics of isolated QDs due to the induced surface state by imposing solvent <span class="hlt">stress</span> on their surface ligands. This study demonstrates that the local <span class="hlt">stress</span> induced by a solvent can serve as a ‘switch’ for the surface electronic states of QDs, which is enabled by the well-studied thermo-physical properties of a liquid solvent.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2003AGUFM.T51D0198S','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2003AGUFM.T51D0198S"><span>Moment <span class="hlt">tensor</span> mechanisms from Iberia</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Stich, D.; Morales, J.</p> <p>2003-12-01</p> <p>New moment <span class="hlt">tensor</span> solutions are presented for small and moderate earthquakes in Spain, Portugal and the westernmost Mediterranean Sea for the period from 2002 to present. Moment <span class="hlt">tensor</span> inversion, to estimate focal mechanism, depth and magnitude, is applied at the Instituto Andaluz de Geof¡sica (IAG) in a routine manner to regional earthquakes with local magnitude larger then or equal 3.5. Recent improvements of broadband network coverage contribute to relatively high rates of success: Since beginning of 2002, we could obtain valuable solutions, in the sense that moment <span class="hlt">tensor</span> synthetic waveforms fit adequately the main characteristics of the observed seismograms, for about 50% of all events of the initial selection. Results are available on-line at http://www.ugr.es/~iag/<span class="hlt">tensor</span>/. To date, the IAG moment <span class="hlt">tensor</span> catalogue contains 90 solutions since 1984 and gives a relatively detailed picture of seismotectonics in the Ibero-maghrebian region, covering also low seismicity areas like intraplate Iberia. Solutions are concentrated in southern Spain and the Alboran Sea along the diffuse African-Eurasian plate boundary. These solutions reveal characteristics of the transition between the reverse faulting regime in Algeria and predominately normal faulting on the Iberian Peninsula. Further we discuss the available mechanisms for intermediate deep events, related to subcrustal tectonic processes at the plate contact.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/1163944','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/1163944"><span><span class="hlt">Tensor</span> Target Polarization at TRIUMF</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Smith, G</p> <p>2014-10-27</p> <p>The first measurements of <span class="hlt">tensor</span> observables in $\\pi \\vec{d}$ scattering experiments were performed in the mid-80's at TRIUMF, and later at SIN/PSI. The full suite of <span class="hlt">tensor</span> observables accessible in $\\pi \\vec{d}$ elastic scattering were measured: $T_{20}$, $T_{21}$, and $T_{22}$. The vector analyzing power $iT_{11}$ was also measured. These results led to a better understanding of the three-body theory used to describe this reaction. %Some measurements were also made in the absorption and breakup channels. A direct measurement of the target <span class="hlt">tensor</span> polarization was also made independent of the usual NMR techniques by exploiting the (nearly) model-independent result for the <span class="hlt">tensor</span> analyzing power at 90$^\\circ _{cm}$ in the $\\pi \\vec{d} \\rightarrow 2p$ reaction. This method was also used to check efforts to enhance the <span class="hlt">tensor</span> polarization by RF burning of the NMR spectrum. A brief description of the methods developed to measure and analyze these experiments is provided.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2011PhRvL.107u7402J','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2011PhRvL.107u7402J"><span>Dependence of the Redshifted and Blueshifted Photoluminescence Spectra of Single InxGa1-xAs/GaAs <span class="hlt">Quantum</span> Dots on the Applied Uniaxial <span class="hlt">Stress</span></span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Jöns, K. D.; Hafenbrak, R.; Singh, R.; Ding, F.; Plumhof, J. D.; Rastelli, A.; Schmidt, O. G.; Bester, G.; Michler, P.</p> <p>2011-11-01</p> <p>We apply external uniaxial <span class="hlt">stress</span> to tailor the optical properties of InxGa1-xAs/GaAs <span class="hlt">quantum</span> dots. Unexpectedly, the emission energy of single <span class="hlt">quantum</span> dots controllably shifts to both higher and lower energies under tensile strain. Theoretical calculations using a million atom empirical pseudopotential many-body method indicate that the shifting direction and magnitude depend on the lateral extension and more interestingly on the gallium content of the <span class="hlt">quantum</span> dots. Our experimental results are in good agreement with the underlying theory.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2009PhDT.......156D','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2009PhDT.......156D"><span><span class="hlt">Quantum</span> games as <span class="hlt">quantum</span> types</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Delbecque, Yannick</p> <p></p> <p>In this thesis, we present a new model for higher-order <span class="hlt">quantum</span> programming languages. The proposed model is an adaptation of the probabilistic game semantics developed by Danos and Harmer [DH02]: we expand it with <span class="hlt">quantum</span> strategies which enable one to represent <span class="hlt">quantum</span> states and <span class="hlt">quantum</span> operations. Some of the basic properties of these strategies are established and then used to construct denotational semantics for three <span class="hlt">quantum</span> programming languages. The first of these languages is a formalisation of the measurement calculus proposed by Danos et al. [DKP07]. The other two are new: they are higher-order <span class="hlt">quantum</span> programming languages. Previous attempts to define a denotational semantics for higher-order <span class="hlt">quantum</span> programming languages have failed. We identify some of the key reasons for this and base the design of our higher-order languages on these observations. The game semantics proposed in this thesis is the first denotational semantics for a lambda-calculus equipped with <span class="hlt">quantum</span> types and with extra operations which allow one to program <span class="hlt">quantum</span> algorithms. The results presented validate the two different approaches used in the design of these two new higher-order languages: a first one where <span class="hlt">quantum</span> states are used through references and a second one where they are introduced as constants in the language. The <span class="hlt">quantum</span> strategies presented in this thesis allow one to understand the constraints that must be imposed on <span class="hlt">quantum</span> type systems with higher-order types. The most significant constraint is the fact that abstraction over part of the <span class="hlt">tensor</span> product of many unknown <span class="hlt">quantum</span> states must not be allowed. <span class="hlt">Quantum</span> strategies are a new mathematical model which describes the interaction between classical and <span class="hlt">quantum</span> data using system-environment dialogues. The interactions between the different parts of a <span class="hlt">quantum</span> system are described using the rich structure generated by composition of strategies. This approach has enough generality to be put in relation with other</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/1984CP.....91...89N','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/1984CP.....91...89N"><span><span class="hlt">Tensor</span> formalism in anharmonic calculations</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Nero, N.</p> <p>1984-11-01</p> <p>A new method is presented to compute cartesian <span class="hlt">tensors</span> in the expansion of curvilinear internal coordinates. Second- and higher-order coefficients are related to the metrics of the space of displacements. Components of the metric <span class="hlt">tensor</span> are taken from existing tables of inverse kinetic energy matrix elements or, when rotations are involved, derived from general invariance conditions of scalars within a molecule. This leads to a <span class="hlt">tensor</span> formalism particularly convenient in dealing with curvilinear coordinates in anharmonic calculations of vibrational frequencies. Formulae are given for elements of the potential energy matrix, related to quadratic and cubic force constants in terms of Christoffel symbols. The latter quantities are also used in the expansion of redundancy relations, with explicit coefficients given up to the third order.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016LMaPh.106.1531C','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016LMaPh.106.1531C"><span>O( N) Random <span class="hlt">Tensor</span> Models</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Carrozza, Sylvain; Tanasa, Adrian</p> <p>2016-11-01</p> <p>We define in this paper a class of three-index <span class="hlt">tensor</span> models, endowed with {O(N)^{⊗ 3}} invariance ( N being the size of the <span class="hlt">tensor</span>). This allows to generate, via the usual QFT perturbative expansion, a class of Feynman <span class="hlt">tensor</span> graphs which is strictly larger than the class of Feynman graphs of both the multi-orientable model (and hence of the colored model) and the U( N) invariant models. We first exhibit the existence of a large N expansion for such a model with general interactions. We then focus on the quartic model and we identify the leading and next-to-leading order (NLO) graphs of the large N expansion. Finally, we prove the existence of a critical regime and we compute the critical exponents, both at leading order and at NLO. This is achieved through the use of various analytic combinatorics techniques.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016PhRvD..94l6013G','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016PhRvD..94l6013G"><span>Towards holographic <span class="hlt">quantum</span> energy teleportation</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Giataganas, Dimitrios; Lin, Feng-Li; Liu, Pei-Hua</p> <p>2016-12-01</p> <p>We propose a simplified protocol of <span class="hlt">quantum</span> energy teleportation (QET) for the holographic conformal field theory in three-dimensional anti-de Sitter space with or without a black hole. As a tentative proposal, we simplify the standard QET by replacing Alice's local measurement with the local projection, which excites the system from the ground state into a particular state dual to a Banados geometry. We then mimic Bob's local operation of the usual QET for extracting energy by deforming the UV surface with a local bump. Adopting the surface-state duality, this deformation corresponds to local unitary. We evaluate the extraction of energy from the holographic <span class="hlt">stress</span> <span class="hlt">tensor</span> and find that Bob always gains energy extraction in our protocol. This could be related to the positive energy theorem of the dual gravity. Moreover, the ratio of extraction energy to the injection one is a universal function of the UV surface deformation profile.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2013CQGra..30s5006K','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2013CQGra..30s5006K"><span>Conformal <span class="hlt">tensors</span> via Lovelock gravity</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Kastor, David</p> <p>2013-10-01</p> <p>Constructs from conformal geometry are important in low dimensional gravity models, while in higher dimensions the higher curvature interactions of Lovelock gravity are similarly prominent. Considering conformal invariance in the context of Lovelock gravity leads to natural, higher curvature generalizations of the Weyl, Schouten, Cotton and Bach <span class="hlt">tensors</span>, with properties that straightforwardly extend those of their familiar counterparts. As a first application, we introduce a new set of conformally invariant gravity theories in D = 4k dimensions, based on the squares of the higher curvature Weyl <span class="hlt">tensors</span>.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/1985PhDT.........6R','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/1985PhDT.........6R"><span>Seismic moment <span class="hlt">tensor</span> recovery at low frequencies</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Riedesel, M. A.</p> <p></p> <p>A low-frequency, normal mode technique which provides estimates of the seismic moment <span class="hlt">tensor</span> in as many as ten separate 1 mHz bands is described. The basic data kernels are integrals of the complex spectra of the untaped seismograms with a bandwidth of .1 mHz, centered on the model frequencies of the fundamental modes. The frequency-domain integration process reduces the sensitivity of the solutions to attenuation and splitting. Adjustments in the phase of the integrals are computed to compensate for the effects of latteral heterogeneity, station timing errors, and centroid time shifts. Estimates of the covariance of the solutions are used to provide uncertainties for the source mechanism and the principle <span class="hlt">stress</span> axes. A graphical method is developed which allows a rapid visual assessment of the significance of nondouble-couple and isotropic components of the solutions. The method was applied to 57 earthquakes recorded on the IDA network between 1977 and 1984. The moment rate <span class="hlt">tensor</span> and its uncertainty was investigated in 1 mHz bands over the 1 to 11 mHz frequency range.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/26773363','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/26773363"><span>Curcumin and β-caryophellene attenuate cadmium <span class="hlt">quantum</span> dots induced oxidative <span class="hlt">stress</span> and lethality in Caenorhabditis elegans model system.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Srivastava, Swati; Pant, Aakanksha; Trivedi, Shalini; Pandey, Rakesh</p> <p>2016-03-01</p> <p>Curcumin (CUR) and β-caryophellene (BCP) are well known bioactive phytomolecules which are known to reduce oxidative <span class="hlt">stress</span> in living organisms. Therefore, the present study was envisaged to explore the possible effects of CUR and BCP in suppression of cadmium <span class="hlt">quantum</span> dots (CdTe QDs) induced toxicity in Caenorhabditis elegans. CdTe QD are luminescent nanoparticles extensively exploited for in vivo imaging, but long term bioaccumulation confer deleterious effects on living organisms. The 24-h LC50 and LC100 of CdTe QD were found to be 18.40 μg/ml and 100 μg/ml respectively. The CdTe QD exposure elevated HSP-16.2 expression mediating induction of the <span class="hlt">stress</span> response. The CdTe QD lethality was due to increment in ROS and decline in SOD and GST expression. The present study demonstrates improved survival in BCP (50 μM) and CUR (20 μM) treated worms by over 60% (P<0.01) and 50% (P<0.029) in CdTe QD (100 μg/ml) exposed worms. Furthermore, BCP and CUR attenuate oxidative <span class="hlt">stress</span> triggered by QD. The present study for the first time demonstrates CdTe QD toxicity remediation via BCP and CUR. The future investigations can unravel underlying protective effects of phytomolceules for remediating cyotoxicolgical effects of QDs.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2001JChPh.115.2908K','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2001JChPh.115.2908K"><span>Nuclear magnetic resonance of J-coupled quadrupolar nuclei: Use of the <span class="hlt">tensor</span> operator product basis</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Kemp-Harper, R.; Philp, D. J.; Kuchel, P. W.</p> <p>2001-08-01</p> <p>In nuclear magnetic resonance (NMR) of I=1/2 nuclei that are scalar coupled to quadrupolar spins, a <span class="hlt">tensor</span> operator product (TOP) basis set provides a convenient description of the time evolution of the density operator. Expressions for the evolution of equivalent I=1/2 spins, coupled to an arbitrary spin S>1/2, were obtained by explicit algebraic density operator calculations in Mathematica, and specific examples are given for S=1 and S=3/2. <span class="hlt">Tensor</span> operators are described by the convenient <span class="hlt">quantum</span> numbers rank and order and this imparts to the TOP basis features that enable an intuitive understanding of NMR behavior of these spin systems. It is shown that evolution as a result of J coupling alone changes the rank of <span class="hlt">tensors</span> for the coupling partner, generating higher-rank <span class="hlt">tensors</span>, which allow efficient excitation of S-spin multiple-<span class="hlt">quantum</span> coherences. Theoretical predictions obtained using the TOP formalism were confirmed using multiple-<span class="hlt">quantum</span> filtered heteronuclear spin-echo experiments and were further employed to demonstrate polarization transfer directly to multiple-<span class="hlt">quantum</span> transitions using the insensitive nucleus enhancement by polarization transfer pulse sequence. This latter experiment is the basis of two-dimensional heteronuclear correlation experiments and direct generation of multiple-<span class="hlt">quantum</span> S-spin coherences can therefore be exploited to yield greater spectral resolution in such experiments. Simulated spectra and experimental results are presented.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.dtic.mil/docs/citations/ADA603921','DTIC-ST'); return false;" href="http://www.dtic.mil/docs/citations/ADA603921"><span>Active <span class="hlt">Tensor</span> Magnetic Gradiometer System</span></a></p> <p><a target="_blank" href="https://publicaccess.dtic.mil/psm/api/service/search/search">DTIC Science & Technology</a></p> <p></p> <p>2007-11-01</p> <p>Modify Forward Computer Models .............................................................................................2 Modify TMGS Simulator...active magnetic gradient measurement system are based upon the existing <span class="hlt">tensor</span> magnetic gradiometer system ( TMGS ) developed under project MM-1328...Magnetic Gradiometer System ( TMGS ) for UXO Detection, Imaging, and Discrimination.” The TMGS developed under MM-1328 was successfully tested at the</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017IJMPD..2650020M','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017IJMPD..2650020M"><span>The electromagnetic signature of gravitational wave interaction with the <span class="hlt">quantum</span> vacuum</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Marongwe, Stuart</p> <p></p> <p>An analysis of the effects of the passage of a gravitational wave (GW) on the <span class="hlt">quantum</span> vacuum is made within the context of the Nexus paradigm of <span class="hlt">quantum</span> gravity. Results indicate that if the <span class="hlt">quantum</span> vacuum includes electrically charged virtual particle fields, then a GW will induce vacuum polarization. The equations of General Relativity (GR) are then reformulated to include electric charge displacements in the <span class="hlt">quantum</span> vacuum imposed by an anisotropic <span class="hlt">stress</span> — momentum <span class="hlt">tensor</span>. It is then demonstrated that as a result of the spacetime piezoelectric effect, a gravitational wave is associated with a rotating electromagnetic wave and that the converse effect produced by strong electromagnetic fields is responsible for the generation of relativistic jets and gamma ray bursts. Objects with strong electromagnetic fields will apparently violate the strong equivalence principle.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19950016048','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19950016048"><span>Databases post-processing in <span class="hlt">Tensoral</span></span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Dresselhaus, Eliot</p> <p>1994-01-01</p> <p>The Center for Turbulent Research (CTR) post-processing effort aims to make turbulence simulations and data more readily and usefully available to the research and industrial communities. The <span class="hlt">Tensoral</span> language, introduced in this document and currently existing in prototype form, is the foundation of this effort. <span class="hlt">Tensoral</span> provides a convenient and powerful protocol to connect users who wish to analyze fluids databases with the authors who generate them. In this document we introduce <span class="hlt">Tensoral</span> and its prototype implementation in the form of a user's guide. This guide focuses on use of <span class="hlt">Tensoral</span> for post-processing turbulence databases. The corresponding document - the <span class="hlt">Tensoral</span> 'author's guide' - which focuses on how authors can make databases available to users via the <span class="hlt">Tensoral</span> system - is currently unwritten. Section 1 of this user's guide defines <span class="hlt">Tensoral</span>'s basic notions: we explain the class of problems at hand and how <span class="hlt">Tensoral</span> abstracts them. Section 2 defines <span class="hlt">Tensoral</span> syntax for mathematical expressions. Section 3 shows how these expressions make up <span class="hlt">Tensoral</span> statements. Section 4 shows how <span class="hlt">Tensoral</span> statements and expressions are embedded into other computer languages (such as C or Vectoral) to make <span class="hlt">Tensoral</span> programs. We conclude with a complete example program.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/scitech/biblio/21254149','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/21254149"><span>Note on <span class="hlt">quantum</span> Minkowski space</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Bentalha, Z.; Tahiri, M.</p> <p>2008-09-15</p> <p>In this work, some interesting details about <span class="hlt">quantum</span> Minkowski space and <span class="hlt">quantum</span> Lorentz group structures are revealed. The task is accomplished by generalizing an approach adopted in a previous work where <span class="hlt">quantum</span> rotation group and <span class="hlt">quantum</span> Euclidean space structures have been investigated. The generalized method is based on a mapping relating the q-spinors (precisely the <span class="hlt">tensor</span> product of dotted and undotted fondamental q-spinors) to Minkowski q-vectors. As a result of this mapping, the <span class="hlt">quantum</span> analog of Minkowski space is constructed (with a definite metric). Also, the matrix representation of the <span class="hlt">quantum</span> Lorentz group is determined together with its corresponding q-deformed orthogonality relation.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2006PhLB..637..350K','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2006PhLB..637..350K"><span>Path integral in area <span class="hlt">tensor</span> Regge calculus and complex connections</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Khatsymovsky, V. M.</p> <p>2006-06-01</p> <p>Euclidean <span class="hlt">quantum</span> measure in Regge calculus with independent area <span class="hlt">tensors</span> is considered using example of the Regge manifold of a simple structure. We go over to integrations along certain contours in the hyperplane of complex connection variables. Discrete connection and curvature on classical solutions of the equations of motion are not, strictly speaking, genuine connection and curvature, but more general quantities and, therefore, these do not appear as arguments of a function to be averaged, but are the integration (dummy) variables. We argue that upon integrating out the latter the resulting measure can be well-defined on physical hypersurface (for the area <span class="hlt">tensors</span> corresponding to certain edge vectors, i.e. to certain metric) as positive and having exponential cutoff at large areas on condition that we confine ourselves to configurations which do not pass through degenerate metrics.</p> </li> </ol> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_8");'>8</a></li> <li><a href="#" onclick='return showDiv("page_9");'>9</a></li> <li class="active"><span>10</span></li> <li><a href="#" onclick='return showDiv("page_11");'>11</a></li> <li><a href="#" onclick='return showDiv("page_12");'>12</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div><!-- col-sm-12 --> </div><!-- row --> </div><!-- page_10 --> <div id="page_11" class="hiddenDiv"> <div class="row"> <div class="col-sm-12"> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_9");'>9</a></li> <li><a href="#" onclick='return showDiv("page_10");'>10</a></li> <li class="active"><span>11</span></li> <li><a href="#" onclick='return showDiv("page_12");'>12</a></li> <li><a href="#" onclick='return showDiv("page_13");'>13</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div> </div> <div class="row"> <div class="col-sm-12"> <ol class="result-class" start="201"> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/scitech/biblio/22156912','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/22156912"><span>Viability of vector-<span class="hlt">tensor</span> theories of gravity</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Jimenez, Jose Beltran; Maroto, Antonio L. E-mail: maroto@fis.ucm.es</p> <p>2009-02-15</p> <p>We present a detailed study of the viability of general vector-<span class="hlt">tensor</span> theories of gravity in the presence of an arbitrary temporal background vector field. We find that there are six different classes of theories which are indistinguishable from General Relativity by means of local gravity experiments. We study the propagation speeds of scalar, vector and <span class="hlt">tensor</span> perturbations and obtain the conditions for classical stability of those models. We compute the energy density of the different modes and find the conditions for the absence of ghosts in the <span class="hlt">quantum</span> theory. We conclude that the only theories which can pass all the viability conditions for arbitrary values of the background vector field are not only those of the pure Maxwell type, but also Maxwell theories supplemented with a (Lorentz type) gauge fixing term.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/26278957','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/26278957"><span><span class="hlt">Stress</span> Test for <span class="hlt">Quantum</span> Dynamics Approximations: Deep Tunneling in the Muonium Exchange Reaction D + HMu → DMu + H.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Pérez de Tudela, Ricardo; Suleimanov, Yury V; Richardson, Jeremy O; Sáez Rábanos, Vicente; Green, William H; Aoiz, F J</p> <p>2014-12-04</p> <p><span class="hlt">Quantum</span> effects play a crucial role in chemical reactions involving light atoms at low temperatures, especially when a light particle is exchanged between two heavier partners. Different theoretical methodologies have been developed in the last decades attempting to describe zero-point energy and tunneling effects without abandoning a classical or semiclassical framework. In this work, we have chosen the D + HMu → DMu + H reaction as a <span class="hlt">stress</span> test system for three well-established methods: two representative versions of transition state theory (TST), canonical variational theory and semiclassical instanton, and ring polymer molecular dynamics (RPMD). These calculations will be compared with accurate <span class="hlt">quantum</span> mechanical results. Despite its apparent simplicity, the exchange of the extremely light muonium atom (0.114 u) becomes a most challenging reaction for conventional methods. The main result of this work is that RPMD provides an overall better performance than TST-based methods for such a demanding reaction. RPMD might well turn out to be a useful tool beyond TST applicability.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/1185465','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/1185465"><span>An efficient <span class="hlt">tensor</span> transpose algorithm for multicore CPU, Intel Xeon Phi, and NVidia Tesla GPU</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Lyakh, Dmitry I.</p> <p>2015-01-05</p> <p>An efficient parallel <span class="hlt">tensor</span> transpose algorithm is suggested for shared-memory computing units, namely, multicore CPU, Intel Xeon Phi, and NVidia GPU. The algorithm operates on dense <span class="hlt">tensors</span> (multidimensional arrays) and is based on the optimization of cache utilization on x86 CPU and the use of shared memory on NVidia GPU. From the applied side, the ultimate goal is to minimize the overhead encountered in the transformation of <span class="hlt">tensor</span> contractions into matrix multiplications in computer implementations of advanced methods of <span class="hlt">quantum</span> many-body theory (e.g., in electronic structure theory and nuclear physics). A particular accent is made on higher-dimensional <span class="hlt">tensors</span> that typically appear in the so-called multireference correlated methods of electronic structure theory. Depending on <span class="hlt">tensor</span> dimensionality, the presented optimized algorithms can achieve an order of magnitude speedup on x86 CPUs and 2-3 times speedup on NVidia Tesla K20X GPU with respect to the na ve scattering algorithm (no memory access optimization). Furthermore, the <span class="hlt">tensor</span> transpose routines developed in this work have been incorporated into a general-purpose <span class="hlt">tensor</span> algebra library (TAL-SH).</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/pages/biblio/1185465-efficient-tensor-transpose-algorithm-multicore-cpu-intel-xeon-phi-nvidia-tesla-gpu','SCIGOV-DOEP'); return false;" href="https://www.osti.gov/pages/biblio/1185465-efficient-tensor-transpose-algorithm-multicore-cpu-intel-xeon-phi-nvidia-tesla-gpu"><span>An efficient <span class="hlt">tensor</span> transpose algorithm for multicore CPU, Intel Xeon Phi, and NVidia Tesla GPU</span></a></p> <p><a target="_blank" href="http://www.osti.gov/pages">DOE PAGES</a></p> <p>Lyakh, Dmitry I.</p> <p>2015-01-05</p> <p>An efficient parallel <span class="hlt">tensor</span> transpose algorithm is suggested for shared-memory computing units, namely, multicore CPU, Intel Xeon Phi, and NVidia GPU. The algorithm operates on dense <span class="hlt">tensors</span> (multidimensional arrays) and is based on the optimization of cache utilization on x86 CPU and the use of shared memory on NVidia GPU. From the applied side, the ultimate goal is to minimize the overhead encountered in the transformation of <span class="hlt">tensor</span> contractions into matrix multiplications in computer implementations of advanced methods of <span class="hlt">quantum</span> many-body theory (e.g., in electronic structure theory and nuclear physics). A particular accent is made on higher-dimensional <span class="hlt">tensors</span> that typicallymore » appear in the so-called multireference correlated methods of electronic structure theory. Depending on <span class="hlt">tensor</span> dimensionality, the presented optimized algorithms can achieve an order of magnitude speedup on x86 CPUs and 2-3 times speedup on NVidia Tesla K20X GPU with respect to the na ve scattering algorithm (no memory access optimization). Furthermore, the <span class="hlt">tensor</span> transpose routines developed in this work have been incorporated into a general-purpose <span class="hlt">tensor</span> algebra library (TAL-SH).« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19780044939&hterms=failure+criterion&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D10%26Ntt%3Dfailure%2Bcriterion','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19780044939&hterms=failure+criterion&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D10%26Ntt%3Dfailure%2Bcriterion"><span>Evaluation of the <span class="hlt">tensor</span> polynomial failure criterion for composite materials</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Tennyson, R. C.; Macdonald, D.; Nanyaro, A. P.</p> <p>1978-01-01</p> <p>A comprehensive experimental and analytical evaluation of the <span class="hlt">tensor</span> polynomial failure criterion was undertaken to determine its capability for predicting the ultimate strength of laminated composite structures subject to a plane <span class="hlt">stress</span> state. Results are presented demonstrating that a quadratic formulation is too conservative and a cubic representation is required. Strength comparisons with test data derived from glass/epoxy and graphite/epoxy tubular specimens are also provided to validate the cubic strength criterion.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19750014738','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19750014738"><span>Experimental evaluation of the <span class="hlt">tensor</span> polynomial failure criterion for the design of composite structures</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Tennyson, R. C.</p> <p>1975-01-01</p> <p>The experimental measures and techniques are described which are used to obtain the strength <span class="hlt">tensor</span> components, including cubic terms. Based on a considerable number of biaxial pressure tests together with specimens subjected to a constant torque and internal pressure, a modified form of the plane <span class="hlt">stress</span> <span class="hlt">tensor</span> polynomial failure equation was obtained that was capable of predicting ultimate strength results well. Preliminary data were obtained to determine the effect of varying post cure times and ambient temperatures (-80 F to 250 F) on the change in two <span class="hlt">tensor</span> strength terms, F sub 2 and F sub 22. Other laminate configurations yield corresponding variations for the remaining strength parameters.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017PhRvD..95d6004K','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017PhRvD..95d6004K"><span>Uncolored random <span class="hlt">tensors</span>, melon diagrams, and the Sachdev-Ye-Kitaev models</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Klebanov, Igor R.; Tarnopolsky, Grigory</p> <p>2017-02-01</p> <p>Certain models with rank-3 <span class="hlt">tensor</span> degrees of freedom have been shown by Gurau and collaborators to possess a novel large N limit, where g2N3 is held fixed. In this limit the perturbative expansion in the quartic coupling constant, g , is dominated by a special class of "melon" diagrams. We study "uncolored" models of this type, which contain a single copy of real rank-3 <span class="hlt">tensor</span>. Its three indices are distinguishable; therefore, the models possess O (N )3 symmetry with the <span class="hlt">tensor</span> field transforming in the tri-fundamental representation. Such uncolored models also possess the large N limit dominated by the melon diagrams. The <span class="hlt">quantum</span> mechanics of a real anticommuting <span class="hlt">tensor</span> therefore has a similar large N limit to the model recently introduced by Witten as an implementation of the Sachdev-Ye-Kitaev (SYK) model which does not require disorder. Gauging the O (N )3 symmetry in our <span class="hlt">quantum</span> mechanical model removes the nonsinglet states; therefore, one can search for its well-defined gravity dual. We point out, however, that the model possesses a vast number of gauge-invariant operators involving higher powers of the <span class="hlt">tensor</span> field, suggesting that the complete gravity dual will be intricate. We also discuss the <span class="hlt">quantum</span> mechanics of a complex 3-index anticommuting <span class="hlt">tensor</span>, which has U (N )2×O (N ) symmetry and argue that it is equivalent in the large N limit to a version of SYK model with complex fermions. Finally, we discuss similar models of a commuting <span class="hlt">tensor</span> in dimension d . While the quartic interaction is not positive definite, we construct the large N Schwinger-Dyson equation for the two-point function and show that its solution is consistent with conformal invariance. We carry out a perturbative check of this result using the 4 -ɛ expansion.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2013AGUFM.S11A2304T','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2013AGUFM.S11A2304T"><span>The classical model for moment <span class="hlt">tensors</span></span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Tape, W.; Tape, C.</p> <p>2013-12-01</p> <p>A seismic moment <span class="hlt">tensor</span> is a description of an earthquake source, but the description is indirect. The moment <span class="hlt">tensor</span> describes seismic radiation rather than the actual physical process that initiates the radiation. A moment <span class="hlt">tensor</span> 'model' then ties the physical process to the moment <span class="hlt">tensor</span>. The model is not unique, and the physical process is therefore not unique. In the classical moment <span class="hlt">tensor</span> model (Aki and Richards, 1980), an earthquake arises from slip along a planar fault, but with the slip not necessarily in the plane of the fault. The model specifies the resulting moment <span class="hlt">tensor</span> in terms of the slip vector, the fault normal vector, and the Lame elastic parameters, assuming isotropy. We review the classical model in the context of the fundamental lune. The lune is closely related to the space of moment <span class="hlt">tensors</span>, and it provides a setting that is conceptually natural as well as pictorial. In addition to the classical model, we consider a crack plus double couple model (CDC model) in which a moment <span class="hlt">tensor</span> is regarded as the sum of a crack <span class="hlt">tensor</span> and a double couple. A compilation of full moment <span class="hlt">tensors</span> from the literature reveals large deviations in Poisson's ratio as implied by the classical model. Either the classical model is inadequate or the published full moment <span class="hlt">tensors</span> have very large uncertainties. We question the common interpretation of the isotropic component as a volume change in the source region.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=4706544','PMC'); return false;" href="https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=4706544"><span>Antisymmetric <span class="hlt">tensor</span> generalizations of affine vector fields</span></a></p> <p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pmc">PubMed Central</a></p> <p>Morisawa, Yoshiyuki; Tomoda, Kentaro</p> <p>2016-01-01</p> <p><span class="hlt">Tensor</span> generalizations of affine vector fields called symmetric and antisymmetric affine <span class="hlt">tensor</span> fields are discussed as symmetry of spacetimes. We review the properties of the symmetric ones, which have been studied in earlier works, and investigate the properties of the antisymmetric ones, which are the main theme in this paper. It is shown that antisymmetric affine <span class="hlt">tensor</span> fields are closely related to one-lower-rank antisymmetric <span class="hlt">tensor</span> fields which are parallelly transported along geodesics. It is also shown that the number of linear independent rank-p antisymmetric affine <span class="hlt">tensor</span> fields in n-dimensions is bounded by (n + 1)!/p!(n − p)!. We also derive the integrability conditions for antisymmetric affine <span class="hlt">tensor</span> fields. Using the integrability conditions, we discuss the existence of antisymmetric affine <span class="hlt">tensor</span> fields on various spacetimes. PMID:26858463</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2015JHEP...09..182C','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015JHEP...09..182C"><span>Killing(-Yano) <span class="hlt">tensors</span> in string theory</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Chervonyi, Yuri; Lunin, Oleg</p> <p>2015-09-01</p> <p>We construct the Killing(-Yano) <span class="hlt">tensors</span> for a large class of charged black holes in higher dimensions and study general properties of such <span class="hlt">tensors</span>, in particular, their behavior under string dualities. Killing(-Yano) <span class="hlt">tensors</span> encode the symmetries beyond isometries, which lead to insights into dynamics of particles and fields on a given geometry by providing a set of conserved quantities. By analyzing the eigenvalues of the Killing <span class="hlt">tensor</span>, we provide a prescription for constructing several conserved quantities starting from a single object, and we demonstrate that Killing <span class="hlt">tensors</span> in higher dimensions are always associated with ellipsoidal coordinates. We also determine the transformations of the Killing(-Yano) <span class="hlt">tensors</span> under string dualities, and find the unique modification of the Killing-Yano equation consistent with these symmetries. These results are used to construct the explicit form of the Killing(-Yano) <span class="hlt">tensors</span> for the Myers-Perry black hole in arbitrary number of dimensions and for its charged version.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/scitech/biblio/22255162','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/22255162"><span>The method of planes pressure <span class="hlt">tensor</span> for a spherical subvolume</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Heyes, D. M. Smith, E. R. Dini, D. Zaki, T. A.</p> <p>2014-02-07</p> <p>Various formulas for the local pressure <span class="hlt">tensor</span> based on a spherical subvolume of radius, R, are considered. An extension of the Method of Planes (MOP) formula of Todd et al. [Phys. Rev. E 52, 1627 (1995)] for a spherical geometry is derived using the recently proposed Control Volume formulation [E. R. Smith, D. M. Heyes, D. Dini, and T. A. Zaki, Phys. Rev. E 85, 056705 (2012)]. The MOP formula for the purely radial component of the pressure <span class="hlt">tensor</span> is shown to be mathematically identical to the Radial Irving-Kirkwood formula. Novel offdiagonal elements which are important for momentum conservation emerge naturally from this treatment. The local pressure <span class="hlt">tensor</span> formulas for a plane are shown to be the large radius limits of those for spherical surfaces. The radial-dependence of the pressure <span class="hlt">tensor</span> computed by Molecular Dynamics simulation is reported for virtual spheres in a model bulk liquid where the sphere is positioned randomly or whose center is also that of a molecule in the liquid. The probability distributions of angles relating to pairs of atoms which cross the surface of the sphere, and the center of the sphere, are presented as a function of R. The variance in the shear <span class="hlt">stress</span> calculated from the spherical Volume Averaging method is shown to converge slowly to the limiting values with increasing radius, and to be a strong function of the number of molecules in the simulation cell.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=52827','PMC'); return false;" href="https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=52827"><span><span class="hlt">Tensor</span> species and symmetric functions.</span></a></p> <p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pmc">PubMed Central</a></p> <p>Méndez, M</p> <p>1991-01-01</p> <p>An equivariant representation of the symmetric group Sn (equivariant representation from here on) is defined as a particular type of <span class="hlt">tensor</span> species. For any <span class="hlt">tensor</span> species R the characteristic generating function of R is defined in a way that generalizes the Frobenius characters of representations of the symmetric groups. If R is an equivariant representation, then the characteristic is a homogeneous symmetric function. The combinatorial operations on equivariant representations correspond to formal operations on the respective characteristic functions. In particular, substitution of equivariant representations corresponds to plethysm of symmetric functions. Equivariant representations are constructed that have as characteristic the elementary, complete, and Schur functions. Bijective proofs are given for the formulas that connect them with the monomial symmetric functions. PMID:11607233</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017JCAP...01..002K','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017JCAP...01..002K"><span>Extended vector-<span class="hlt">tensor</span> theories</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Kimura, Rampei; Naruko, Atsushi; Yoshida, Daisuke</p> <p>2017-01-01</p> <p>Recently, several extensions of massive vector theory in curved space-time have been proposed in many literatures. In this paper, we consider the most general vector-<span class="hlt">tensor</span> theories that contain up to two derivatives with respect to metric and vector field. By imposing a degeneracy condition of the Lagrangian in the context of ADM decomposition of space-time to eliminate an unwanted mode, we construct a new class of massive vector theories where five degrees of freedom can propagate, corresponding to three for massive vector modes and two for massless <span class="hlt">tensor</span> modes. We find that the generalized Proca and the beyond generalized Proca theories up to the quartic Lagrangian, which should be included in this formulation, are degenerate theories even in curved space-time. Finally, introducing new metric and vector field transformations, we investigate the properties of thus obtained theories under such transformations.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017JCAP...04..007A','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017JCAP...04..007A"><span>Scalar-<span class="hlt">tensor</span> linear inflation</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Artymowski, Michał; Racioppi, Antonio</p> <p>2017-04-01</p> <p>We investigate two approaches to non-minimally coupled gravity theories which present linear inflation as attractor solution: a) the scalar-<span class="hlt">tensor</span> theory approach, where we look for a scalar-<span class="hlt">tensor</span> theory that would restore results of linear inflation in the strong coupling limit for a non-minimal coupling to gravity of the form of f(varphi)R/2; b) the particle physics approach, where we motivate the form of the Jordan frame potential by loop corrections to the inflaton field. In both cases the Jordan frame potentials are modifications of the induced gravity inflationary scenario, but instead of the Starobinsky attractor they lead to linear inflation in the strong coupling limit.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016CQGra..33iLT01N','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016CQGra..33iLT01N"><span>Gravitational scalar-<span class="hlt">tensor</span> theory</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Naruko, Atsushi; Yoshida, Daisuke; Mukohyama, Shinji</p> <p>2016-05-01</p> <p>We consider a new form of gravity theories in which the action is written in terms of the Ricci scalar and its first and second derivatives. Despite the higher derivative nature of the action, the theory is ghost-free under an appropriate choice of the functional form of the Lagrangian. This model possesses 2 + 2 physical degrees of freedom, namely 2 scalar degrees and 2 <span class="hlt">tensor</span> degrees. We exhaust all such theories with the Lagrangian of the form f(R,{({{\</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=2885356','PMC'); return false;" href="https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=2885356"><span>Multireference Ab Initio Calculations of g <span class="hlt">tensors</span> for Trinuclear Copper Clusters in Multicopper Oxidases</span></a></p> <p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pmc">PubMed Central</a></p> <p>Vancoillie, Steven; Chalupský, Jakub; Ryde, Ulf; Solomon, Edward I.; Pierloot, Kristine; Neese, Frank; Rulíšek, Lubomír</p> <p>2010-01-01</p> <p>EPR spectroscopy has proven to be an indispensable tool in elucidating the structure of metal sites in proteins. In recent years, experimental EPR data have been complemented by theoretical calculations, which have become a standard tool of many <span class="hlt">quantum</span> chemical packages. However, there have only been a few attempts to calculate EPR g <span class="hlt">tensors</span> for exchange-coupled systems with more than two spins. In this work, we present a <span class="hlt">quantum</span> chemical study of structural, electronic, and magnetic properties of intermediates in the reaction cycle of multicopper oxidases and of their inorganic models. All these systems contain three copper(II) ions bridged by hydroxide or O2− anions and their ground states are antiferromagnetically coupled doublets. We demonstrate that only multireference methods, such as CASSCF/CASPT2 or MRCI can yield qualitatively correct results (compared to the experimental values) and consider the accuracy of the calculated EPR g <span class="hlt">tensors</span> as the current benchmark of <span class="hlt">quantum</span> chemical methods. By decomposing the calculated g <span class="hlt">tensors</span> into terms arising from interactions of the ground state with the various excited states, the origin of the zero-field splitting is explained. The results of the study demonstrate that a truly quantitative prediction of the g <span class="hlt">tensors</span> of exchange-coupled systems is a great challenge to contemporary theory. The predictions strongly depend on small energy differences that are difficult to predict with sufficient accuracy by any <span class="hlt">quantum</span> chemical method that is applicable to systems of the size of our target systems. PMID:20469875</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2014IJTP...53.4049W','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2014IJTP...53.4049W"><span>Weighted Hardy-Littlewood Theorems for Conjugate A-Harmonic <span class="hlt">Tensors</span></span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Wen, Haiyu</p> <p>2014-11-01</p> <p>In this paper, we establish some versions of A( φ 1( x), φ 2( x), τ, Ω)-weighted Hardy-Littlewood inequalities for conjugate A-harmonic <span class="hlt">tensors</span>, the theory of harmonic analysis and A-harmonic differential forms largely pertain to applications in mathematical physics, <span class="hlt">quantum</span> field theory, elementary particle physics, etc.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/scitech/biblio/22382020','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/22382020"><span>Generalised <span class="hlt">tensor</span> fluctuations and inflation</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Cannone, Dario; Tasinato, Gianmassimo; Wands, David E-mail: g.tasinato@swansea.ac.uk</p> <p>2015-01-01</p> <p>Using an effective field theory approach to inflation, we examine novel properties of the spectrum of inflationary <span class="hlt">tensor</span> fluctuations, that arise when breaking some of the symmetries or requirements usually imposed on the dynamics of perturbations. During single-clock inflation, time-reparameterization invariance is broken by a time-dependent cosmological background. In order to explore more general scenarios, we consider the possibility that spatial diffeomorphism invariance is also broken by effective mass terms or by derivative operators for the metric fluctuations in the Lagrangian. We investigate the cosmological consequences of the breaking of spatial diffeomorphisms, focussing on operators that affect the power spectrum of fluctuations. We identify the operators for <span class="hlt">tensor</span> fluctuations that can provide a blue spectrum without violating the null energy condition, and operators for scalar fluctuations that lead to non-conservation of the comoving curvature perturbation on superhorizon scales even in single-clock inflation. In the last part of our work, we also examine the consequences of operators containing more than two spatial derivatives, discussing how they affect the sound speed of <span class="hlt">tensor</span> fluctuations, and showing that they can mimic some of the interesting effects of symmetry breaking operators, even in scenarios that preserve spatial diffeomorphism invariance.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/25291733','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/25291733"><span>Sparse alignment for robust <span class="hlt">tensor</span> learning.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Lai, Zhihui; Wong, Wai Keung; Xu, Yong; Zhao, Cairong; Sun, Mingming</p> <p>2014-10-01</p> <p>Multilinear/<span class="hlt">tensor</span> extensions of manifold learning based algorithms have been widely used in computer vision and pattern recognition. This paper first provides a systematic analysis of the multilinear extensions for the most popular methods by using alignment techniques, thereby obtaining a general <span class="hlt">tensor</span> alignment framework. From this framework, it is easy to show that the manifold learning based <span class="hlt">tensor</span> learning methods are intrinsically different from the alignment techniques. Based on the alignment framework, a robust <span class="hlt">tensor</span> learning method called sparse <span class="hlt">tensor</span> alignment (STA) is then proposed for unsupervised <span class="hlt">tensor</span> feature extraction. Different from the existing <span class="hlt">tensor</span> learning methods, L1- and L2-norms are introduced to enhance the robustness in the alignment step of the STA. The advantage of the proposed technique is that the difficulty in selecting the size of the local neighborhood can be avoided in the manifold learning based <span class="hlt">tensor</span> feature extraction algorithms. Although STA is an unsupervised learning method, the sparsity encodes the discriminative information in the alignment step and provides the robustness of STA. Extensive experiments on the well-known image databases as well as action and hand gesture databases by encoding object images as <span class="hlt">tensors</span> demonstrate that the proposed STA algorithm gives the most competitive performance when compared with the <span class="hlt">tensor</span>-based unsupervised learning methods.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2010PhRvL.104n0401B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2010PhRvL.104n0401B"><span>Local <span class="hlt">Quantum</span> Measurement and No-Signaling Imply <span class="hlt">Quantum</span> Correlations</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Barnum, H.; Beigi, S.; Boixo, S.; Elliott, M. B.; Wehner, S.</p> <p>2010-04-01</p> <p>We show that, assuming that <span class="hlt">quantum</span> mechanics holds locally, the finite speed of information is the principle that limits all possible correlations between distant parties to be <span class="hlt">quantum</span> mechanical as well. Local <span class="hlt">quantum</span> mechanics means that a Hilbert space is assigned to each party, and then all local positive-operator-valued measurements are (in principle) available; however, the joint system is not necessarily described by a Hilbert space. In particular, we do not assume the <span class="hlt">tensor</span> product formalism between the joint systems. Our result shows that if any experiment would give nonlocal correlations beyond <span class="hlt">quantum</span> mechanics, <span class="hlt">quantum</span> theory would be invalidated even locally.</p> </li> </ol> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_9");'>9</a></li> <li><a href="#" onclick='return showDiv("page_10");'>10</a></li> <li class="active"><span>11</span></li> <li><a href="#" onclick='return showDiv("page_12");'>12</a></li> <li><a href="#" onclick='return showDiv("page_13");'>13</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div><!-- col-sm-12 --> </div><!-- row --> </div><!-- page_11 --> <div id="page_12" class="hiddenDiv"> <div class="row"> <div class="col-sm-12"> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_10");'>10</a></li> <li><a href="#" onclick='return showDiv("page_11");'>11</a></li> <li class="active"><span>12</span></li> <li><a href="#" onclick='return showDiv("page_13");'>13</a></li> <li><a href="#" onclick='return showDiv("page_14");'>14</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div> </div> <div class="row"> <div class="col-sm-12"> <ol class="result-class" start="221"> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/20481921','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/20481921"><span>Local <span class="hlt">quantum</span> measurement and no-signaling imply <span class="hlt">quantum</span> correlations.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Barnum, H; Beigi, S; Boixo, S; Elliott, M B; Wehner, S</p> <p>2010-04-09</p> <p>We show that, assuming that <span class="hlt">quantum</span> mechanics holds locally, the finite speed of information is the principle that limits all possible correlations between distant parties to be <span class="hlt">quantum</span> mechanical as well. Local <span class="hlt">quantum</span> mechanics means that a Hilbert space is assigned to each party, and then all local positive-operator-valued measurements are (in principle) available; however, the joint system is not necessarily described by a Hilbert space. In particular, we do not assume the <span class="hlt">tensor</span> product formalism between the joint systems. Our result shows that if any experiment would give nonlocal correlations beyond <span class="hlt">quantum</span> mechanics, <span class="hlt">quantum</span> theory would be invalidated even locally.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016APS..MARS20001A','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016APS..MARS20001A"><span><span class="hlt">Tensor</span> Network Algorithms for Braiding Anyons</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Ayeni, Babatunde; Singh, Sukhwinder; Pfeifer, Robert; Brennen, Gavin</p> <p></p> <p>Anyons are point-like (quasi)particles which exist only in two-dimensional systems and have exchange statistics that are neither bosonic nor fermionic. These particles were first proposed as a mere theoretical curiosity, but it was later shown that they arise in topological states of matter and that certain species of non-Abelian anyons can be used for low error <span class="hlt">quantum</span> computation. Despite the importance of anyons, fundamentally and technologically, comparatively little is understood about their many body behaviour especially when the non local effects of braiding are taken into account. This largely due to the lack of efficient numerical methods to study them. In order to circumvent this problem, and to broaden our understanding of the physics of anyons, the authors have developed several numerical methods based on <span class="hlt">tensor</span> network algorithms including: anyonic Matrix Product States (MPS), anyonic Time Evolving Block Decimation (TEBD), anyonic Density Matrix Renormalization Group (DMRG), and Anyonic U(1) MPS. These can be used to simulate static interacting and itinerant braiding anyons on a finite or infinite lattice. We have used our methods to study the phase diagrams of some species, such as Abelian Z3 anyons and non-Abelian Fibonacci and Ising.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/scitech/biblio/21250371','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/21250371"><span>Gravitoelectromagnetic analogy based on tidal <span class="hlt">tensors</span></span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Costa, L. Filipe O.; Herdeiro, Carlos A. R.</p> <p>2008-07-15</p> <p>We propose a new approach to a physical analogy between general relativity and electromagnetism, based on tidal <span class="hlt">tensors</span> of both theories. Using this approach we write a covariant form for the gravitational analogues of the Maxwell equations, which makes transparent both the similarities and key differences between the two interactions. The following realizations of the analogy are given. The first one matches linearized gravitational tidal <span class="hlt">tensors</span> to exact electromagnetic tidal <span class="hlt">tensors</span> in Minkowski spacetime. The second one matches exact magnetic gravitational tidal <span class="hlt">tensors</span> for ultrastationary metrics to exact magnetic tidal <span class="hlt">tensors</span> of electromagnetism in curved spaces. In the third we show that our approach leads to a two-step exact derivation of Papapetrou's equation describing the force exerted on a spinning test particle. Analogous scalar invariants built from tidal <span class="hlt">tensors</span> of both theories are also discussed.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017NRL....12..120L','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017NRL....12..120L"><span>Strained Germanium <span class="hlt">Quantum</span> Well PMOSFETs on SOI with Mobility Enhancement by External Uniaxial <span class="hlt">Stress</span></span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Liu, Yan; Niu, Jiebin; Wang, Hongjuan; Han, Genquan; Zhang, Chunfu; Feng, Qian; Zhang, Jincheng; Hao, Yue</p> <p>2017-02-01</p> <p>Well-behaved Ge <span class="hlt">quantum</span> well (QW) p-channel metal-oxide-semiconductor field-effect transistors (pMOSFETs) were fabricated on silicon-on-insulator (SOI) substrate. By optimizing the growth conditions, ultrathin fully strained Ge film was directly epitaxially grown on SOI at about 450 °C using ultra-high vacuum chemical vapor deposition. In situ Si2H6 passivation of Ge was utilized to form a high-quality SiO2/Si interfacial layer between the high-κ dielectric and channels. Strained Ge QW pMOSFETs achieve the significantly improved effective hole mobility μ eff as compared with the relaxed Si and Ge control devices. At an inversion charge density of Q inv of 2 × 1012 cm-2, Ge QW pMOSFETs on SOI exhibit a 104% μ eff enhancement over relaxed Ge control transistors. It is also demonstrated that μ eff of Ge pMOSFETs on SOI can be further boosted by applying an external uniaxial compressive strain.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2013JMP....54h2303G','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2013JMP....54h2303G"><span>Some classes of renormalizable <span class="hlt">tensor</span> models</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Geloun, Joseph Ben; Livine, Etera R.</p> <p>2013-08-01</p> <p>We identify new families of renormalizable <span class="hlt">tensor</span> models from anterior renormalizable <span class="hlt">tensor</span> models via a mapping capable of reducing or increasing the rank of the theory without having an effect on the renormalizability property. Mainly, a version of the rank 3 <span class="hlt">tensor</span> model as defined by Ben Geloun and Samary [Ann. Henri Poincare 14, 1599 (2013); e-print arXiv:1201.0176 [hep-th</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2006MPLA...21.2599D','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2006MPLA...21.2599D"><span>Magnetic Branes from Generalized 't Hooft <span class="hlt">Tensor</span></span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Duan, Yi-Shi; Wu, Shao-Feng</p> <p></p> <p>'t Hooft-Polykov magnetic monopole regularly realizes the Dirac magnetic monopole in terms of a two-rank <span class="hlt">tensor</span>, the so-called 't Hooft <span class="hlt">tensor</span> in 3D space. Based on the Chern kernel method, we propose the arbitrary rank 't Hooft <span class="hlt">tensors</span>, which universally determine the quantized low energy boundaries of generalized Georgi-Glashow models under asymptotic conditions. Furthermore, the dual magnetic branes theory is built up in terms of ϕ-mapping theory.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016PhRvD..94b4011S','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016PhRvD..94b4011S"><span>Wormholes, the weak energy condition, and scalar-<span class="hlt">tensor</span> gravity</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Shaikh, Rajibul; Kar, Sayan</p> <p>2016-07-01</p> <p>We obtain a large class of Lorentzian wormhole spacetimes in scalar-<span class="hlt">tensor</span> gravity, for which the matter <span class="hlt">stress</span> energy does satisfy the weak energy condition. Our constructions have zero Ricci scalar and an everywhere finite, nonzero scalar field profile. Interpreting the scalar-<span class="hlt">tensor</span> gravity as an effective on-brane theory resulting from a two-brane Randall-Sundrum model of warped extra dimensions, it is possible to link wormhole existence with that of extra dimensions. We study the geometry, matter content, gravitational redshift and circular orbits in such wormholes and argue that our examples are perhaps among those which may have some observational relevance in astrophysics in the future. We also study traversability and find that our wormholes are indeed traversable for values of the metric parameters satisfying the weak energy condition.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/scitech/biblio/22156296','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/22156296"><span>Dirac <span class="hlt">tensor</span> with heavy photon</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Bytev, V. V.; Kuraev, E. A.; Scherbakova, E. S.</p> <p>2013-03-15</p> <p>For the large-angle hard-photon emission by initial leptons in the process of high-energy annihilation of e{sup +}e{sup -} to hadrons, the Dirac <span class="hlt">tensor</span> is obtained by taking the lowest-order radiative corrections into account. The case of large-angle emission of two hard photons by initial leptons is considered. In the final result, the kinematic case of collinear emission of hard photons and soft virtual and real photons is included; it can be used for the construction of Monte-Carlo generators.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=4534832','PMC'); return false;" href="https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=4534832"><span>Realgar <span class="hlt">quantum</span> dots induce apoptosis and necrosis in HepG2 cells through endoplasmic reticulum <span class="hlt">stress</span></span></a></p> <p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pmc">PubMed Central</a></p> <p>QIN, YU; WANG, HUAN; LIU, ZHENG-YUN; LIU, JIE; WU, JIN-ZHU</p> <p>2015-01-01</p> <p>Realgar (As4S4) has been used in traditional Chinese medicines for treatment of malignancies. However, the poor water solubility of realgar limits its clinical application. To overcome this problem, realgar <span class="hlt">quantum</span> dots (RQDs; 5.48±1.09 nm) were prepared by a photoluminescence method. The mean particle size was characterized by high-resolution transmission electron microscopy and scanning electron microscopy. Our recent studies revealed that the RQDs were effective against tumor growth in tumor-bearing mice without producing apparent toxicity. The present study investigated their anticancer effects and mechanisms in human hepatocellular carcinoma (HepG2) cells. The HepG2 cells and human normal liver (L02) cells were used to determine the cytotoxicity of RQDs. The portion of apoptotic and dead cells were measured by flow cytometry with Annexin V-fluorescein isothiocyanate/propidium iodide double staining. Apoptosis-related proteins and genes were examined by western blot analysis and reverse transcription-quantitative polymerase chain reaction, and the mitochondrial membrane potential was assayed by confocal microscope with JC-1 as a probe. RQDs exhibited cytotoxicity in a concentration-dependent manner and HepG2 cells were more sensitive compared with normal L02 cells. At 15 µg/ml, 20% of the cells were apoptotic, while 60% of the cells were necrotic at 30 µg/ml. The anti-apoptosis protein Bcl-2 was dose-dependently decreased, while pro-apoptotic protein Bax was increased. There was a loss of mitochondrial membrane potential and expression of the <span class="hlt">stress</span> genes C/EBP-homologous protein 10 and glucose-regulated protein 78 was increased by RQDs. RQDs were effective in the inhibition of HepG2 cell proliferation and this effect was due to induction of apoptosis and necrosis through endoplasmic reticulum <span class="hlt">stress</span>. PMID:26405541</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2013GeoJI.195.1701T','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2013GeoJI.195.1701T"><span>The classical model for moment <span class="hlt">tensors</span></span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Tape, Walter; Tape, Carl</p> <p>2013-12-01</p> <p>A seismic moment <span class="hlt">tensor</span> is a description of an earthquake source, but the description is indirect. The moment <span class="hlt">tensor</span> describes seismic radiation rather than the actual physical process that initiates the radiation. A moment <span class="hlt">tensor</span> `model' then ties the physical process to the moment <span class="hlt">tensor</span>. The model is not unique, and the physical process is therefore not unique. In the classical moment <span class="hlt">tensor</span> model, an earthquake arises from slip along a planar fault, but with the slip not necessarily in the plane of the fault. The model specifies the resulting moment <span class="hlt">tensor</span> in terms of the slip vector, the fault normal vector and the Lamé elastic parameters, assuming isotropy. We review the classical model in the context of the fundamental lune. The lune is closely related to the space of moment <span class="hlt">tensors</span>, and it provides a setting that is conceptually natural as well as pictorial. In addition to the classical model, we consider a crack plus double-couple model (CDC model) in which a moment <span class="hlt">tensor</span> is regarded as the sum of a crack <span class="hlt">tensor</span> and a double couple.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/19257730','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/19257730"><span>Cosmological footprints of loop <span class="hlt">quantum</span> gravity.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Grain, J; Barrau, A</p> <p>2009-02-27</p> <p>The primordial spectrum of cosmological <span class="hlt">tensor</span> perturbations is considered as a possible probe of <span class="hlt">quantum</span> gravity effects. Together with string theory, loop <span class="hlt">quantum</span> gravity is one of the most promising frameworks to study <span class="hlt">quantum</span> effects in the early universe. We show that the associated corrections should modify the potential seen by gravitational waves during the inflationary amplification. The resulting power spectrum should exhibit a characteristic tilt. This opens a new window for cosmological tests of <span class="hlt">quantum</span> gravity.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=4632698','PMC'); return false;" href="https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=4632698"><span>Liver Toxicity of Cadmium Telluride <span class="hlt">Quantum</span> Dots (CdTe QDs) Due to Oxidative <span class="hlt">Stress</span> in Vitro and in Vivo</span></a></p> <p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pmc">PubMed Central</a></p> <p>Zhang, Ting; Hu, Yuanyuan; Tang, Meng; Kong, Lu; Ying, Jiali; Wu, Tianshu; Xue, Yuying; Pu, Yuepu</p> <p>2015-01-01</p> <p>With the applications of <span class="hlt">quantum</span> dots (QDs) expanding, many studies have described the potential adverse effects of QDs, yet little attention has been paid to potential toxicity of QDs in the liver. The aim of this study was to investigate the effects of cadmium telluride (CdTe) QDs in mice and murine hepatoma cells alpha mouse liver 12 (AML 12). CdTe QDs administration significantly increased the level of lipid peroxides marker malondialdehyde (MDA) in the livers of treated mice. Furthermore, CdTe QDs caused cytotoxicity in AML 12 cells in a dose- and time-dependent manner, which was likely mediated through the generation of reactive oxygen species (ROS) and the induction of apoptosis. An increase in ROS generation with a concomitant increase in the gene expression of the tumor suppressor gene p53, the pro-apoptotic gene Bcl-2 and a decrease in the anti-apoptosis gene Bax, suggested that a mitochondria mediated pathway was involved in CdTe QDs’ induced apoptosis. Finally, we showed that NF-E2-related factor 2 (Nrf2) deficiency blocked induced oxidative <span class="hlt">stress</span> to protect cells from injury induced by CdTe QDs. These findings provide insights into the regulatory mechanisms involved in the activation of Nrf2 signaling that confers protection against CdTe QDs-induced apoptosis in hepatocytes. PMID:26404244</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/24440963','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/24440963"><span>Dietary CdSe/ZnS <span class="hlt">quantum</span> dot exposure in estuarine fish: bioavailability, oxidative <span class="hlt">stress</span> responses, reproduction, and maternal transfer.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Blickley, T Michelle; Matson, Cole W; Vreeland, Wyatt N; Rittschof, Daniel; Di Giulio, Richard T; McClellan-Green, Patricia D</p> <p>2014-03-01</p> <p>Continued development, use, and disposal of <span class="hlt">quantum</span> dots (QDs) ensure their entrance into aquatic environments where they could pose a risk to biological organisms as whole nanoparticles or as degraded metal constituents. Reproductive Fundulus heteroclitus were fed a control diet with lecithin, diets containing 1 or 10 μg of lecithin-encapsulated CdSe/ZnS QD/day, or a diet containing 5.9 μg CdCl2/day for 85 days. Cadmium concentrations in liver, intestine, and eggs were quantified with inductively coupled plasma mass spectrometry. In fish fed 10 μg QD/day, QDs or their degradation products traversed the intestinal epithelia and accumulated in the liver. Less than 0.01% of the QD's cadmium was retained in the liver or intestinal tissues. This compares to 0.9% and 0.5% of the cadmium in the intestine and liver, respectively of fish fed a CdCl2 diet. Cadmium was also detected in the eggs from parents fed 10 μg QD/day. No significant changes in hepatic total glutathione, lipid peroxidation, or expression of genes involved in metal metabolism or oxidative <span class="hlt">stress</span> were observed. While QDs in the diet are minimally bioavailable, unusual levels of vitellogenin transcription in male fish as well as declining fecundity require further investigation to determine if endocrine disruption is of environmental concern.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2014AnPhy.349..117O','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2014AnPhy.349..117O"><span>A practical introduction to <span class="hlt">tensor</span> networks: Matrix product states and projected entangled pair states</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Orús, Román</p> <p>2014-10-01</p> <p>This is a partly non-technical introduction to selected topics on <span class="hlt">tensor</span> network methods, based on several lectures and introductory seminars given on the subject. It should be a good place for newcomers to get familiarized with some of the key ideas in the field, specially regarding the numerics. After a very general introduction we motivate the concept of <span class="hlt">tensor</span> network and provide several examples. We then move on to explain some basics about Matrix Product States (MPS) and Projected Entangled Pair States (PEPS). Selected details on some of the associated numerical methods for 1d and 2d <span class="hlt">quantum</span> lattice systems are also discussed.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/scitech/biblio/22572198','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/22572198"><span>Modifications to cosmological power spectra from scalar-<span class="hlt">tensor</span> entanglement and their observational consequences</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Bolis, Nadia; Albrecht, Andreas; Holman, R.</p> <p>2016-12-06</p> <p>We consider the effects of entanglement in the initial <span class="hlt">quantum</span> state of scalar and <span class="hlt">tensor</span> fluctuations during inflation. We allow the gauge-invariant scalar and <span class="hlt">tensor</span> fluctuations to be entangled in the initial state and compute modifications to the various cosmological power spectra. We compute the angular power spectra (C{sub l}’s) for some specific cases of our entangled state and discuss what signals one might expect to find in CMB data. This entanglement also can break rotational invariance, allowing for the possibility that some of the large scale anomalies in the CMB power spectrum might be explained by this mechanism.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/838184','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/838184"><span>3D reconstruction of <span class="hlt">tensors</span> and vectors</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Defrise, Michel; Gullberg, Grant T.</p> <p>2005-02-17</p> <p>Here we have developed formulations for the reconstruction of 3D <span class="hlt">tensor</span> fields from planar (Radon) and line-integral (X-ray) projections of 3D vector and <span class="hlt">tensor</span> fields. Much of the motivation for this work is the potential application of MRI to perform diffusion <span class="hlt">tensor</span> tomography. The goal is to develop a theory for the reconstruction of both Radon planar and X-ray or line-integral projections because of the flexibility of MRI to obtain both of these type of projections in 3D. The development presented here for the linear <span class="hlt">tensor</span> tomography problem provides insight into the structure of the nonlinear MRI diffusion <span class="hlt">tensor</span> inverse problem. A particular application of <span class="hlt">tensor</span> imaging in MRI is the potential application of cardiac diffusion <span class="hlt">tensor</span> tomography for determining in vivo cardiac fiber structure. One difficulty in the cardiac application is the motion of the heart. This presents a need for developing future theory for <span class="hlt">tensor</span> tomography in a motion field. This means developing a better understanding of the MRI signal for diffusion processes in a deforming media. The techniques developed may allow the application of MRI <span class="hlt">tensor</span> tomography for the study of structure of fiber tracts in the brain, atherosclerotic plaque, and spine in addition to fiber structure in the heart. However, the relations presented are also applicable to other fields in medical imaging such as diffraction tomography using ultrasound. The mathematics presented can also be extended to exponential Radon transform of <span class="hlt">tensor</span> fields and to other geometric acquisitions such as cone beam tomography of <span class="hlt">tensor</span> fields.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://medlineplus.gov/stress.html','NIH-MEDLINEPLUS'); return false;" href="https://medlineplus.gov/stress.html"><span><span class="hlt">Stress</span></span></a></p> <p><a target="_blank" href="http://medlineplus.gov/">MedlinePlus</a></p> <p></p> <p></p> <p>... flu shot, are less effective for them. Some people cope with <span class="hlt">stress</span> more effectively than others. It's important to know your limits when it comes to <span class="hlt">stress</span>, so you can avoid more serious health effects. NIH: National Institute of Mental Health</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/scitech/biblio/21409414','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/21409414"><span><span class="hlt">Quantum</span> vacuum effects as generalized f(R) gravity: Application to stars</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Santos, Emilio</p> <p>2010-03-15</p> <p>It is assumed that, for weak space-time curvature, the main gravitational effect of the <span class="hlt">quantum</span> vacuum <span class="hlt">stress</span> energy corresponds to adding two terms to the Einstein-Hilbert action, proportional to the square of the curvature scalar and to the contraction of two Ricci <span class="hlt">tensors</span>, respectively. It is shown that compatibility with terrestrial and Solar System observations implies that the square roots of the coefficients of these terms should be either a few millimeters or a few hundred meters. It is shown that the vacuum contribution increase the stability of massive white dwarfs.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/1996AIPC..359..413L','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/1996AIPC..359..413L"><span>Effects of <span class="hlt">tensor</span> interactions in τ decays</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>López Castro, G.; Godina Nava, J. J.</p> <p>1996-02-01</p> <p>Recent claims for the observation of antisymmetric weak <span class="hlt">tensor</span> currents in π and K decays are considered for the case of τ→Kπν transitions. Assuming the existence of symmetric <span class="hlt">tensor</span> currents, a mechanism for the direct production of the K2*(1430) spin-2 meson in τ decays is proposed.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=2824337','PMC'); return false;" href="https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=2824337"><span>In Vivo Generalized Diffusion <span class="hlt">Tensor</span> Imaging (GDTI) Using Higher-Order <span class="hlt">Tensors</span> (HOT)</span></a></p> <p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pmc">PubMed Central</a></p> <p>Liu, Chunlei; Mang, Sarah C.; Moseley, Michael E.</p> <p>2009-01-01</p> <p>Generalized diffusion <span class="hlt">tensor</span> imaging (GDTI) using higher order <span class="hlt">tensor</span> statistics (HOT) generalizes the technique of diffusion <span class="hlt">tensor</span> imaging (DTI) by including the effect of non-Gaussian diffusion on the signal of magnetic resonance imaging (MRI). In GDTI-HOT, the effect of non-Gaussian diffusion is characterized by higher order <span class="hlt">tensor</span> statistics (i.e. the cumulant <span class="hlt">tensors</span> or the moment <span class="hlt">tensors</span>) such as the covariance matrix (the second-order cumulant <span class="hlt">tensor</span>), the skewness <span class="hlt">tensor</span> (the third-order cumulant <span class="hlt">tensor</span>) and the kurtosis <span class="hlt">tensor</span> (the fourth-order cumulant <span class="hlt">tensor</span>) etc. Previously, Monte Carlo simulations have been applied to verify the validity of this technique in reconstructing complicated fiber structures. However, no in vivo implementation of GDTI-HOT has been reported. The primary goal of this study is to establish GDTI-HOT as a feasible in vivo technique for imaging non-Gaussian diffusion. We show that probability distribution function (PDF) of the molecular diffusion process can be measured in vivo with GDTI-HOT and be visualized with 3D glyphs. By comparing GDTI-HOT to fiber structures that are revealed by the highest resolution DWI possible in vivo, we show that the GDTI-HOT can accurately predict multiple fiber orientations within one white matter voxel. Furthermore, through bootstrap analysis we demonstrate that in vivo measurement of HOT elements is reproducible with a small statistical variation that is similar to that of DTI. PMID:19953513</p> </li> </ol> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_10");'>10</a></li> <li><a href="#" onclick='return showDiv("page_11");'>11</a></li> <li class="active"><span>12</span></li> <li><a href="#" onclick='return showDiv("page_13");'>13</a></li> <li><a href="#" onclick='return showDiv("page_14");'>14</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div><!-- col-sm-12 --> </div><!-- row --> </div><!-- page_12 --> <div id="page_13" class="hiddenDiv"> <div class="row"> <div class="col-sm-12"> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_11");'>11</a></li> <li><a href="#" onclick='return showDiv("page_12");'>12</a></li> <li class="active"><span>13</span></li> <li><a href="#" onclick='return showDiv("page_14");'>14</a></li> <li><a href="#" onclick='return showDiv("page_15");'>15</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div> </div> <div class="row"> <div class="col-sm-12"> <ol class="result-class" start="241"> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2014IJTP...53.1840F','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2014IJTP...53.1840F"><span>A General Method of Selecting <span class="hlt">Quantum</span> Channel for Bidirectional <span class="hlt">Quantum</span> Teleportation</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Fu, Hong-Zi; Tian, Xiu-Lao; Hu, Yang</p> <p>2014-06-01</p> <p>Based on <span class="hlt">tensor</span> representation and Bell basis measurement in bidirectional <span class="hlt">quantum</span> teleportation, a criterion that can be used to judge whether a four-qubit <span class="hlt">quantum</span> state can be regarded as <span class="hlt">quantum</span> channel or not in bidirectional teleportation is suggested and a theoretical scheme of bidirectional teleportation via four-qubit state as the <span class="hlt">quantum</span> channel is proposed. In accordance with this criterion we give a general method of selecting <span class="hlt">quantum</span> channel in bidirectional teleportation, which is determined by the channel parameter matrix R in the Bell basis measurement. This general method provide a theoretical basis for <span class="hlt">quantum</span> channel selection in bidirectional <span class="hlt">quantum</span> teleportation experiments.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2014EL....10538002M','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2014EL....10538002M"><span>X-ray <span class="hlt">tensor</span> tomography</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Malecki, A.; Potdevin, G.; Biernath, T.; Eggl, E.; Willer, K.; Lasser, T.; Maisenbacher, J.; Gibmeier, J.; Wanner, A.; Pfeiffer, F.</p> <p>2014-02-01</p> <p>Here we introduce a new concept for x-ray computed tomography that yields information about the local micro-morphology and its orientation in each voxel of the reconstructed 3D tomogram. Contrary to conventional x-ray CT, which only reconstructs a single scalar value for each point in the 3D image, our approach provides a full scattering <span class="hlt">tensor</span> with multiple independent structural parameters in each volume element. In the application example shown in this study, we highlight that our method can visualize sub-pixel fiber orientations in a carbon composite sample, hence demonstrating its value for non-destructive testing applications. Moreover, as the method is based on the use of a conventional x-ray tube, we believe that it will also have a great impact in the wider range of material science investigations and in future medical diagnostics. The authors declare no competing financial interests.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2015APS..MARJ38010G','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015APS..MARJ38010G"><span>Jordan Algebraic <span class="hlt">Quantum</span> Categories</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Graydon, Matthew; Barnum, Howard; Ududec, Cozmin; Wilce, Alexander</p> <p>2015-03-01</p> <p>State cones in orthodox <span class="hlt">quantum</span> theory over finite dimensional complex Hilbert spaces enjoy two particularly essential features: homogeneity and self-duality. Orthodox <span class="hlt">quantum</span> theory is not, however, unique in that regard. Indeed, all finite dimensional formally real Jordan algebras -- arenas for generalized <span class="hlt">quantum</span> theories with close algebraic kinship to the orthodox theory -- admit homogeneous self-dual positive cones. We construct categories wherein these theories are unified. The structure of composite systems is cast from universal <span class="hlt">tensor</span> products of the universal C*-algebras enveloping ambient spaces for the constituent state cones. We develop, in particular, a notion of composition that preserves the local distinction of constituent systems in quaternionic <span class="hlt">quantum</span> theory. More generally, we explicitly derive the structure of hybrid <span class="hlt">quantum</span> composites with subsystems of arbitrary Jordan algebraic type.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19780033878&hterms=strength+materials&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D60%26Ntt%3Dstrength%2Bmaterials','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19780033878&hterms=strength+materials&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D60%26Ntt%3Dstrength%2Bmaterials"><span>Evaluation of the <span class="hlt">Tensor</span> Polynomial and Hoffman strength theories for composite materials</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Narayanaswami, R.; Adelman, H. M.</p> <p>1977-01-01</p> <p>The Hoffman theory and the <span class="hlt">Tensor</span> Polynomial (Tsai-Wu) theory with the <span class="hlt">stress</span> interaction term set equal to zero have been found to be preferred alternatives to the general <span class="hlt">Tensor</span> Polynomial theory for predicting strength of filamentary composite laminae. These theories were used to predict failure of off-axis boron/epoxy and E-glass/epoxy test specimens and gave excellent agreement with available experimental results. A numerical experiment was also performed to estimate the errors for ten different composite systems under six different loadings. The maximum error in predicted failure loads among all cases was below 10 percent. These results suggest that the Hoffman failure theory and the <span class="hlt">Tensor</span> Polynomial theory with the <span class="hlt">stress</span> interaction term equal to zero can predict failure of practical filamentary composite materials under general biaxial loading with sufficient accuracy for engineering applications.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2014PMag...94.4080L','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2014PMag...94.4080L"><span>Fundamentals in generalized elasticity and dislocation theory of quasicrystals: Green <span class="hlt">tensor</span>, dislocation key-formulas and dislocation loops</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Lazar, Markus; Agiasofitou, Eleni</p> <p>2014-12-01</p> <p>The present work provides fundamental quantities in generalized elasticity and dislocation theory of quasicrystals. In a clear and straightforward manner, the three-dimensional Green <span class="hlt">tensor</span> of generalized elasticity theory and the extended displacement vector for an arbitrary extended force are derived. Next, in the framework of dislocation theory of quasicrystals, the solutions of the field equations for the extended displacement vector and the extended elastic distortion <span class="hlt">tensor</span> are given; that is, the generalized Burgers equation for arbitrary sources and the generalized Mura-Willis formula, respectively. Moreover, important quantities of the theory of dislocations as the Eshelby <span class="hlt">stress</span> <span class="hlt">tensor</span>, Peach-Koehler force, <span class="hlt">stress</span> function <span class="hlt">tensor</span> and the interaction energy are derived for general dislocations. The application to dislocation loops gives rise to the generalized Burgers equation, where the displacement vector can be written as a sum of a line integral plus a purely geometric part. Finally, using the Green <span class="hlt">tensor</span>, all other dislocation key-formulas for loops, known from the theory of anisotropic elasticity, like the Peach-Koehler <span class="hlt">stress</span> formula, Mura-Willis equation, Volterra equation, <span class="hlt">stress</span> function <span class="hlt">tensor</span> and the interaction energy are derived for quasicrystals.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/22540445','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/22540445"><span>Preparing projected entangled pair states on a <span class="hlt">quantum</span> computer.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Schwarz, Martin; Temme, Kristan; Verstraete, Frank</p> <p>2012-03-16</p> <p>We present a <span class="hlt">quantum</span> algorithm to prepare injective projected entangled pair states (PEPS) on a <span class="hlt">quantum</span> computer, a class of open <span class="hlt">tensor</span> networks representing <span class="hlt">quantum</span> states. The run time of our algorithm scales polynomially with the inverse of the minimum condition number of the PEPS projectors and, essentially, with the inverse of the spectral gap of the PEPS's parent Hamiltonian.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=4538590','PMC'); return false;" href="https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=4538590"><span>Incremental Discriminant Analysis in <span class="hlt">Tensor</span> Space</span></a></p> <p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pmc">PubMed Central</a></p> <p>Chang, Liu; Weidong, Zhao; Tao, Yan; Qiang, Pu; Xiaodan, Du</p> <p>2015-01-01</p> <p>To study incremental machine learning in <span class="hlt">tensor</span> space, this paper proposes incremental <span class="hlt">tensor</span> discriminant analysis. The algorithm employs <span class="hlt">tensor</span> representation to carry on discriminant analysis and combine incremental learning to alleviate the computational cost. This paper proves that the algorithm can be unified into the graph framework theoretically and analyzes the time and space complexity in detail. The experiments on facial image detection have shown that the algorithm not only achieves sound performance compared with other algorithms, but also reduces the computational issues apparently. PMID:26339229</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016MSSP...68..207B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016MSSP...68..207B"><span>Low uncertainty method for inertia <span class="hlt">tensor</span> identification</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Barreto, J. P.; Muñoz, L. E.</p> <p>2016-02-01</p> <p>The uncertainty associated with the experimental identification of the inertia <span class="hlt">tensor</span> can be reduced by implementing adequate rotational and translational motions in the experiment. This paper proposes a particular 3D trajectory that improves the experimental measurement of the inertia <span class="hlt">tensor</span> of rigid bodies. Such a trajectory corresponds to a motion in which the object is rotated around a large number of instantaneous axes, while the center of gravity remains static. The uncertainty in the inertia <span class="hlt">tensor</span> components obtained with this practice is reduced by 45% in average, compared with those calculated using simple rotations around three perpendicular axes (Roll, Pitch, Yaw).</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/409872','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/409872"><span><span class="hlt">Tensor</span> methods for large, sparse unconstrained optimization</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Bouaricha, A.</p> <p>1996-11-01</p> <p><span class="hlt">Tensor</span> methods for unconstrained optimization were first introduced by Schnabel and Chow [SIAM J. Optimization, 1 (1991), pp. 293-315], who describe these methods for small to moderate size problems. This paper extends these methods to large, sparse unconstrained optimization problems. This requires an entirely new way of solving the <span class="hlt">tensor</span> model that makes the methods suitable for solving large, sparse optimization problems efficiently. We present test results for sets of problems where the Hessian at the minimizer is nonsingular and where it is singular. These results show that <span class="hlt">tensor</span> methods are significantly more efficient and more reliable than standard methods based on Newton`s method.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016APS..DMP.Q1210W','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016APS..DMP.Q1210W"><span>ConnesFusion<span class="hlt">Tensor</span>Product/Photon GluonFusion in Mitochondria</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Wh-Maksoed, Prodi Of Physics Ui, Depok 16415-Indonesia; Ssi, Wh-Maksoed</p> <p>2016-05-01</p> <p>As in AJ Wassermann distinguished of classical invariant theory & <span class="hlt">quantum</span> invariant theory subfactor, in S. Palcoux:``From Neveu-Schwarz Subfactors & Connes Fusion'' described the subfactor theory & Witt-algebra whereas Andreas Thom's explanation about ConnesFusion<span class="hlt">Tensor</span>Product/CFTP related Connes fusion to composition of homomorphism (i). classical <span class="hlt">tensor</span> product O-X adds the changes,(ii). Relative <span class="hlt">tensor</span> product H-X preserve the changes. For photonGluonFusion/PGF defined:''photon is the gauge boson of QED, the simplest of all boson'' devotes to CFT as ``<span class="hlt">quantum</span> field theory which are invariant under conformal transformation & in 2D there are infinite dimensional algebra. Alain Connes states theirselves Connes fusion as ``associative <span class="hlt">tensor</span> operation'' to be in coincidences with ``their dynamic behavior driven by the balance in mitochondrial fusion & fission (Carveney, 2007) from Peter Alexander Williams: ``Retinal neuronal remodeling in a model of Optic Atrophy'', Dec, 2011. Great acknowledged to the VicePresident of the R.I, HE.Mr. Drs. M. JUSUF KALLA.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016GReGr..48..124P','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016GReGr..48..124P"><span>The energy-momentum <span class="hlt">tensor</span> for a dissipative fluid in general relativity</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Pimentel, Oscar M.; Lora-Clavijo, F. D.; González, Guillermo A.</p> <p>2016-10-01</p> <p>Considering the growing interest of the astrophysicist community in the study of dissipative fluids with the aim of getting a more realistic description of the universe, we present in this paper a physical analysis of the energy-momentum <span class="hlt">tensor</span> of a viscous fluid with heat flux. We introduce the general form of this <span class="hlt">tensor</span> and, using the approximation of small velocity gradients, we relate the <span class="hlt">stresses</span> of the fluid with the viscosity coefficients, the shear <span class="hlt">tensor</span> and the expansion factor. Exploiting these relations, we can write the <span class="hlt">stresses</span> in terms of the extrinsic curvature of the normal surface to the 4-velocity vector of the fluid, and we can also establish a connection between the perfect fluid and the symmetries of the spacetime. On the other hand, we calculate the energy conditions for a dissipative fluid through contractions of the energy-momentum <span class="hlt">tensor</span> with the 4-velocity vector of an arbitrary observer. This method is interesting because it allows us to compute the conditions in a reasonably easy way and without considering any approximation or restriction on the energy-momentum <span class="hlt">tensor</span>.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017APS..APR.B5001L','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017APS..APR.B5001L"><span>The Viability of Phantom Dark Energy as a <span class="hlt">Quantum</span> Field in 1st-Order FLRW Space</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Ludwick, Kevin</p> <p>2017-01-01</p> <p>In the standard cosmological framework of the 0th-order FLRW metric and the use of perfect fluids in the <span class="hlt">stress</span>-energy <span class="hlt">tensor</span>, dark energy with an equation-of-state parameter w < - 1 (known as phantom dark energy) implies negative kinetic energy and vacuum instability when modeled as a scalar field. However, the accepted values for present-day w from Planck and WMAP9 include a significant range of values less than - 1 . We consider a more accurate description of the universe through the 1st-order perturbing of the isotropic and homogeneous FLRW metric and the components of the <span class="hlt">stress</span>-energy <span class="hlt">tensor</span> and investigate whether a field with an apparent w < - 1 may still have positive kinetic energy. Treating dark energy as a classical scalar field in this metric, we find that it is not as obvious as one might think that phantom dark energy has negative kinetic energy categorically. Analogously, we find that field models of quintessence dark energy (w > - 1) do not necessarily have positive kinetic energy categorically. We then investigate the same question treating dark energy as a <span class="hlt">quantum</span> field in 1st-order FLRW space-time and examining the expectation value of the <span class="hlt">stress</span>-energy <span class="hlt">tensor</span> for w < - 1 using adiabatic expansion.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016GReGr..48..109A','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016GReGr..48..109A"><span>Vacuum for a massless <span class="hlt">quantum</span> scalar field outside a collapsing shell in anti-de Sitter space-time</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Abel, Paul G.; Winstanley, Elizabeth</p> <p>2016-08-01</p> <p>We consider a massless <span class="hlt">quantum</span> scalar field on a two-dimensional space-time describing a thin shell of matter collapsing to form a Schwarzschild-anti-de Sitter black hole. At early times, before the shell starts to collapse, the <span class="hlt">quantum</span> field is in the vacuum state, corresponding to the Boulware vacuum on an eternal black hole space-time. The scalar field satisfies reflecting boundary conditions on the anti-de Sitter boundary. Using the Davies-Fulling-Unruh prescription for computing the renormalized expectation value of the <span class="hlt">stress</span>-energy <span class="hlt">tensor</span>, we find that at late times the black hole is in thermal equilibrium with a heat bath at the Hawking temperature, so the <span class="hlt">quantum</span> field is in a state analogous to the Hartle-Hawking vacuum on an eternal black hole space-time.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/scitech/biblio/21020158','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/21020158"><span>Evolution of <span class="hlt">tensor</span> perturbations in scalar-<span class="hlt">tensor</span> theories of gravity</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Carloni, Sante; Dunsby, Peter K. S.</p> <p>2007-03-15</p> <p>The evolution equations for <span class="hlt">tensor</span> perturbations in a generic scalar-<span class="hlt">tensor</span> theory of gravity are presented. Exact solutions are given for a specific class of theories and Friedmann-Lemaitre-Robertson-Walker backgrounds. In these cases it is shown that, although the evolution of <span class="hlt">tensor</span> models depends on the choice of parameters of the theory, no amplification is possible if the gravitational interaction is attractive.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016JCAP...11..059C','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016JCAP...11..059C"><span>Entangled scalar and <span class="hlt">tensor</span> fluctuations during inflation</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Collins, Hael; Vardanyan, Tereza</p> <p>2016-11-01</p> <p>We show how the choice of an inflationary state that entangles scalar and <span class="hlt">tensor</span> fluctuations affects the angular two-point correlation functions of the T, E, and B modes of the cosmic microwave background. The propagators for a state starting with some general quadratic entanglement are solved exactly, leading to predictions for the primordial scalar-scalar, <span class="hlt">tensor-tensor</span>, and scalar-<span class="hlt">tensor</span> power spectra. These power spectra are expressed in terms of general functions that describe the entangling structure of the initial state relative to the standard Bunch-Davies vacuum. We illustrate how such a state would modify the angular correlations in the CMB with a simple example where the initial state is a small perturbation away from the Bunch-Davies state. Because the state breaks some of the rotational symmetries, the angular power spectra no longer need be strictly diagonal.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/27642720','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/27642720"><span>Unsupervised <span class="hlt">Tensor</span> Mining for Big Data Practitioners.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Papalexakis, Evangelos E; Faloutsos, Christos</p> <p>2016-09-01</p> <p>Multiaspect data are ubiquitous in modern Big Data applications. For instance, different aspects of a social network are the different types of communication between people, the time stamp of each interaction, and the location associated to each individual. How can we jointly model all those aspects and leverage the additional information that they introduce to our analysis? <span class="hlt">Tensors</span>, which are multidimensional extensions of matrices, are a principled and mathematically sound way of modeling such multiaspect data. In this article, our goal is to popularize <span class="hlt">tensors</span> and <span class="hlt">tensor</span> decompositions to Big Data practitioners by demonstrating their effectiveness, outlining challenges that pertain to their application in Big Data scenarios, and presenting our recent work that tackles those challenges. We view this work as a step toward a fully automated, unsupervised <span class="hlt">tensor</span> mining tool that can be easily and broadly adopted by practitioners in academia and industry.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/1005408','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/1005408"><span>Shifted power method for computing <span class="hlt">tensor</span> eigenpairs.</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Mayo, Jackson R.; Kolda, Tamara Gibson</p> <p>2010-10-01</p> <p>Recent work on eigenvalues and eigenvectors for <span class="hlt">tensors</span> of order m {>=} 3 has been motivated by applications in blind source separation, magnetic resonance imaging, molecular conformation, and more. In this paper, we consider methods for computing real symmetric-<span class="hlt">tensor</span> eigenpairs of the form Ax{sup m-1} = {lambda}x subject to {parallel}x{parallel} = 1, which is closely related to optimal rank-1 approximation of a symmetric <span class="hlt">tensor</span>. Our contribution is a novel shifted symmetric higher-order power method (SS-HOPM), which we showis guaranteed to converge to a <span class="hlt">tensor</span> eigenpair. SS-HOPM can be viewed as a generalization of the power iteration method for matrices or of the symmetric higher-order power method. Additionally, using fixed point analysis, we can characterize exactly which eigenpairs can and cannot be found by the method. Numerical examples are presented, including examples from an extension of the method to fnding complex eigenpairs.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/scitech/biblio/22382092','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/22382092"><span>The Weyl <span class="hlt">tensor</span> correlator in cosmological spacetimes</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Fröb, Markus B.</p> <p>2014-12-01</p> <p>We give a general expression for the Weyl <span class="hlt">tensor</span> two-point function in a general Friedmann-Lemaître-Robertson-Walker spacetime. We work in reduced phase space for the perturbations, i.e., quantize only the dynamical degrees of freedom without adding any gauge-fixing term. The general formula is illustrated by a calculation in slow-roll single-field inflation to first order in the slow-roll parameters ε and δ, and the result is shown to have the correct de Sitter limit as ε, δ → 0. Furthermore, it is seen that the Weyl <span class="hlt">tensor</span> correlation function in slow-roll does not suffer from infrared divergences, unlike the two-point functions of the metric and scalar field perturbations. Lastly, we show how to recover the usual <span class="hlt">tensor</span> power spectrum from the Weyl <span class="hlt">tensor</span> correlation function.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/scitech/biblio/22454505','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/22454505"><span>The Weyl <span class="hlt">tensor</span> correlator in cosmological spacetimes</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Fröb, Markus B.</p> <p>2014-12-05</p> <p>We give a general expression for the Weyl <span class="hlt">tensor</span> two-point function in a general Friedmann-Lemaître-Robertson-Walker spacetime. We work in reduced phase space for the perturbations, i.e., quantize only the dynamical degrees of freedom without adding any gauge-fixing term. The general formula is illustrated by a calculation in slow-roll single-field inflation to first order in the slow-roll parameters ϵ and δ, and the result is shown to have the correct de Sitter limit as ϵ,δ→0. Furthermore, it is seen that the Weyl <span class="hlt">tensor</span> correlation function in slow-roll does not suffer from infrared divergences, unlike the two-point functions of the metric and scalar field perturbations. Lastly, we show how to recover the usual <span class="hlt">tensor</span> power spectrum from the Weyl <span class="hlt">tensor</span> correlation function.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/scitech/biblio/22572195','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/22572195"><span>Entangled scalar and <span class="hlt">tensor</span> fluctuations during inflation</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Collins, Hael; Vardanyan, Tereza</p> <p>2016-11-29</p> <p>We show how the choice of an inflationary state that entangles scalar and <span class="hlt">tensor</span> fluctuations affects the angular two-point correlation functions of the T, E, and B modes of the cosmic microwave background. The propagators for a state starting with some general quadratic entanglement are solved exactly, leading to predictions for the primordial scalar-scalar, <span class="hlt">tensor-tensor</span>, and scalar-<span class="hlt">tensor</span> power spectra. These power spectra are expressed in terms of general functions that describe the entangling structure of the initial state relative to the standard Bunch-Davies vacuum. We illustrate how such a state would modify the angular correlations in the CMB with a simple example where the initial state is a small perturbation away from the Bunch-Davies state. Because the state breaks some of the rotational symmetries, the angular power spectra no longer need be strictly diagonal.</p> </li> </ol> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_11");'>11</a></li> <li><a href="#" onclick='return showDiv("page_12");'>12</a></li> <li class="active"><span>13</span></li> <li><a href="#" onclick='return showDiv("page_14");'>14</a></li> <li><a href="#" onclick='return showDiv("page_15");'>15</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div><!-- col-sm-12 --> </div><!-- row --> </div><!-- page_13 --> <div id="page_14" class="hiddenDiv"> <div class="row"> <div class="col-sm-12"> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_12");'>12</a></li> <li><a href="#" onclick='return showDiv("page_13");'>13</a></li> <li class="active"><span>14</span></li> <li><a href="#" onclick='return showDiv("page_15");'>15</a></li> <li><a href="#" onclick='return showDiv("page_16");'>16</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div> </div> <div class="row"> <div class="col-sm-12"> <ol class="result-class" start="261"> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/pages/biblio/1324568-energy-momentum-tensor-classical-gauge-theories','SCIGOV-DOEP'); return false;" href="https://www.osti.gov/pages/biblio/1324568-energy-momentum-tensor-classical-gauge-theories"><span>The energy-momentum <span class="hlt">tensor(s</span>) in classical gauge theories</span></a></p> <p><a target="_blank" href="http://www.osti.gov/pages">DOE PAGES</a></p> <p>Blaschke, Daniel N.; Gieres, François; Reboud, Méril; ...</p> <p>2016-07-12</p> <p>We give an introduction to, and review of, the energy-momentum <span class="hlt">tensors</span> in classical gauge field theories in Minkowski space, and to some extent also in curved space-time. For the canonical energy-momentum <span class="hlt">tensor</span> of non-Abelian gauge fields and of matter fields coupled to such fields, we present a new and simple improvement procedure based on gauge invariance for constructing a gauge invariant, symmetric energy-momentum <span class="hlt">tensor</span>. In conclusion, the relationship with the Einstein-Hilbert <span class="hlt">tensor</span> following from the coupling to a gravitational field is also discussed.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.dtic.mil/docs/citations/ADA538435','DTIC-ST'); return false;" href="http://www.dtic.mil/docs/citations/ADA538435"><span>Observability of the Doi Orientation <span class="hlt">Tensor</span> Model</span></a></p> <p><a target="_blank" href="https://publicaccess.dtic.mil/psm/api/service/search/search">DTIC Science & Technology</a></p> <p></p> <p>2011-01-01</p> <p>We also run simulations using the un- scented Kalman filter (UKF) to reconstruct the orientation <span class="hlt">tensor</span> from observations without and with noises ...The UKF gives good estimates for the orientation <span class="hlt">tensor</span> both in the absence and in the presence of observation noises . 1 Introduction Observability of a...quantities [5, 8]. In practice, noise may occur in both the obser- vations and the system dynamics. If the system is not observable, then it is hopeless</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/scitech/biblio/130740','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/130740"><span>Temperature-polarization correlations from <span class="hlt">tensor</span> fluctuations</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Crittenden, R.G.; Coulson, D.; Turok, N.G. |</p> <p>1995-11-15</p> <p>We study the polarization-temperature correlations on the cosmic microwave sky resulting from an initial scale-invariant spectrum of <span class="hlt">tensor</span> (gravity wave) fluctuations, such as those which might arise during inflation. The correlation function has the opposite sign to that for scalar fluctuations on large scales, raising the possibility of a direct determination of whether the microwave anisotropies have a significant <span class="hlt">tensor</span> component. We briefly discuss the important problem of estimating the expected foreground contamination.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/1039397','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/1039397"><span>C%2B%2B <span class="hlt">tensor</span> toolbox user manual.</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Plantenga, Todd D.; Kolda, Tamara Gibson</p> <p>2012-04-01</p> <p>The C++ <span class="hlt">Tensor</span> Toolbox is a software package for computing <span class="hlt">tensor</span> decompositions. It is based on the Matlab <span class="hlt">Tensor</span> Toolbox, and is particularly optimized for sparse data sets. This user manual briefly overviews <span class="hlt">tensor</span> decomposition mathematics, software capabilities, and installation of the package. <span class="hlt">Tensors</span> (also known as multidimensional arrays or N-way arrays) are used in a variety of applications ranging from chemometrics to network analysis. The <span class="hlt">Tensor</span> Toolbox provides classes for manipulating dense, sparse, and structured <span class="hlt">tensors</span> in C++. The Toolbox compiles into libraries and is intended for use with custom applications written by users.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2014PhRvX...4d1024T','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2014PhRvX...4d1024T"><span><span class="hlt">Tensor</span> Networks for Lattice Gauge Theories with Continuous Groups</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Tagliacozzo, L.; Celi, A.; Lewenstein, M.</p> <p>2014-10-01</p> <p>We discuss how to formulate lattice gauge theories in the <span class="hlt">tensor</span>-network language. In this way, we obtain both a consistent-truncation scheme of the Kogut-Susskind lattice gauge theories and a <span class="hlt">tensor</span>-network variational ansatz for gauge-invariant states that can be used in actual numerical computations. Our construction is also applied to the simplest realization of the <span class="hlt">quantum</span> link models or gauge magnets and provides a clear way to understand their microscopic relation with the Kogut-Susskind lattice gauge theories. We also introduce a new set of gauge-invariant operators that modify continuously Rokhsar-Kivelson wave functions and can be used to extend the phase diagrams of known models. As an example, we characterize the transition between the deconfined phase of the Z2 lattice gauge theory and the Rokhsar-Kivelson point of the U (1 ) gauge magnet in 2D in terms of entanglement entropy. The topological entropy serves as an order parameter for the transition but not the Schmidt gap.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19960039931','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19960039931"><span>Visualization of 3-D <span class="hlt">tensor</span> fields</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Hesselink, L.</p> <p>1996-01-01</p> <p>Second-order <span class="hlt">tensor</span> fields have applications in many different areas of physics, such as general relativity and fluid mechanics. The wealth of multivariate information in <span class="hlt">tensor</span> fields makes them more complex and abstract than scalar and vector fields. Visualization is a good technique for scientists to gain new insights from them. Visualizing a 3-D continuous <span class="hlt">tensor</span> field is equivalent to simultaneously visualizing its three eigenvector fields. In the past, research has been conducted in the area of two-dimensional <span class="hlt">tensor</span> fields. It was shown that degenerate points, defined as points where eigenvalues are equal to each other, are the basic singularities underlying the topology of <span class="hlt">tensor</span> fields. Moreover, it was shown that eigenvectors never cross each other except at degenerate points. Since we live in a three-dimensional world, it is important for us to understand the underlying physics of this world. In this report, we describe a new method for locating degenerate points along with the conditions for classifying them in three-dimensional space. Finally, we discuss some topological features of three-dimensional <span class="hlt">tensor</span> fields, and interpret topological patterns in terms of physical properties.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2004AGUFM.G21A0101Z','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2004AGUFM.G21A0101Z"><span>A Comparison of Geodetic Strain Rates With Earthquake Moment <span class="hlt">Tensors</span></span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Zhu, W.; Holt, W. E.</p> <p>2004-12-01</p> <p>In this paper we compare the global model from interpolation of GPS data with the global model inferred from earthquake moment <span class="hlt">tensors</span>. We use the Harvard CMT catalog to calculate moment rates based on 3 assumptions: a. we assume earthquakes are self-similar; b. we assume a uniform Beta value of the Gutenberg-Richter distribution; c. we assume that all of the long-term strain is accommodated seismically. If these assumptions are correct then the seismicity rate is proportional to the tectonic moment rate. We then inferred a long-term moment rate <span class="hlt">tensor</span> field estimate for all plate boundary zones from which we inferred a long-term seismic strain rate estimate. Using this estimate we solved for a self-consistent kinematic global solution (motions of rigid spherical caps and motions within plate boundary zones) using bi-cubic spline interpolation of the inferred strain rates. We tested the above assumptions by comparing the global kinematic model obtained from earthquake data with a global model inferred from interpolation of space geodetic data [Kreemer et al., 2003]. A comparison between the two models shows good agreement for motion directions of the North American, and Eurasian plates and for the plate boundary zones within these regions (e.g., Tibet). Problems arise, and our assumptions break down, for plates adjacent to fast spreading ridges where divergence of plates appears to be accommodated aseismically. We next investigated the correlation of strain rate <span class="hlt">tensor</span> inferred from the interpolation of GPS observations within deforming Asia with the earthquake moment <span class="hlt">tensors</span>, using both elastic and viscous rheologies. Our solutions satisfy the force balance equations for a given rheology. Our goal for this exercise is to investigate whether the interseismic signal, inferred from GPS, correlates better with moment <span class="hlt">tensor</span> style for an elastic rheology as opposed to a viscous rheology. Results to date suggest that the viscous models only provide a better agreement</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/scitech/biblio/21149172','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/21149172"><span>Non-standard symmetries and <span class="hlt">quantum</span> anomalies</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Visinescu, Anca; Visinescu, Mihai</p> <p>2008-08-31</p> <p><span class="hlt">Quantum</span> anomalies are investigated on curved spacetimes. The intimate relation between Killing-Yano <span class="hlt">tensors</span> and non-standard symmetries is pointed out. The gravitational anomalies are absent if the hidden symmetry is associated to a Killing-Yano <span class="hlt">tensor</span>. The axial anomaly in a background gravitational field is directly related with the index of the Dirac operator. In the Dirac theory on curved spaces, Killing-Yano <span class="hlt">tensors</span> generate Dirac-type operators involved in interesting algebraic structures. The general results are applied to the 4-dimensional Euclidean Taub-NUT space.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016PhRvB..94k5150L','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016PhRvB..94k5150L"><span>Classification of trivial spin-1 <span class="hlt">tensor</span> network states on a square lattice</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Lee, Hyunyong; Han, Jung Hoon</p> <p>2016-09-01</p> <p>Classification of possible <span class="hlt">quantum</span> spin liquid (QSL) states of interacting spin-1/2's in two dimensions has been a fascinating topic of condensed matter for decades, resulting in enormous progress in our understanding of low-dimensional <span class="hlt">quantum</span> matter. By contrast, relatively little work exists on the identification, let alone classification, of QSL phases for spin-1 systems in dimensions higher than one. Employing the powerful ideas of <span class="hlt">tensor</span> network theory and its classification, we develop general methods for writing QSL wave functions of spin-1 respecting all the lattice symmetries, spin rotation, and time reversal with trivial gauge structure on the square lattice. We find 25 distinct classes characterized by five binary <span class="hlt">quantum</span> numbers. Several explicit constructions of such wave functions are given for bond dimensions D ranging from two to four, along with thorough numerical analyses to identify their physical characters. Both gapless and gapped states are found. The topological entanglement entropy of the gapped states is close to zero, indicative of topologically trivial states. In D =4 , several different <span class="hlt">tensors</span> can be linearly combined to produce a family of states within the same symmetry class. A rich "phase diagram" can be worked out among the phases of these <span class="hlt">tensors</span>, as well as the phase transitions among them. Among the states we identified in this putative phase diagram is the plaquette-ordered phase, gapped resonating valence bond phase, and a critical phase. A continuous transition separates the plaquette-ordered phase from the resonating valence bond phase.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016APS..MARX12010W','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016APS..MARX12010W"><span>Symmetry-enriched topological invariants from <span class="hlt">tensor</span> network representations</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Ware, Brayden; Cheng, Meng; Bauer, Bela</p> <p></p> <p>We examine topologically ordered <span class="hlt">quantum</span> phases in 2+1 dimensions where in the presence of symmetries the topological phase splits into multiple symmetry enriched topological (SET) phases. These SET phases become adiabatically connected when the symmetry is broken, but are separated by phase transitions when symmetry is enforced. Using <span class="hlt">tensor</span> network representations of representative wavefunctions for certain SET phases, we demonstrate the calculation of the extended modular matrices, a generalization of the well-known modular matrices that have been used to robustly characterize topological phases in numerical calculations. Here, the crucial extension is to systems with symmetry defects. The extended modular matrices are used to form symmetry-enriched topological invariants which distinguish different SET phases.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19980009683','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19980009683"><span>Time Evolution of Modeled Reynolds <span class="hlt">Stresses</span> in Planar Homogeneous Flows</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Jongen, T.; Gatski, T. B.</p> <p>1997-01-01</p> <p>The analytic expression of the time evolution of the Reynolds <span class="hlt">stress</span> anisotropy <span class="hlt">tensor</span> in all planar homogeneous flows is obtained by exact integration of the modeled differential Reynolds <span class="hlt">stress</span> equations. The procedure is based on results of <span class="hlt">tensor</span> representation theory, is applicable for general pressure-strain correlation <span class="hlt">tensors</span>, and can account for any additional turbulence anisotropy effects included in the closure. An explicit solution of the resulting system of scalar ordinary differential equations is obtained for the case of a linear pressure-strain correlation <span class="hlt">tensor</span>. The properties of this solution are discussed, and the dynamic behavior of the Reynolds <span class="hlt">stresses</span> is studied, including limit cycles and sensitivity to initial anisotropies.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017PhPl...24b2114A','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017PhPl...24b2114A"><span>Kinetic analysis of spin current contribution to spectrum of electromagnetic waves in spin-1/2 plasma. I. Dielectric permeability <span class="hlt">tensor</span> for magnetized plasmas</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Andreev, Pavel A.</p> <p>2017-02-01</p> <p>The dielectric permeability <span class="hlt">tensor</span> for spin polarized plasmas is derived in terms of the spin-1/2 <span class="hlt">quantum</span> kinetic model in six-dimensional phase space. Expressions for the distribution function and spin distribution function are derived in linear approximations on the path of dielectric permeability <span class="hlt">tensor</span> derivation. The dielectric permeability <span class="hlt">tensor</span> is derived for the spin-polarized degenerate electron gas. It is also discussed at the finite temperature regime, where the equilibrium distribution function is presented by the spin-polarized Fermi-Dirac distribution. Consideration of the spin-polarized equilibrium states opens possibilities for the kinetic modeling of the thermal spin current contribution in the plasma dynamics.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/1999PhDT.......215S','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/1999PhDT.......215S"><span>Development and analysis of a well-posed model for the turbulent dispersion <span class="hlt">tensor</span></span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Shabany Sheikhan Gafsheh, Younes</p> <p>1999-10-01</p> <p>The transport of a passive scalar in high-Reynolds-number turbulent flows is controlled by the flow and is independent from the passive scalar itself. Therefore, turbulent dispersion is a function of the velocity field and Reynolds <span class="hlt">stresses</span>. On the other hand, the transport equation for a passive scalar is a linear partial differential equation; any modeled form of the equation has to preserve this property and the superposition principle. It is shown that, in a homogeneous and high-Reynolds- number flow, an evolution equation for the dispersion <span class="hlt">tensor</span> can be obtained from a model transport equation for the turbulent scalar flux and the definition of the dispersion <span class="hlt">tensor</span>. This equation shows that the dispersion <span class="hlt">tensor</span> is a function of the flow field only. It is shown that, in the limit of high Reynolds/Peclet number flows, the symmetric part of the dispersion <span class="hlt">tensor</span> has to be a positive semidefinite <span class="hlt">tensor</span>. This is the well-posedness condition for the dispersion <span class="hlt">tensor</span>. It is observed that the solution of the evolution equation for the dispersion <span class="hlt">tensor</span>, obtained from the general linear transport equation for the turbulent scalar fluxes, does not satisfy this condition in some cases. A modification to this model is proposed to prevent any solution which is not well posed. The equilibrium assumption for the normalized dispersion <span class="hlt">tensor</span> results in an implicit algebraic expression for the dispersion <span class="hlt">tensor</span>. A new method is proposed to solve the implicit expression in order to obtain an explicit algebraic model for the dispersion <span class="hlt">tensor</span>. The model constants are found using channel flow DNS data as well as turbulent boundary layer experimental data. The present model gives good predictions of the heat transfer rates and the temperature profiles in boundary layers with constant wall temperature and with a step change in wall temperature. The model predictions show good agreements with the experimental data on channel flows with constant wall temperature and with a step</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://eric.ed.gov/?q=diffusion&pg=6&id=ED552116','ERIC'); return false;" href="http://eric.ed.gov/?q=diffusion&pg=6&id=ED552116"><span>An Adaptive Spectrally Weighted Structure <span class="hlt">Tensor</span> Applied to <span class="hlt">Tensor</span> Anisotropic Nonlinear Diffusion for Hyperspectral Images</span></a></p> <p><a target="_blank" href="http://www.eric.ed.gov/ERICWebPortal/search/extended.jsp?_pageLabel=advanced">ERIC Educational Resources Information Center</a></p> <p>Marin Quintero, Maider J.</p> <p>2013-01-01</p> <p>The structure <span class="hlt">tensor</span> for vector valued images is most often defined as the average of the scalar structure <span class="hlt">tensors</span> in each band. The problem with this definition is the assumption that all bands provide the same amount of edge information giving them the same weights. As a result non-edge pixels can be reinforced and edges can be weakened…</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/18270068','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/18270068"><span>Generalized <span class="hlt">tensor</span>-based morphometry of HIV/AIDS using multivariate statistics on deformation <span class="hlt">tensors</span>.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Lepore, N; Brun, C; Chou, Y Y; Chiang, M C; Dutton, R A; Hayashi, K M; Luders, E; Lopez, O L; Aizenstein, H J; Toga, A W; Becker, J T; Thompson, P M</p> <p>2008-01-01</p> <p>This paper investigates the performance of a new multivariate method for <span class="hlt">tensor</span>-based morphometry (TBM). Statistics on Riemannian manifolds are developed that exploit the full information in deformation <span class="hlt">tensor</span> fields. In TBM, multiple brain images are warped to a common neuroanatomical template via 3-D nonlinear registration; the resulting deformation fields are analyzed statistically to identify group differences in anatomy. Rather than study the Jacobian determinant (volume expansion factor) of these deformations, as is common, we retain the full deformation <span class="hlt">tensors</span> and apply a manifold version of Hotelling's $T(2) test to them, in a Log-Euclidean domain. In 2-D and 3-D magnetic resonance imaging (MRI) data from 26 HIV/AIDS patients and 14 matched healthy subjects, we compared multivariate <span class="hlt">tensor</span> analysis versus univariate tests of simpler <span class="hlt">tensor</span>-derived indices: the Jacobian determinant, the trace, geodesic anisotropy, and eigenvalues of the deformation <span class="hlt">tensor</span>, and the angle of rotation of its eigenvectors. We detected consistent, but more extensive patterns of structural abnormalities, with multivariate tests on the full <span class="hlt">tensor</span> manifold. Their improved power was established by analyzing cumulative p-value plots using false discovery rate (FDR) methods, appropriately controlling for false positives. This increased detection sensitivity may empower drug trials and large-scale studies of disease that use <span class="hlt">tensor</span>-based morphometry.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2012MeSol..47..538G','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2012MeSol..47..538G"><span>Linear reduced cosserat medium with spherical <span class="hlt">tensor</span> of inertia, where rotations are not observed in experiment</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Grekova, E. F.</p> <p>2012-09-01</p> <p>We consider a linear reduced Cosserat medium: a linear elastic continuum, whose point bodies possess kinematically independent translational and rotational degrees of freedom, but the strain energy does not depend on the gradient of rotation of particles. In such a medium the force <span class="hlt">stress</span> <span class="hlt">tensor</span> is asymmetric, but the couple <span class="hlt">stress</span> <span class="hlt">tensor</span> is zero. This model can be applied for description of soils and granular media. Since for the time being the experimental technique for measurement of rotational deformations is not well developed, we investigate how the presence of rotational degrees of freedom affects the dynamics of translational displacements. We consider the case of the spherical <span class="hlt">tensor</span> of inertia and isotropy with respect to the rotational degrees of freedom. Integration of the equation of balance of torques lets us in several cases to put in correspondence a linear reduced Cosserat continuum with the spherical <span class="hlt">tensor</span> of inertia with a classical (non-polar elastic linear) medium with memory with the same equation for the balance of forces, written in terms of translational displacements. This is possible for the isotropic case and also if the anisotropy is present only in the <span class="hlt">tensor</span> of elastic constants corresponding to the classical strain <span class="hlt">tensor</span>. If the material is isotropic with respect to rotational deformations but the (anisotropic) coupling between rotational and classical translational strains is present, then the corresponding classical medium does not exist. If we ignore the rotational degrees of freedom when this coupling is present, this will lead us to the conclusion that the principle of material objectivity is violated.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2014AGUFM.S11H..04M','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2014AGUFM.S11H..04M"><span>Assessing the Uncertainties on Seismic Source Parameters: Towards Realistic Estimates of Moment <span class="hlt">Tensor</span> Determinations</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Magnoni, F.; Scognamiglio, L.; Tinti, E.; Casarotti, E.</p> <p>2014-12-01</p> <p>Seismic moment <span class="hlt">tensor</span> is one of the most important source parameters defining the earthquake dimension and style of the activated fault. Moment <span class="hlt">tensor</span> catalogues are ordinarily used by geoscientists, however, few attempts have been done to assess possible impacts of moment magnitude uncertainties upon their own analysis. The 2012 May 20 Emilia mainshock is a representative event since it is defined in literature with a moment magnitude value (Mw) spanning between 5.63 and 6.12. An uncertainty of ~0.5 units in magnitude leads to a controversial knowledge of the real size of the event. The possible uncertainty associated to this estimate could be critical for the inference of other seismological parameters, suggesting caution for seismic hazard assessment, coulomb <span class="hlt">stress</span> transfer determination and other analyses where self-consistency is important. In this work, we focus on the variability of the moment <span class="hlt">tensor</span> solution, highlighting the effect of four different velocity models, different types and ranges of filtering, and two different methodologies. Using a larger dataset, to better quantify the source parameter uncertainty, we also analyze the variability of the moment <span class="hlt">tensor</span> solutions depending on the number, the epicentral distance and the azimuth of used stations. We endorse that the estimate of seismic moment from moment <span class="hlt">tensor</span> solutions, as well as the estimate of the other kinematic source parameters, cannot be considered an absolute value and requires to come out with the related uncertainties and in a reproducible framework characterized by disclosed assumptions and explicit processing workflows.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/27458495','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/27458495"><span>MULTILINEAR <span class="hlt">TENSOR</span> REGRESSION FOR LONGITUDINAL RELATIONAL DATA.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Hoff, Peter D</p> <p>2015-09-01</p> <p>A fundamental aspect of relational data, such as from a social network, is the possibility of dependence among the relations. In particular, the relations between members of one pair of nodes may have an effect on the relations between members of another pair. This article develops a type of regression model to estimate such effects in the context of longitudinal and multivariate relational data, or other data that can be represented in the form of a <span class="hlt">tensor</span>. The model is based on a general multilinear <span class="hlt">tensor</span> regression model, a special case of which is a <span class="hlt">tensor</span> autoregression model in which the <span class="hlt">tensor</span> of relations at one time point are parsimoniously regressed on relations from previous time points. This is done via a separable, or Kronecker-structured, regression parameter along with a separable covariance model. In the context of an analysis of longitudinal multivariate relational data, it is shown how the multilinear <span class="hlt">tensor</span> regression model can represent patterns that often appear in relational and network data, such as reciprocity and transitivity.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017AAS...22912506L','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017AAS...22912506L"><span>Testing gravity theories using <span class="hlt">tensor</span> perturbations</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Lin, Weikang; Ishak-Boushaki, Mustapha B.</p> <p>2017-01-01</p> <p>Primordial gravitational waves constitute a promising probe of the very early universe physics and the laws of gravity. We study the changes to <span class="hlt">tensor</span>-mode perturbations that can arise in various modified gravity theories. These include a modified friction and a nonstandard dispersion relation. We introduce a physically motivated parametrization of these effects and use current data to obtain excluded parameter spaces. Taking into account the foreground subtraction, we then perform a forecast analysis focusing on the <span class="hlt">tensor</span>-mode modified-gravity parameters as constrained by future experiments COrE, Stage-IV and PIXIE. For the <span class="hlt">tensor</span>-to-scalar ratio r=0.01, we find the minimum detectible modified-gravity effects. In particular, the minimum detectable graviton mass is about 7.8˜9.7×10-33 eV, which is of the same order of magnitude as the graviton mass that allows massive gravity to produce late-time cosmic acceleration. Finally, we study the <span class="hlt">tensor</span>-mode perturbations in modified gravity during inflation. We find that, the <span class="hlt">tensor</span> spectral index would be additionally related to the friction parameter ν0 by nT=-3ν0-r/8. In some cases, the future experiments will be able to distinguish this relation from the standard one. In sum, primordial gravitational waves provide a complementary avenue to test gravity theories.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/27120169','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/27120169"><span>Susceptibility <span class="hlt">tensor</span> imaging (STI) of the brain.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Li, Wei; Liu, Chunlei; Duong, Timothy Q; van Zijl, Peter C M; Li, Xu</p> <p>2017-04-01</p> <p>Susceptibility <span class="hlt">tensor</span> imaging (STI) is a recently developed MRI technique that allows quantitative determination of orientation-independent magnetic susceptibility parameters from the dependence of gradient echo signal phase on the orientation of biological tissues with respect to the main magnetic field. By modeling the magnetic susceptibility of each voxel as a symmetric rank-2 <span class="hlt">tensor</span>, individual magnetic susceptibility <span class="hlt">tensor</span> elements as well as the mean magnetic susceptibility and magnetic susceptibility anisotropy can be determined for brain tissues that would still show orientation dependence after conventional scalar-based quantitative susceptibility mapping to remove such dependence. Similar to diffusion <span class="hlt">tensor</span> imaging, STI allows mapping of brain white matter fiber orientations and reconstruction of 3D white matter pathways using the principal eigenvectors of the susceptibility <span class="hlt">tensor</span>. In contrast to diffusion anisotropy, the main determinant factor of the susceptibility anisotropy in brain white matter is myelin. Another unique feature of the susceptibility anisotropy of white matter is its sensitivity to gadolinium-based contrast agents. Mechanistically, MRI-observed susceptibility anisotropy is mainly attributed to the highly ordered lipid molecules in the myelin sheath. STI provides a consistent interpretation of the dependence of phase and susceptibility on orientation at multiple scales. This article reviews the key experimental findings and physical theories that led to the development of STI, its practical implementations, and its applications for brain research. Copyright © 2016 John Wiley & Sons, Ltd.</p> </li> </ol> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_12");'>12</a></li> <li><a href="#" onclick='return showDiv("page_13");'>13</a></li> <li class="active"><span>14</span></li> <li><a href="#" onclick='return showDiv("page_15");'>15</a></li> <li><a href="#" onclick='return showDiv("page_16");'>16</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div><!-- col-sm-12 --> </div><!-- row --> </div><!-- page_14 --> <div id="page_15" class="hiddenDiv"> <div class="row"> <div class="col-sm-12"> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_13");'>13</a></li> <li><a href="#" onclick='return showDiv("page_14");'>14</a></li> <li class="active"><span>15</span></li> <li><a href="#" onclick='return showDiv("page_16");'>16</a></li> <li><a href="#" onclick='return showDiv("page_17");'>17</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div> </div> <div class="row"> <div class="col-sm-12"> <ol class="result-class" start="281"> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/7025476','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/7025476"><span>Physics and numerics of the <span class="hlt">tensor</span> code (incomplete preliminary documentation)</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Burton, D.E.; Lettis, L.A. Jr.; Bryan, J.B.; Frary, N.R.</p> <p>1982-07-15</p> <p>The present <span class="hlt">TENSOR</span> code is a descendant of a code originally conceived by Maenchen and Sack and later adapted by Cherry. Originally, the code was a two-dimensional Lagrangian explicit finite difference code which solved the equations of continuum mechanics. Since then, implicit and arbitrary Lagrange-Euler (ALE) algorithms have been added. The code has been used principally to solve problems involving the propagation of <span class="hlt">stress</span> waves through earth materials, and considerable development of rock and soil constitutive relations has been done. The code has been applied extensively to the containment of underground nuclear tests, nuclear and high explosive surface and subsurface cratering, and energy and resource recovery. <span class="hlt">TENSOR</span> is supported by a substantial array of ancillary routines. The initial conditions are set up by a generator code TENGEN. ZON is a multipurpose code which can be used for zoning, rezoning, overlaying, and linking from other codes. Linking from some codes is facilitated by another code RADTEN. TENPLT is a fixed time graphics code which provides a wide variety of plotting options and output devices, and which is capable of producing computer movies by postprocessing problem dumps. Time history graphics are provided by the TIMPLT code from temporal dumps produced during production runs. While <span class="hlt">TENSOR</span> can be run as a stand-alone controllee, a special controller code TCON is available to better interface the code with the LLNL computer system during production jobs. In order to standardize compilation procedures and provide quality control, a special compiler code BC is used. A number of equation of state generators are available among them ROC and PMUGEN.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/1992GeoJI.111..159R','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/1992GeoJI.111..159R"><span>Spectral analysis of the full gravity <span class="hlt">tensor</span></span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Rummel, R.; van Gelderen, M.</p> <p>1992-10-01</p> <p>It is shown that, when the five independent components of the gravity <span class="hlt">tensor</span> are grouped into (Gamma-zz), (Gamma-xz, Gamma-yz), and (Gamma-xx - Gamma-yy, 2Gamma-xy) sets and expanded into an infinite series of pure-spin spherical harmonic <span class="hlt">tensors</span>, it is possible to derive simple eigenvalue connections between these three sets and the spherical harmonic expansion of the gravity potential. The three eigenvalues are (n + 1)(n + 2), -(n + 2) sq rt of n(n + 1), and sq rt of (n - 1)n(n + 1)(n + 2). The joint ESA and NASA Aristoteles mission is designed to measure with high precision the <span class="hlt">tensor</span> components Gamma-zz, Gamma-yz, and Gamma-yy, which will make it possible to determine the global gravity field in six months time with a high precision.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017EJPh...38b5801E','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017EJPh...38b5801E"><span>Combinatorics in <span class="hlt">tensor</span>-integral reduction</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Ee, June-Haak; Jung, Dong-Won; Kim, U.-Rae; Lee, Jungil</p> <p>2017-03-01</p> <p>We illustrate a rigorous approach to express the totally symmetric isotropic <span class="hlt">tensors</span> of arbitrary rank in the n-dimensional Euclidean space as a linear combination of products of Kronecker deltas. By making full use of the symmetries, one can greatly reduce the efforts to compute cumbersome angular integrals into straightforward combinatoric counts. This method is generalised into the cases in which such symmetries are present in subspaces. We further demonstrate the mechanism of the <span class="hlt">tensor</span>-integral reduction that is widely used in various physics problems such as perturbative calculations of the gauge-field theory in which divergent integrals are regularised in d=4-2ɛ space-time dimensions. The main derivation is given in the n-dimensional Euclidean space. The generalisation of the result to the Minkowski space is also discussed in order to provide graduate students and researchers with techniques of <span class="hlt">tensor</span>-integral reduction for particle physics problems.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=4239671','PMC'); return false;" href="https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=4239671"><span>Diffusion <span class="hlt">tensor</span> smoothing through weighted Karcher means</span></a></p> <p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pmc">PubMed Central</a></p> <p>Carmichael, Owen; Chen, Jun; Paul, Debashis; Peng, Jie</p> <p>2014-01-01</p> <p>Diffusion <span class="hlt">tensor</span> magnetic resonance imaging (MRI) quantifies the spatial distribution of water Diffusion at each voxel on a regular grid of locations in a biological specimen by Diffusion tensors– 3 × 3 positive definite matrices. Removal of noise from DTI is an important problem due to the high scientific relevance of DTI and relatively low signal to noise ratio it provides. Leading approaches to this problem amount to estimation of weighted Karcher means of Diffusion <span class="hlt">tensors</span> within spatial neighborhoods, under various metrics imposed on the space of <span class="hlt">tensors</span>. However, it is unclear how the behavior of these estimators varies with the magnitude of DTI sensor noise (the noise resulting from the thermal e!ects of MRI scanning) as well as the geometric structure of the underlying Diffusion <span class="hlt">tensor</span> neighborhoods. In this paper, we combine theoretical analysis, empirical analysis of simulated DTI data, and empirical analysis of real DTI scans to compare the noise removal performance of three kernel-based DTI smoothers that are based on Euclidean, log-Euclidean, and affine-invariant metrics. The results suggest, contrary to conventional wisdom, that imposing a simplistic Euclidean metric may in fact provide comparable or superior noise removal, especially in relatively unstructured regions and/or in the presence of moderate to high levels of sensor noise. On the contrary, log-Euclidean and affine-invariant metrics may lead to better noise removal in highly structured anatomical regions, especially when the sensor noise is of low magnitude. These findings emphasize the importance of considering the interplay of sensor noise magnitude and <span class="hlt">tensor</span> field geometric structure when assessing Diffusion <span class="hlt">tensor</span> smoothing options. They also point to the necessity for continued development of smoothing methods that perform well across a large range of scenarios. PMID:25419264</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/scitech/biblio/21250525','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/21250525"><span><span class="hlt">Quantum</span> fields near phantom-energy ''sudden'' singularities</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Calderon, Hector H.</p> <p>2008-08-15</p> <p>This paper is committed to calculations near a type of future singularity driven by phantom energy. At the singularities considered, the scale factor remains finite but its derivative diverges. The general behavior of barotropic phantom energy producing this singularity is calculated under the assumption that near the singularity such fluid is the dominant contributor. We use the semiclassical formula for renormalized <span class="hlt">stress</span> <span class="hlt">tensors</span> of conformally invariant fields in conformally flat spacetimes and analyze the softening/enhancing of the singularity due to <span class="hlt">quantum</span> vacuum contributions. This dynamical analysis is then compared to results from thermodynamical considerations. In both cases, the vacuum states of quantized scalar and spinor fields strengthen the accelerating expansion near the singularity whereas the vacuum states of vector fields weaken it.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/27058099','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/27058099"><span>Raman <span class="hlt">Tensor</span> Formalism for Optically Anisotropic Crystals.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Kranert, Christian; Sturm, Chris; Schmidt-Grund, Rüdiger; Grundmann, Marius</p> <p>2016-03-25</p> <p>We present a formalism for calculating the Raman scattering intensity dependent on the polarization configuration for optically anisotropic crystals. It can be applied to crystals of arbitrary orientation and crystal symmetry measured in normal incidence backscattering geometry. The classical Raman <span class="hlt">tensor</span> formalism cannot be used for optically anisotropic materials due to birefringence causing the polarization within the crystal to be depth dependent. We show that in the limit of averaging over a sufficiently large scattering depth, the observed Raman intensities converge and can be described by an effective Raman <span class="hlt">tensor</span> given here. Full agreement with experimental results for uniaxial and biaxial crystals is demonstrated.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/scitech/biblio/21541603','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/21541603"><span><span class="hlt">Tensor</span> mesons produced in tau lepton decays</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Lopez Castro, G.; Munoz, J. H.</p> <p>2011-05-01</p> <p>Light <span class="hlt">tensor</span> mesons (T=a{sub 2}, f{sub 2} and K{sub 2}*) can be produced in decays of {tau} leptons. In this paper we compute the branching ratios of {tau}{yields}T{pi}{nu} decays by assuming the dominance of intermediate virtual states to model the form factors involved in the relevant hadronic matrix elements. The exclusive f{sub 2}(1270){pi}{sup -} decay mode turns out to have the largest branching ratio, of O(10{sup -4}). Our results indicate that the contribution of <span class="hlt">tensor</span> meson intermediate states to the three-pseudoscalar channels of {tau} decays are rather small.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/scitech/biblio/21420967','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/21420967"><span><span class="hlt">Quantum</span> corrected spherical collapse: A phenomenological framework</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Ziprick, Jonathan; Kunstatter, Gabor</p> <p>2010-08-15</p> <p>A phenomenological framework is presented for incorporating <span class="hlt">quantum</span> gravity motivated corrections into the dynamics of spherically symmetric collapse. The effective equations are derived from a variational principle that guarantees energy conservation and the existence of a Birkhoff theorem. The gravitational potential can be chosen as a function of the areal radius to yield specific nonsingular static spherically symmetric solutions that generically have two horizons. For a specific choice of potential, the effective <span class="hlt">stress</span> energy <span class="hlt">tensor</span> violates only the dominant energy condition. The violations are maximum near the inner horizon and die off rapidly. A numerical study of the <span class="hlt">quantum</span> corrected collapse of a spherically symmetric scalar field in this case reveals that the modified gravitational potential prevents the formation of a central singularity and ultimately yields a static, mostly vacuum, spacetime with two horizons. The matter 'piles up' on the inner horizon giving rise to mass inflation at late times. The Cauchy horizon is transformed into a null, weak singularity, but in contrast to Einstein gravity, the absence of a central singularity renders this null singularity stable.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2007SIGMA...3..089H','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2007SIGMA...3..089H"><span>The Symmetric <span class="hlt">Tensor</span> Lichnerowicz Algebra and a Novel Associative Fourier-Jacobi Algebra</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Hallowell, Karl; Waldron, Andrew</p> <p>2007-09-01</p> <p>Lichnerowicz's algebra of differential geometric operators acting on symmetric <span class="hlt">tensors</span> can be obtained from generalized geodesic motion of an observer carrying a complex tangent vector. This relation is based upon quantizing the classical evolution equations, and identifying wavefunctions with sections of the symmetric <span class="hlt">tensor</span> bundle and Noether charges with geometric operators. In general curved spaces these operators obey a deformation of the Fourier-Jacobi Lie algebra of sp(2,R). These results have already been generalized by the authors to arbitrary <span class="hlt">tensor</span> and spinor bundles using supersymmetric <span class="hlt">quantum</span> mechanical models and have also been applied to the theory of higher spin particles. These Proceedings review these results in their simplest, symmetric <span class="hlt">tensor</span> setting. New results on a novel and extremely useful reformulation of the rank 2 deformation of the Fourier-Jacobi Lie algebra in terms of an associative algebra are also presented. This new algebra! was originally motivated by studies of operator orderings in enveloping algebras. It provides a new method that is superior in many respects to common techniques such as Weyl or normal ordering.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/1999CompM..24..187B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/1999CompM..24..187B"><span>Large strain elastic-plastic theory and nonlinear finite element analysis based on metric transformation <span class="hlt">tensors</span></span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Brünig, M.</p> <p></p> <p>The present paper is concerned with an efficient framework for a nonlinear finite element procedure for the rate-independent finite strain analysis of solids undergoing large elastic-plastic deformations. The formulation relies on the introduction of a mixed-variant metric transformation <span class="hlt">tensor</span> which will be multiplicatively decomposed into a plastic and an elastic part. This leads to the definition of an appropriate logarithmic strain measure whose rate is shown to be additively decomposed into elastic and plastic strain rate <span class="hlt">tensors</span>. The mixed-variant logarithmic elastic strain <span class="hlt">tensor</span> provides a basis for the definition of a local isotropic hyperelastic <span class="hlt">stress</span> response in the elastic-plastic solid. Additionally, the plastic material behavior is assumed to be governed by a generalized J2 yield criterion and rate-independent isochoric plastic strain rates are computed using an associated flow rule. On the numerical side, the computation of the logarithmic strain <span class="hlt">tensors</span> is based on 1st and higher order Padé approximations. Estimates of the <span class="hlt">stress</span> and strain histories are obtained via a highly stable and accurate explicit scalar integration procedure which employs a plastic predictor followed by an elastic corrector step. The development of a consistent elastic-plastic tangent operator as well as its implementation into a nonlinear finite element program will also be discussed. Finally, the numerical solution of finite strain elastic-plastic problems is presented to demonstrate the efficiency of the algorithm.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2007MeSol..42..883U','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2007MeSol..42..883U"><span>Irreducible <span class="hlt">tensors</span> and their applications in problems of dynamics of solids</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Urman, Yu. M.</p> <p>2007-12-01</p> <p>One difficulty encountered in solving mechanical problems with complicated interaction is to express either the moments of forces or the force function via the phase variables of the problem. Here various transformations of coordinate systems are used, because interactions are determined by a relation between <span class="hlt">tensor</span> variables one of which refers to the body and the other refers to the field. In this connection, the usual definition of a <span class="hlt">tensor</span> in Cartesian coordinates is inconvenient because of the fact that the components of a <span class="hlt">tensor</span> of rank l ≥ 2 can be arranged as several linear combinations that behave differently under rotations of the coordinate system. Naturally, one needs to define <span class="hlt">tensors</span> in such a way that their components and linear combinations of these be transformed in a unified manner under rotations of the coordinate system. This requirement is satisfied by irreducible <span class="hlt">tensors</span>. The mathematical apparatus of irreducible <span class="hlt">tensors</span> was created to satisfy the requirements of <span class="hlt">quantum</span> mechanics and turned out to be rather universal. As far as the author knows, this apparatus was first used in mechanics by G. G. Denisov and the author of the present paper [1]. Using this apparatus, one can see the clear physical meaning of complicated interactions, express these interactions in invariant form, easily perform transformations from one coordinate system to another coordinate system turned relative to the first, consider rather complicated types of interactions writing them in compact form explicitly depending on the phase variables of the problem, easily use the symmetry of both the rigid body and the force field structure, and perform the averaging procedure for the entire object rather than componentwise. The present paper further develops the paper [1]. We present a brief introduction to the theory of irreducible <span class="hlt">tensors</span>. We show that the force function of various interactions between a rigid body and a force field can be represented as the scalar product</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017PhRvD..95a4024C','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017PhRvD..95a4024C"><span>Finite-width Laplacian sum rules for 2++ <span class="hlt">tensor</span> glueball in the instanton vacuum model</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Chen, Junlong; Liu, Jueping</p> <p>2017-01-01</p> <p>The more carefully defined and more appropriate 2++ <span class="hlt">tensor</span> glueball current is a S Uc(3 ) gauge-invariant, symmetric, traceless, and conserved Lorentz-irreducible <span class="hlt">tensor</span>. After Lorentz decomposition, the invariant amplitude of the correlation function is abstracted and calculated based on the semiclassical expansion for <span class="hlt">quantum</span> chromodynamics (QCD) in the instanton liquid background. In addition to taking the perturbative contribution into account, we calculate the contribution arising from the interaction (or the interference) between instantons and the <span class="hlt">quantum</span> gluon fields, which is infrared free. Instead of the usual zero-width approximation for the resonances, the Breit-Wigner form with a correct threshold behavior for the spectral function of the finite-width three resonances is adopted. The properties of the 2++ <span class="hlt">tensor</span> glueball are investigated via a family of the QCD Laplacian sum rules for the invariant amplitude. The values of the mass, decay width, and coupling constants for the 2++ resonance in which the glueball fraction is dominant are obtained.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19900019806','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19900019806"><span>Second order <span class="hlt">tensor</span> finite element</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Oden, J. Tinsley; Fly, J.; Berry, C.; Tworzydlo, W.; Vadaketh, S.; Bass, J.</p> <p>1990-01-01</p> <p>The results of a research and software development effort are presented for the finite element modeling of the static and dynamic behavior of anisotropic materials, with emphasis on single crystal alloys. Various versions of two dimensional and three dimensional hybrid finite elements were implemented and compared with displacement-based elements. Both static and dynamic cases are considered. The hybrid elements developed in the project were incorporated into the SPAR finite element code. In an extension of the first phase of the project, optimization of experimental tests for anisotropic materials was addressed. In particular, the problem of calculating material properties from tensile tests and of calculating <span class="hlt">stresses</span> from strain measurements were considered. For both cases, numerical procedures and software for the optimization of strain gauge and material axes orientation were developed.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016EPJWC.12503021T','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016EPJWC.12503021T"><span>Horndeski scalar-<span class="hlt">tensor</span> black hole geodesics</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Tretyakova, Darya; Melkoserov, Dmitry; Adyev, Timur</p> <p>2016-10-01</p> <p>We examine massive particles and null geodesics for the scalar-<span class="hlt">tensor</span> black hole in the Horndeski-Galileon framework. Our analysis shows that first kind relativistic orbits, corresponding to circular and elliptic orbits, are absent for the black hole solution with the static scalar field. This is a highly pathological behavior contradicting to the black hole accretion and Solar System observations.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016JCAP...09..041B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016JCAP...09..041B"><span><span class="hlt">Tensor</span> squeezed limits and the Higuchi bound</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Bordin, Lorenzo; Creminelli, Paolo; Mirbabayi, Mehrdad; Noreña, Jorge</p> <p>2016-09-01</p> <p>We point out that <span class="hlt">tensor</span> consistency relations—i.e. the behavior of primordial correlation functions in the limit a <span class="hlt">tensor</span> mode has a small momentum—are more universal than scalar consistency relations. They hold in the presence of multiple scalar fields and as long as anisotropies are diluted exponentially fast. When de Sitter isometries are approximately respected during inflation this is guaranteed by the Higuchi bound, which forbids the existence of light particles with spin: de Sitter space can support scalar hair but no curly hair. We discuss two indirect ways to look for the violation of <span class="hlt">tensor</span> consistency relations in observations, as a signature of models in which inflation is not a strong isotropic attractor, such as solid inflation: (a) graviton exchange contribution to the scalar four-point function; (b) quadrupolar anisotropy of the scalar power spectrum due to super-horizon <span class="hlt">tensor</span> modes. This anisotropy has a well-defined statistics which can be distinguished from cases in which the background has a privileged direction.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/16848448','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/16848448"><span>Multiple alignment <span class="hlt">tensors</span> from a denatured protein.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Gebel, Erika B; Ruan, Ke; Tolman, Joel R; Shortle, David</p> <p>2006-07-26</p> <p>The structural content of the denatured state has yet to be fully characterized. In recent years, large residual dipolar couplings (RDCs) from denatured proteins have been observed under alignment conditions produced by bicelles and strained polyacrylamide gels. In this report, we describe efforts to extend our picture of the residual structure in denatured nuclease by measuring RDCs with multiple alignment <span class="hlt">tensors</span>. Backbone amide 15N-1H RDCs were collected from 4 M urea for a total of eight RDC data sets. The RDCs were analyzed by singular value decomposition (SVD) to determine the number of independent alignment <span class="hlt">tensors</span> present in the data. On the basis of the resultant singular values and propagated error estimates, it is clear that there are at least three independent alignment <span class="hlt">tensors</span>. These three independent RDC datasets can be reconstituted as orthogonal linear combinations, (OLC)-RDC datasets, of the eight actually recorded. The first, second, and third OLC-RDC datasets are highly robust to the removal of any single experimental RDC dataset, establishing the presence of three independent alignment <span class="hlt">tensors</span>, sampled well above the level of experimental uncertainty. The observation that the RDC data span three or more dimensions of the five-dimensional parameter space demonstrates that the ensemble average structure of denatured nuclease must be asymmetric with respect to these three orthogonal principal axes, which is not inconsistent with earlier work demonstrating that it has a nativelike topology.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/scitech/biblio/21409022','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/21409022"><span>Spacetime encodings. III. Second order Killing <span class="hlt">tensors</span></span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Brink, Jeandrew</p> <p>2010-01-15</p> <p>This paper explores the Petrov type D, stationary axisymmetric vacuum (SAV) spacetimes that were found by Carter to have separable Hamilton-Jacobi equations, and thus admit a second-order Killing <span class="hlt">tensor</span>. The derivation of the spacetimes presented in this paper borrows from ideas about dynamical systems, and illustrates concepts that can be generalized to higher-order Killing <span class="hlt">tensors</span>. The relationship between the components of the Killing equations and metric functions are given explicitly. The origin of the four separable coordinate systems found by Carter is explained and classified in terms of the analytic structure associated with the Killing equations. A geometric picture of what the orbital invariants may represent is built. Requiring that a SAV spacetime admits a second-order Killing <span class="hlt">tensor</span> is very restrictive, selecting very few candidates from the group of all possible SAV spacetimes. This restriction arises due to the fact that the consistency conditions associated with the Killing equations require that the field variables obey a second-order differential equation, as opposed to a fourth-order differential equation that imposes the weaker condition that the spacetime be SAV. This paper introduces ideas that could lead to the explicit computation of more general orbital invariants in the form of higher-order Killing <span class="hlt">tensors</span>.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=2824084','PMC'); return false;" href="https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=2824084"><span>Efficient Anisotropic Filtering of Diffusion <span class="hlt">Tensor</span> Images</span></a></p> <p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pmc">PubMed Central</a></p> <p>Xu, Qing; Anderson, Adam W.; Gore, John C.; Ding, Zhaohua</p> <p>2009-01-01</p> <p>To improve the accuracy of structural and architectural characterization of living tissue with diffusion <span class="hlt">tensor</span> imaging, an efficient smoothing algorithm is presented for reducing noise in diffusion <span class="hlt">tensor</span> images. The algorithm is based on anisotropic diffusion filtering, which allows both image detail preservation and noise reduction. However, traditional numerical schemes for anisotropic filtering have the drawback of inefficiency and inaccuracy due to their poor stability and first order time accuracy. To address this, an unconditionally stable and second order time accuracy semi-implicit Craig-Sneyd scheme is adapted in our anisotropic filtering. By using large step size, unconditional stability allows this scheme to take much fewer iterations and thus less computation time than the explicit scheme to achieve a certain degree of smoothing. Second order time accuracy makes the algorithm reduce noise more effectively than a first order scheme with the same total iteration time. Both the efficiency and effectiveness are quantitatively evaluated based on synthetic and in vivo human brain diffusion <span class="hlt">tensor</span> images, and these tests demonstrate that our algorithm is an efficient and effective tool for denoising diffusion <span class="hlt">tensor</span> images. PMID:20061113</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/scitech/biblio/653473','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/653473"><span>Investigation of the permeability <span class="hlt">tensor</span> of electrical steel sheet</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Birkfeld, M.</p> <p>1998-09-01</p> <p>The permeability <span class="hlt">tensor</span> is a mathematical model for the description of the electro-magnetic behavior of electrical silicon iron steel sheet under two-dimensional magnetizing conditions. In this paper, an interpretation of the properties of this <span class="hlt">tensor</span> is given, the investigation of the <span class="hlt">tensor</span> elements from measurements under two-dimensional magnetizing conditions is described, and some examples of measurements and the corresponding permeability <span class="hlt">tensor</span> elements are indicated.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=58792','PMC'); return false;" href="https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=58792"><span>Conductivity <span class="hlt">tensor</span> mapping of the human brain using diffusion <span class="hlt">tensor</span> MRI</span></a></p> <p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pmc">PubMed Central</a></p> <p>Tuch, David S.; Wedeen, Van J.; Dale, Anders M.; George, John S.; Belliveau, John W.</p> <p>2001-01-01</p> <p>Knowledge of the electrical conductivity properties of excitable tissues is essential for relating the electromagnetic fields generated by the tissue to the underlying electrophysiological currents. Efforts to characterize these endogenous currents from measurements of the associated electromagnetic fields would significantly benefit from the ability to measure the electrical conductivity properties of the tissue noninvasively. Here, using an effective medium approach, we show how the electrical conductivity <span class="hlt">tensor</span> of tissue can be quantitatively inferred from the water self-diffusion <span class="hlt">tensor</span> as measured by diffusion <span class="hlt">tensor</span> magnetic resonance imaging. The effective medium model indicates a strong linear relationship between the conductivity and diffusion <span class="hlt">tensor</span> eigenvalues (respectively, σ and d) in agreement with theoretical bounds and experimental measurements presented here (σ/d ≈ 0.844 ± 0.0545 S⋅s/mm3, r2 = 0.945). The extension to other biological transport phenomena is also discussed. PMID:11573005</p> </li> </ol> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_13");'>13</a></li> <li><a href="#" onclick='return showDiv("page_14");'>14</a></li> <li class="active"><span>15</span></li> <li><a href="#" onclick='return showDiv("page_16");'>16</a></li> <li><a href="#" onclick='return showDiv("page_17");'>17</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div><!-- col-sm-12 --> </div><!-- row --> </div><!-- page_15 --> <div id="page_16" class="hiddenDiv"> <div class="row"> <div class="col-sm-12"> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_14");'>14</a></li> <li><a href="#" onclick='return showDiv("page_15");'>15</a></li> <li class="active"><span>16</span></li> <li><a href="#" onclick='return showDiv("page_17");'>17</a></li> <li><a href="#" onclick='return showDiv("page_18");'>18</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div> </div> <div class="row"> <div class="col-sm-12"> <ol class="result-class" start="301"> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017PhRvB..95d5112S','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017PhRvB..95d5112S"><span>Kitaev honeycomb <span class="hlt">tensor</span> networks: Exact unitary circuits and applications</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Schmoll, Philipp; Orús, Román</p> <p>2017-01-01</p> <p>The Kitaev honeycomb model is a paradigm of exactly solvable models, showing nontrivial physical properties such as topological <span class="hlt">quantum</span> order, Abelian and non-Abelian anyons, and chirality. Its solution is one of the most beautiful examples of the interplay of different mathematical techniques in condensed matter physics. In this paper, we show how to derive a <span class="hlt">tensor</span> network (TN) description of the eigenstates of this spin-1/2 model in the thermodynamic limit, and in particular for its ground state. In our setting, eigenstates are naturally encoded by an exact 3d TN structure made of fermionic unitary operators, corresponding to the unitary <span class="hlt">quantum</span> circuit building up the many-body <span class="hlt">quantum</span> state. In our derivation we review how the different "solution ingredients" of the Kitaev honeycomb model can be accounted for in the TN language, namely, Jordan-Wigner transformation, braidings of Majorana modes, fermionic Fourier transformation, and Bogoliubov transformation. The TN built in this way allows for a clear understanding of several properties of the model. In particular, we show how the fidelity diagram is straightforward both at zero temperature and at finite temperature in the vortex-free sector. We also show how the properties of two-point correlation functions follow easily. Finally, we also discuss the pros and cons of contracting of our 3d TN down to a 2d projected entangled pair state (PEPS) with finite bond dimension. The results in this paper can be extended to generalizations of the Kitaev model, e.g., to other lattices, spins, and dimensions.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2013PhDT.......300K','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2013PhDT.......300K"><span>Multidimensional seismic data reconstruction using <span class="hlt">tensor</span> analysis</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Kreimer, Nadia</p> <p></p> <p>Exploration seismology utilizes the seismic wavefield for prospecting oil and gas. The seismic reflection experiment consists on deploying sources and receivers in the surface of an area of interest. When the sources are activated, the receivers measure the wavefield that is reflected from different subsurface interfaces and store the information as time-series called traces or seismograms. The seismic data depend on two source coordinates, two receiver coordinates and time (a 5D volume). Obstacles in the field, logistical and economical factors constrain seismic data acquisition. Therefore, the wavefield sampling is incomplete in the four spatial dimensions. Seismic data undergoes different processes. In particular, the reconstruction process is responsible for correcting sampling irregularities of the seismic wavefield. This thesis focuses on the development of new methodologies for the reconstruction of multidimensional seismic data. This thesis examines techniques based on <span class="hlt">tensor</span> algebra and proposes three methods that exploit the <span class="hlt">tensor</span> nature of the seismic data. The fully sampled volume is low-rank in the frequency-space domain. The rank increases when we have missing traces and/or noise. The methods proposed perform rank reduction on frequency slices of the 4D spatial volume. The first method employs the Higher-Order Singular Value Decomposition (HOSVD) immersed in an iterative algorithm that reinserts weighted observations. The second method uses a sequential truncated SVD on the unfoldings of the <span class="hlt">tensor</span> slices (SEQ-SVD). The third method formulates the rank reduction problem as a convex optimization problem. The measure of the rank is replaced by the nuclear norm of the <span class="hlt">tensor</span> and the alternating direction method of multipliers (ADMM) minimizes the cost function. All three methods have the interesting property that they are robust to curvature of the reflections, unlike many reconstruction methods. Finally, we present a comparison between the methods</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016PhRvC..93e4617S','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016PhRvC..93e4617S"><span>Skyrme <span class="hlt">tensor</span> force in heavy ion collisions</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Stevenson, P. D.; Suckling, E. B.; Fracasso, S.; Barton, M. C.; Umar, A. S.</p> <p>2016-05-01</p> <p>Background: It is generally acknowledged that the time-dependent Hartree-Fock (TDHF) method provides a useful foundation for a fully microscopic many-body theory of low-energy heavy ion reactions. The TDHF method is also known in nuclear physics in the small-amplitude domain, where it provides a useful description of collective states, and is based on the mean-field formalism, which has been a relatively successful approximation to the nuclear many-body problem. Currently, the TDHF theory is being widely used in the study of fusion excitation functions, fission, and deep-inelastic scattering of heavy mass systems, while providing a natural foundation for many other studies. Purpose: With the advancement of computational power it is now possible to undertake TDHF calculations without any symmetry assumptions and incorporate the major strides made by the nuclear structure community in improving the energy density functionals used in these calculations. In particular, time-odd and <span class="hlt">tensor</span> terms in these functionals are naturally present during the dynamical evolution, while being absent or minimally important for most static calculations. The parameters of these terms are determined by the requirement of Galilean invariance or local gauge invariance but their significance for the reaction dynamics have not been fully studied. This work addresses this question with emphasis on the <span class="hlt">tensor</span> force. Method: The full version of the Skyrme force, including terms arising only from the Skyrme <span class="hlt">tensor</span> force, is applied to the study of collisions within a completely symmetry-unrestricted TDHF implementation. Results: We examine the effect on upper fusion thresholds with and without the <span class="hlt">tensor</span> force terms and find an effect on the fusion threshold energy of the order several MeV. Details of the distribution of the energy within terms in the energy density functional are also discussed. Conclusions: Terms in the energy density functional linked to the <span class="hlt">tensor</span> force can play a non</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/scitech/biblio/21612769','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/21612769"><span>On stability of diagonal actions and <span class="hlt">tensor</span> invariants</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Anisimov, Artem B</p> <p>2012-04-30</p> <p>For a connected simply connected semisimple algebraic group G we prove the existence of invariant <span class="hlt">tensors</span> in certain <span class="hlt">tensor</span> powers of rational G-modules and establish relations between the existence of such invariant <span class="hlt">tensors</span> and stability of diagonal actions of G on affine algebraic varieties. Bibliography: 12 titles.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/897641','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/897641"><span>Efficient MATLAB computations with sparse and factored <span class="hlt">tensors</span>.</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Bader, Brett William; Kolda, Tamara Gibson (Sandia National Lab, Livermore, CA)</p> <p>2006-12-01</p> <p>In this paper, the term <span class="hlt">tensor</span> refers simply to a multidimensional or N-way array, and we consider how specially structured <span class="hlt">tensors</span> allow for efficient storage and computation. First, we study sparse <span class="hlt">tensors</span>, which have the property that the vast majority of the elements are zero. We propose storing sparse <span class="hlt">tensors</span> using coordinate format and describe the computational efficiency of this scheme for various mathematical operations, including those typical to <span class="hlt">tensor</span> decomposition algorithms. Second, we study factored <span class="hlt">tensors</span>, which have the property that they can be assembled from more basic components. We consider two specific types: a Tucker <span class="hlt">tensor</span> can be expressed as the product of a core <span class="hlt">tensor</span> (which itself may be dense, sparse, or factored) and a matrix along each mode, and a Kruskal <span class="hlt">tensor</span> can be expressed as the sum of rank-1 <span class="hlt">tensors</span>. We are interested in the case where the storage of the components is less than the storage of the full <span class="hlt">tensor</span>, and we demonstrate that many elementary operations can be computed using only the components. All of the efficiencies described in this paper are implemented in the <span class="hlt">Tensor</span> Toolbox for MATLAB.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2011JMP....52g3514T','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2011JMP....52g3514T"><span>Generalization of the Bollobás-Riordan polynomial for <span class="hlt">tensor</span> graphs</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Tanasa, Adrian</p> <p>2011-07-01</p> <p><span class="hlt">Tensor</span> models are used nowadays for implementing a fundamental theory of <span class="hlt">quantum</span> gravity. We define here a polynomial T encoding the supplementary topological information. This polynomial is a natural generalization of the Bollobás-Riordan polynomial (used to characterize matrix graphs) and is different from the Gurău polynomial [R. Gurău, Ann. Henri Poincare 11, 565 (2010)], 10.1007/s00023-010-0035-6, defined for a particular class of <span class="hlt">tensor</span> graphs, the colorable ones. The polynomial T is defined for both colorable and non-colorable graphs and it is proved to satisfy the deletion/contraction relation. A non-trivial example of a non-colorable graphs is analyzed.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/scitech/biblio/22525534','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/22525534"><span>Large <span class="hlt">tensor</span> mode, field range bound and consistency in generalized G-inflation</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Kunimitsu, Taro; Suyama, Teruaki; Watanabe, Yuki; Yokoyama, Jun'ichi E-mail: suyama@resceu.s.u-tokyo.ac.jp E-mail: yokoyama@resceu.s.u-tokyo.ac.jp</p> <p>2015-08-01</p> <p>We systematically show that in potential driven generalized G-inflation models, <span class="hlt">quantum</span> corrections coming from new physics at the strong coupling scale can be avoided, while producing observable <span class="hlt">tensor</span> modes. The effective action can be approximated by the tree level action, and as a result, these models are internally consistent, despite the fact that we introduced new mass scales below the energy scale of inflation. Although observable <span class="hlt">tensor</span> modes are produced with sub-strong coupling scale field excursions, this is not an evasion of the Lyth bound, since the models include higher-derivative non-canonical kinetic terms, and effective rescaling of the field would result in super-Planckian field excursions. We argue that the enhanced kinetic term of the inflaton screens the interactions with other fields, keeping the system weakly coupled during inflation.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/974887','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/974887"><span>A preliminary report on the development of MATLAB <span class="hlt">tensor</span> classes for fast algorithm prototyping.</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Bader, Brett William; Kolda, Tamara Gibson</p> <p>2004-07-01</p> <p>We describe three MATLAB classes for manipulating <span class="hlt">tensors</span> in order to allow fast algorithm prototyping. A <span class="hlt">tensor</span> is a multidimensional or N-way array. We present a <span class="hlt">tensor</span> class for manipulating <span class="hlt">tensors</span> which allows for <span class="hlt">tensor</span> multiplication and 'matricization.' We have further added two classes for representing <span class="hlt">tensors</span> in decomposed format: cp{_}<span class="hlt">tensor</span> and tucker{_}<span class="hlt">tensor</span>. We demonstrate the use of these classes by implementing several algorithms that have appeared in the literature.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19780024526','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19780024526"><span>Adding <span class="hlt">stress</span> plot function to NASTRAN</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Katoh, S.</p> <p>1978-01-01</p> <p><span class="hlt">Stress</span> plot function was developed and added to the NASTRAN level 15.5. Computed <span class="hlt">stress</span> distribution can be displayed by this function, with vectors showing the principal <span class="hlt">stresses</span> of the finite elements over the specified portions of the structure. NASTRAN is reviewed in the aspect of plotting capabilities. <span class="hlt">Stress</span> <span class="hlt">tensor</span> field is examined in preparation of <span class="hlt">stress</span> display. Then the <span class="hlt">stress</span> plot function as added to the NASTRAN is described. A sample plotout by this function is shown.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2011PhDT.......316K','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2011PhDT.......316K"><span><span class="hlt">Quantum</span> Field Theory and Decoherence in the Early Universe</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Koksma, J. F.</p> <p>2011-06-01</p> <p><span class="hlt">Quantum</span> field theory is indispensable for understanding many aspects of cosmology, both in the early Universe and today. For example, <span class="hlt">quantum</span> processes could be paramount to understand the nature of the mysterious dark energy resulting in the Universe’s recently observed accelerated expansion. Inspired by these considerations, this PhD thesis is concerned with two aspects of <span class="hlt">quantum</span> field theory relevant to cosmology: <span class="hlt">quantum</span> backreaction and decoherence. <span class="hlt">Quantum</span> backreaction is a line of research where the impact of <span class="hlt">quantum</span> fluctuations on the background spacetime geometry in perturbative <span class="hlt">quantum</span> gravity is investigated. The cosmological constant problem and the process of <span class="hlt">quantum</span> backreaction are intimately related: <span class="hlt">quantum</span> backreaction might provide us with a dynamical mechanism to effectively make the cosmological constant almost vanish. We investigate the <span class="hlt">quantum</span> backreaction of the trace anomaly and of fermions. We find that the trace anomaly does not dynamically influence the effective value of the cosmological constant. We furthermore evaluate the fermion propagator in FLRW spacetimes with constant deceleration. Although the dynamics resulting from the one-loop <span class="hlt">stress</span>-energy <span class="hlt">tensor</span> need yet to be investigated, we find that we certainly cannot exclude a significant effect due to the <span class="hlt">quantum</span> backreaction on the Universe’s expansion. Decoherence is a <span class="hlt">quantum</span> theory which addresses the <span class="hlt">quantum</span>-to-classical transition of a particular system. The idea of the decoherence formalism is that a macroscopic system cannot be separated from its environment. The framework of decoherence is widely used, e.g. in <span class="hlt">quantum</span> computing, black hole physics, inflationary perturbation theory, and in elementary particle physics, such as electroweak baryogenesis models. We formulate a novel “correlator approach” to decoherence: neglecting observationally inaccessible correlators gives rise to an increase in entropy of the system, as perceived by an observer. This is inspired</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/28179844','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/28179844"><span><span class="hlt">Quantum</span>-Spacetime Phenomenology.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Amelino-Camelia, Giovanni</p> <p>2013-01-01</p> <p>I review the current status of phenomenological programs inspired by <span class="hlt">quantum</span>-spacetime research. I <span class="hlt">stress</span> in particular the significance of results establishing that certain data analyses provide sensitivity to effects introduced genuinely at the Planck scale. My main focus is on phenomenological programs that affect the directions taken by studies of <span class="hlt">quantum</span>-spacetime theories.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2011AGUFM.S51A2202S','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2011AGUFM.S51A2202S"><span>Global moment <span class="hlt">tensor</span> computation at GFZ Potsdam</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Saul, J.; Becker, J.; Hanka, W.</p> <p>2011-12-01</p> <p>As part of its earthquake information service, GFZ Potsdam has started to provide seismic moment <span class="hlt">tensor</span> solutions for significant earthquakes world-wide. The software used to compute the moment <span class="hlt">tensors</span> is a GFZ-Potsdam in-house development, which uses the framework of the software SeisComP 3 (Hanka et al., 2010). SeisComP 3 (SC3) is a software package for seismological data acquisition, archival, quality control and analysis. SC3 is developed by GFZ Potsdam with significant contributions from its user community. The moment <span class="hlt">tensor</span> inversion technique uses a combination of several wave types, time windows and frequency bands depending on magnitude and station distance. Wave types include body, surface and mantle waves as well as the so-called 'W-Phase' (Kanamori and Rivera, 2008). The inversion is currently performed in the time domain only. An iterative centroid search can be performed independently both horizontally and in depth. Moment <span class="hlt">tensors</span> are currently computed in a semi-automatic fashion. This involves inversions that are performed automatically in near-real time, followed by analyst review prior to publication. The automatic results are quite often good enough to be published without further improvements, sometimes in less than 30 minutes from origin time. In those cases where a manual interaction is still required, the automatic inversion usually does a good job at pre-selecting those traces that are the most relevant for the inversion, keeping the work required for the analyst at a minimum. Our published moment <span class="hlt">tensors</span> are generally in good agreement with those published by the Global Centroid-Moment-<span class="hlt">Tensor</span> (GCMT) project for earthquakes above a magnitude of about Mw 5. Additionally we provide solutions for smaller earthquakes above about Mw 4 in Europe, which are normally not analyzed by the GCMT project. We find that for earthquakes above Mw 6, the most robust automatic inversions can usually be obtained using the W-Phase time window. The GFZ earthquake</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016PhRvD..94l3011L','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016PhRvD..94l3011L"><span>Testing gravity theories using <span class="hlt">tensor</span> perturbations</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Lin, Weikang; Ishak, Mustapha</p> <p>2016-12-01</p> <p>Primordial gravitational waves constitute a promising probe of the very early Universe and the laws of gravity. We study in this work changes to <span class="hlt">tensor</span>-mode perturbations that can arise in various proposed modified gravity theories. These include additional friction effects, nonstandard dispersion relations involving a massive graviton, a modified speed, and a small-scale modification. We introduce a physically motivated parametrization of these effects and use current available data to obtain exclusion regions in the parameter spaces. Taking into account the foreground subtraction, we then perform a forecast analysis focusing on the <span class="hlt">tensor</span>-mode modified-gravity parameters as constrained by the future experiments COrE, Stage-IV and PIXIE. For a fiducial value of the <span class="hlt">tensor</span>-to-scalar ratio r =0.01 , we find that an additional friction of 3.5-4.5% compared to GR will be detected at 3 -σ by these experiments, while a decrease in friction will be more difficult to detect. The speed of gravitational waves needs to be by 5-15% different from the speed of light for detection. We find that the minimum detectable graviton mass is about 7.8 - 9.7 ×10-33 eV , which is of the same order of magnitude as the graviton mass that allows massive gravity theories to produce late-time cosmic acceleration. Finally, we study the <span class="hlt">tensor</span>-mode perturbations in modified gravity during inflation using our parametrization. We find that, in addition to being related to r , the <span class="hlt">tensor</span> spectral index would be related to the friction parameter ν0 by nT=-3 ν0-r /8 . Assuming that the friction parameter is unchanged throughout the history of the Universe, and that ν0 is much larger than r , the future experiments considered here will be able to distinguish this modified-gravity consistency relation from the standard inflation consistency relation, and thus can be used as a further test of modified gravity. In summary, <span class="hlt">tensor</span>-mode perturbations and cosmic-microwave-background B</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/10109420','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/10109420"><span><span class="hlt">Quantum</span> corrections for a cosmological string solution</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Behrndt, K.</p> <p>1994-08-01</p> <p>The author investigates <span class="hlt">quantum</span> corrections for a cosmological solution of the string effective action. Starting point is a classical solution containing an antisymmetric <span class="hlt">tensor</span> field, a dilaton and a modulus field which has singularities in the scalar fields. As a first step he quantizes the scalar fields near the singularity with the result that the singularities disappear and that in general non-perturbative <span class="hlt">quantum</span> corrections form a potential in the scalar fields.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/1985AnPhy.162...31F','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/1985AnPhy.162...31F"><span><span class="hlt">Quantum</span> equivalence of dual field theories</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Fradkin, E. S.; Tseytlin, A. A.</p> <p>1985-06-01</p> <p>Motivated by the study of ultraviolet properties of different versions of supergravities duality transformations at the <span class="hlt">quantum</span> level are discussed. Using the background field method it is proven on shell <span class="hlt">quantum</span> equivalence for several pairs of dual field theories known to be classically equivalent. The examples considered include duality in chiral model, duality of scalars and second rank antisymmetric gauge <span class="hlt">tensors</span>, vector duality and duality of the Einstein theory with cosmological term and the Eddington-Schrödinger theory.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2002PhRvE..66d6417S','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2002PhRvE..66d6417S"><span>Analytic electrical-conductivity <span class="hlt">tensor</span> of a nondegenerate Lorentz plasma</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Stygar, W. A.; Gerdin, G. A.; Fehl, D. L.</p> <p>2002-10-01</p> <p>We have developed explicit <span class="hlt">quantum</span>-mechanical expressions for the conductivity and resistivity <span class="hlt">tensors</span> of a Lorentz plasma in a magnetic field. The expressions are based on a solution to the Boltzmann equation that is exact when the electric field is weak, the electron-Fermi-degeneracy parameter Θ>>1, and the electron-ion Coulomb-coupling parameter Γ/Z<<1. (Γ is the ion-ion coupling parameter and Z is the ion charge state.) Assuming a screened 1/r electron-ion scattering potential, we calculate the Coulomb logarithm in the second Born approximation. The ratio of the term obtained in the second approximation to that obtained in the first is used to define the parameter regime over which the calculation is valid. We find that the accuracy of the approximation is determined by Γ/Z and not simply the temperature, and that a <span class="hlt">quantum</span>-mechanical description can be required at temperatures orders of magnitude less than assumed by Spitzer [Physics of Fully Ionized Gases (Wiley, New York, 1962)]. When the magnetic field B=0, the conductivity is identical to the Spitzer result except the Coulomb logarithm ln Λ1=(ln χ1- 1/2)+[(2Ze2/λmev2e1)(ln χ1-ln 24/3)], where χ1≡2meve1λ/ħ, me is the electron mass, ve1≡(7kBT/me)1/2, kB is the Boltzmann constant, T is the temperature, λ is the screening length, ħ is Planck's constant divided by 2π, and e is the absolute value of the electron charge. When the plasma Debye length λD is greater than the ion-sphere radius a, we assume λ=λD otherwise we set λ=a. The B=0 conductivity is consistent with measurements when Z>~1, Θ>~2, and Γ/Z<~1, and in this parameter regime appears to be more accurate than previous analytic models. The minimum value of ln Λ1 when Z>=1, Θ>=2, and Γ/Z<=1 is 1.9. The expression obtained for the resistivity <span class="hlt">tensor</span> (B≠0) predicts that η⊥/η∥ (where η⊥ and η∥ are the resistivities perpendicular and parallel to the magnetic field) can be as much as 40% less than previous analytic</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19940019696','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19940019696"><span><span class="hlt">Tensoral</span> for post-processing users and simulation authors</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Dresselhaus, Eliot</p> <p>1993-01-01</p> <p>The CTR post-processing effort aims to make turbulence simulations and data more readily and usefully available to the research and industrial communities. The <span class="hlt">Tensoral</span> language, which provides the foundation for this effort, is introduced here in the form of a user's guide. The <span class="hlt">Tensoral</span> user's guide is presented in two main sections. Section one acts as a general introduction and guides database users who wish to post-process simulation databases. Section two gives a brief description of how database authors and other advanced users can make simulation codes and/or the databases they generate available to the user community via <span class="hlt">Tensoral</span> database back ends. The two-part structure of this document conforms to the two-level design structure of the <span class="hlt">Tensoral</span> language. <span class="hlt">Tensoral</span> has been designed to be a general computer language for performing <span class="hlt">tensor</span> calculus and statistics on numerical data. <span class="hlt">Tensoral</span>'s generality allows it to be used for stand-alone native coding of high-level post-processing tasks (as described in section one of this guide). At the same time, <span class="hlt">Tensoral</span>'s specialization to a minute task (namely, to numerical <span class="hlt">tensor</span> calculus and statistics) allows it to be easily embedded into applications written partly in <span class="hlt">Tensoral</span> and partly in other computer languages (here, C and Vectoral). Embedded <span class="hlt">Tensoral</span>, aimed at advanced users for more general coding (e.g. of efficient simulations, for interfacing with pre-existing software, for visualization, etc.), is described in section two of this guide.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017PhRvD..95c6011M','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017PhRvD..95c6011M"><span>Local effects of the <span class="hlt">quantum</span> vacuum in Lorentz-violating electrodynamics</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Martín-Ruiz, A.; Escobar, C. A.</p> <p>2017-02-01</p> <p>The Casimir effect is one of the most remarkable consequences of the nonzero vacuum energy predicted by <span class="hlt">quantum</span> field theory. In this paper we use a local approach to study the Lorentz violation effects of the minimal standard model extension on the Casimir force between two parallel conducting plates in the vacuum. Using a perturbative method similar to that used for obtaining the Born series for the scattering amplitudes in <span class="hlt">quantum</span> mechanics, we compute, at leading order in the Lorentz-violating coefficients, the relevant Green's function which satisfies given boundary conditions. The standard point-splitting technique allow us to express the vacuum expectation value of the <span class="hlt">stress</span>-energy <span class="hlt">tensor</span> in terms of the Green's function. We discuss its structure in the region between the plates. We compute the renormalized vacuum <span class="hlt">stress</span>, which is obtained as the difference between the vacuum <span class="hlt">stress</span> in the presence of the plates and that of the vacuum. The Casimir force is evaluated in an analytical fashion by two methods: by differentiating the renormalized global energy density and by computing the normal-normal component of the renormalized vacuum <span class="hlt">stress</span>. We compute the local Casimir energy, which is found to diverge as approaching the plates, and we demonstrate that it does not contribute to the observable force.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/20110013590','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20110013590"><span>Exploiting <span class="hlt">Quantum</span> Resonance to Solve Combinatorial Problems</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Zak, Michail; Fijany, Amir</p> <p>2006-01-01</p> <p><span class="hlt">Quantum</span> resonance would be exploited in a proposed <span class="hlt">quantum</span>-computing approach to the solution of combinatorial optimization problems. In <span class="hlt">quantum</span> computing in general, one takes advantage of the fact that an algorithm cannot be decoupled from the physical effects available to implement it. Prior approaches to <span class="hlt">quantum</span> computing have involved exploitation of only a subset of known <span class="hlt">quantum</span> physical effects, notably including parallelism and entanglement, but not including resonance. In the proposed approach, one would utilize the combinatorial properties of <span class="hlt">tensor</span>-product decomposability of unitary evolution of many-particle <span class="hlt">quantum</span> systems for physically simulating solutions to NP-complete problems (a class of problems that are intractable with respect to classical methods of computation). In this approach, reinforcement and selection of a desired solution would be executed by means of <span class="hlt">quantum</span> resonance. Classes of NP-complete problems that are important in practice and could be solved by the proposed approach include planning, scheduling, search, and optimal design.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/scitech/biblio/22572066','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/22572066"><span>Extended scalar-<span class="hlt">tensor</span> theories of gravity</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Crisostomi, Marco; Koyama, Kazuya; Tasinato, Gianmassimo</p> <p>2016-04-21</p> <p>We study new consistent scalar-<span class="hlt">tensor</span> theories of gravity recently introduced by Langlois and Noui with potentially interesting cosmological applications. We derive the conditions for the existence of a primary constraint that prevents the propagation of an additional dangerous mode associated with higher order equations of motion. We then classify the most general, consistent scalar-<span class="hlt">tensor</span> theories that are at most quadratic in the second derivatives of the scalar field. In addition, we investigate the possible connection between these theories and (beyond) Horndeski through conformal and disformal transformations. Finally, we point out that these theories can be associated with new operators in the effective field theory of dark energy, which might open up new possibilities to test dark energy models in future surveys.</p> </li> </ol> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_14");'>14</a></li> <li><a href="#" onclick='return showDiv("page_15");'>15</a></li> <li class="active"><span>16</span></li> <li><a href="#" onclick='return showDiv("page_17");'>17</a></li> <li><a href="#" onclick='return showDiv("page_18");'>18</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div><!-- col-sm-12 --> </div><!-- row --> </div><!-- page_16 --> <div id="page_17" class="hiddenDiv"> <div class="row"> <div class="col-sm-12"> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_15");'>15</a></li> <li><a href="#" onclick='return showDiv("page_16");'>16</a></li> <li class="active"><span>17</span></li> <li><a href="#" onclick='return showDiv("page_18");'>18</a></li> <li><a href="#" onclick='return showDiv("page_19");'>19</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div> </div> <div class="row"> <div class="col-sm-12"> <ol class="result-class" start="321"> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016JCAP...04..044C','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016JCAP...04..044C"><span>Extended scalar-<span class="hlt">tensor</span> theories of gravity</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Crisostomi, Marco; Koyama, Kazuya; Tasinato, Gianmassimo</p> <p>2016-04-01</p> <p>We study new consistent scalar-<span class="hlt">tensor</span> theories of gravity recently introduced by Langlois and Noui with potentially interesting cosmological applications. We derive the conditions for the existence of a primary constraint that prevents the propagation of an additional dangerous mode associated with higher order equations of motion. We then classify the most general, consistent scalar-<span class="hlt">tensor</span> theories that are at most quadratic in the second derivatives of the scalar field. In addition, we investigate the possible connection between these theories and (beyond) Horndeski through conformal and disformal transformations. Finally, we point out that these theories can be associated with new operators in the effective field theory of dark energy, which might open up new possibilities to test dark energy models in future surveys.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/26357122','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/26357122"><span>Derived Metric <span class="hlt">Tensors</span> for Flow Surface Visualization.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Obermaier, H; Joy, K I</p> <p>2012-12-01</p> <p>Integral flow surfaces constitute a widely used flow visualization tool due to their capability to convey important flow information such as fluid transport, mixing, and domain segmentation. Current flow surface rendering techniques limit their expressiveness, however, by focusing virtually exclusively on displacement visualization, visually neglecting the more complex notion of deformation such as shearing and stretching that is central to the field of continuum mechanics. To incorporate this information into the flow surface visualization and analysis process, we derive a metric <span class="hlt">tensor</span> field that encodes local surface deformations as induced by the velocity gradient of the underlying flow field. We demonstrate how properties of the resulting metric <span class="hlt">tensor</span> field are capable of enhancing present surface visualization and generation methods and develop novel surface querying, sampling, and visualization techniques. The provided results show how this step towards unifying classic flow visualization and more advanced concepts from continuum mechanics enables more detailed and improved flow analysis.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/scitech/biblio/20705462','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/20705462"><span><span class="hlt">Quantum</span> inflaton, primordial perturbations, and CMB fluctuations</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Cao, F.J.; Vega, H.J. de; Sanchez, N.G.</p> <p>2004-10-15</p> <p>We compute the primordial scalar, vector and <span class="hlt">tensor</span> metric perturbations arising from <span class="hlt">quantum</span> field inflation. <span class="hlt">Quantum</span> field inflation takes into account the nonperturbative <span class="hlt">quantum</span> dynamics of the inflaton consistently coupled to the dynamics of the (classical) cosmological metric. For chaotic inflation, the <span class="hlt">quantum</span> treatment avoids the unnatural requirements of an initial state with all the energy in the zero mode. For new inflation it allows a consistent treatment of the explosive particle production due to spinodal instabilities. <span class="hlt">Quantum</span> field inflation (under conditions that are the <span class="hlt">quantum</span> analog of slow-roll) leads, upon evolution, to the formation of a condensate starting a regime of effective classical inflation. We compute the primordial perturbations taking the dominant <span class="hlt">quantum</span> effects into account. The results for the scalar, vector and <span class="hlt">tensor</span> primordial perturbations are expressed in terms of the classical inflation results. For a N-component field in a O(N) symmetric model, adiabatic fluctuations dominate while isocurvature or entropy fluctuations are negligible. The results agree with the current Wilkinson Microwave Anisotropy Probe observations and predict corrections to the power spectrum in classical inflation. Such corrections are estimated to be of the order of (m{sup 2}/NH{sup 2}), where m is the inflaton mass and H the Hubble constant at the moment of horizon crossing. An upper estimate turns to be about 4% for the cosmologically relevant scales. This <span class="hlt">quantum</span> field treatment of inflation provides the foundations to the classical inflation and permits to compute <span class="hlt">quantum</span> corrections to it.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19890007068','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19890007068"><span>Inflation in anisotropic scalar-<span class="hlt">tensor</span> theories</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Pimentel, Luis O.; Stein-Schabes, Jaime</p> <p>1988-01-01</p> <p>The existence of an inflationary phase in anisotropic Scalar-<span class="hlt">Tensor</span> Theories is investigated by means of a conformal transformation that allows us to rewrite these theories as gravity minimally coupled to a scalar field with a nontrivial potential. The explicit form of the potential is then used and the No Hair Theorem concludes that there is an inflationary phase in all open or flat anisotropic spacetimes in these theories. Several examples are constructed where the effect becomes manifest.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2015AGUFM.S51D2721W','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015AGUFM.S51D2721W"><span>Monte Carlo Volcano Seismic Moment <span class="hlt">Tensors</span></span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Waite, G. P.; Brill, K. A.; Lanza, F.</p> <p>2015-12-01</p> <p>Inverse modeling of volcano seismic sources can provide insight into the geometry and dynamics of volcanic conduits. But given the logistical challenges of working on an active volcano, seismic networks are typically deficient in spatial and temporal coverage; this potentially leads to large errors in source models. In addition, uncertainties in the centroid location and moment-<span class="hlt">tensor</span> components, including volumetric components, are difficult to constrain from the linear inversion results, which leads to a poor understanding of the model space. In this study, we employ a nonlinear inversion using a Monte Carlo scheme with the objective of defining robustly resolved elements of model space. The model space is randomized by centroid location and moment <span class="hlt">tensor</span> eigenvectors. Point sources densely sample the summit area and moment <span class="hlt">tensors</span> are constrained to a randomly chosen geometry within the inversion; Green's functions for the random moment <span class="hlt">tensors</span> are all calculated from modeled single forces, making the nonlinear inversion computationally reasonable. We apply this method to very-long-period (VLP) seismic events that accompany minor eruptions at Fuego volcano, Guatemala. The library of single force Green's functions is computed with a 3D finite-difference modeling algorithm through a homogeneous velocity-density model that includes topography, for a 3D grid of nodes, spaced 40 m apart, within the summit region. The homogenous velocity and density model is justified by long wavelength of VLP data. The nonlinear inversion reveals well resolved model features and informs the interpretation through a better understanding of the possible models. This approach can also be used to evaluate possible station geometries in order to optimize networks prior to deployment.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/26099143','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/26099143"><span>Detecting Curvilinear Features Using Structure <span class="hlt">Tensors</span>.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Vicas, Cristian; Nedevschi, Sergiu</p> <p>2015-11-01</p> <p>Few published articles on curvilinear structures exist compared with works on detecting lines or corners with high accuracy. In medical ultrasound imaging, the structures that need to be detected appear as a collection of microstructures correlated along a path. In this paper, we investigated techniques that extract meaningful low-level information for curvilinear structures, using techniques based on structure <span class="hlt">tensor</span>. We proposed a novel structure <span class="hlt">tensor</span> enhancement inspired by bilateral filtering. We compared the proposed approach with five state-of-the-art curvilinear structure detectors. We tested the algorithms against simulated images with known ground truth and real images from three different domains (medical ultrasound, scanning electron microscope, and astronomy). For the real images, we employed experts to delineate the ground truth for each domain. Techniques borrowed from machine learning robustly assessed the performance of the methods (area under curve and cross validation). As a practical application, we used the proposed method to label a set of 5000 ultrasound images. We conclude that the proposed <span class="hlt">tensor</span>-based approach outperforms the state-of-the-art methods in providing magnitude and orientation information for curvilinear structures. The evaluation methodology ensures that the employed feature-detection method will yield reproducible performance on new, unseen images. We published all the implemented methods as open-source software.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/1281026','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/1281026"><span><span class="hlt">Tensor</span> integrand reduction via Laurent expansion</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Hirschi, Valentin; Peraro, Tiziano</p> <p>2016-06-09</p> <p>We introduce a new method for the application of one-loop integrand reduction via the Laurent expansion algorithm, as implemented in the public C++ library Ninja. We show how the coefficients of the Laurent expansion can be computed by suitable contractions of the loop numerator <span class="hlt">tensor</span> with cut-dependent projectors, making it possible to interface Ninja to any one-loop matrix element generator that can provide the components of this <span class="hlt">tensor</span>. We implemented this technique in the Ninja library and interfaced it to MadLoop, which is part of the public MadGraph5_aMC@NLO framework. We performed a detailed performance study, comparing against other public reduction tools, namely CutTools, Samurai, IREGI, PJFry++ and Golem95. We find that Ninja out-performs traditional integrand reduction in both speed and numerical stability, the latter being on par with that of the <span class="hlt">tensor</span> integral reduction tool Golem95 which is however more limited and slower than Ninja. Lastly, we considered many benchmark multi-scale processes of increasing complexity, involving QCD and electro-weak corrections as well as effective non-renormalizable couplings, showing that Ninja’s performance scales well with both the rank and multiplicity of the considered process.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/20587369','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/20587369"><span>Myelin water weighted diffusion <span class="hlt">tensor</span> imaging.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Avram, Alexandru V; Guidon, Arnaud; Song, Allen W</p> <p>2010-10-15</p> <p>In this study we describe our development and implementation of a magnetization transfer (MT) prepared stimulated-echo diffusion <span class="hlt">tensor</span> imaging (DTI) technique that can be made sensitive to the microanatomy of myelin tissue. The short echo time (TE) enabled by the stimulated-echo acquisition preserves significant signal from the short T(2) component (myelin water), and the MT preparation further provides differentiating sensitization to this signal. It was found that this combined strategy could provide sufficient sensitivity in our first attempt to image myelin microstructure. Compared to the diffusion <span class="hlt">tensor</span> derived from the conventional DTI technique, the myelin water weighted (MWW) <span class="hlt">tensor</span> has the same principal diffusion direction but exhibits a significant increase in fractional anisotropy (FA), which is mainly due to a decrease in radial diffusivity. These findings are consistent with the microstructural organization of the myelin sheaths that wrap around the axons in the white matter and therefore hinder radial diffusion. Given that many white matter diseases (e.g. multiple sclerosis) begin with a degradation of myelin microanatomy but not a loss of myelin content (e.g. loosening of the myelin sheaths), our newly implemented MWW DTI has the potential to lead to improved assessment of myelin pathology and early detection of demyelination.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/pages/biblio/1281026-tensor-integrand-reduction-via-laurent-expansion','SCIGOV-DOEP'); return false;" href="https://www.osti.gov/pages/biblio/1281026-tensor-integrand-reduction-via-laurent-expansion"><span><span class="hlt">Tensor</span> integrand reduction via Laurent expansion</span></a></p> <p><a target="_blank" href="http://www.osti.gov/pages">DOE PAGES</a></p> <p>Hirschi, Valentin; Peraro, Tiziano</p> <p>2016-06-09</p> <p>We introduce a new method for the application of one-loop integrand reduction via the Laurent expansion algorithm, as implemented in the public C++ library Ninja. We show how the coefficients of the Laurent expansion can be computed by suitable contractions of the loop numerator <span class="hlt">tensor</span> with cut-dependent projectors, making it possible to interface Ninja to any one-loop matrix element generator that can provide the components of this <span class="hlt">tensor</span>. We implemented this technique in the Ninja library and interfaced it to MadLoop, which is part of the public MadGraph5_aMC@NLO framework. We performed a detailed performance study, comparing against other public reductionmore » tools, namely CutTools, Samurai, IREGI, PJFry++ and Golem95. We find that Ninja out-performs traditional integrand reduction in both speed and numerical stability, the latter being on par with that of the <span class="hlt">tensor</span> integral reduction tool Golem95 which is however more limited and slower than Ninja. Lastly, we considered many benchmark multi-scale processes of increasing complexity, involving QCD and electro-weak corrections as well as effective non-renormalizable couplings, showing that Ninja’s performance scales well with both the rank and multiplicity of the considered process.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=1275686','PMC'); return false;" href="https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=1275686"><span>MR diffusion <span class="hlt">tensor</span> spectroscopy and imaging.</span></a></p> <p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pmc">PubMed Central</a></p> <p>Basser, P J; Mattiello, J; LeBihan, D</p> <p>1994-01-01</p> <p>This paper describes a new NMR imaging modality--MR diffusion <span class="hlt">tensor</span> imaging. It consists of estimating an effective diffusion <span class="hlt">tensor</span>, Deff, within a voxel, and then displaying useful quantities derived from it. We show how the phenomenon of anisotropic diffusion of water (or metabolites) in anisotropic tissues, measured noninvasively by these NMR methods, is exploited to determine fiber tract orientation and mean particle displacements. Once Deff is estimated from a series of NMR pulsed-gradient, spin-echo experiments, a tissue's three orthotropic axes can be determined. They coincide with the eigenvectors of Deff, while the effective diffusivities along these orthotropic directions are the eigenvalues of Deff. Diffusion ellipsoids, constructed in each voxel from Deff, depict both these orthotropic axes and the mean diffusion distances in these directions. Moreover, the three scalar invariants of Deff, which are independent of the tissue's orientation in the laboratory frame of reference, reveal useful information about molecular mobility reflective of local microstructure and anatomy. Inherently <span class="hlt">tensors</span> (like Deff) describing transport processes in anisotropic media contain new information within a macroscopic voxel that scalars (such as the apparent diffusivity, proton density, T1, and T2) do not. Images FIGURE 4 FIGURE 5 FIGURE 6 FIGURE 7 FIGURE 8 PMID:8130344</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=3589706','PMC'); return false;" href="https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=3589706"><span>Probing white-matter microstructure with higher-order diffusion <span class="hlt">tensors</span> and susceptibility <span class="hlt">tensor</span> MRI</span></a></p> <p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pmc">PubMed Central</a></p> <p>Liu, Chunlei; Murphy, Nicole E.; Li, Wei</p> <p>2012-01-01</p> <p>Diffusion MRI has become an invaluable tool for studying white matter microstructure and brain connectivity. The emergence of quantitative susceptibility mapping and susceptibility <span class="hlt">tensor</span> imaging (STI) has provided another unique tool for assessing the structure of white matter. In the highly ordered white matter structure, diffusion MRI measures hindered water mobility induced by various tissue and cell membranes, while susceptibility sensitizes to the molecular composition and axonal arrangement. Integrating these two methods may produce new insights into the complex physiology of white matter. In this study, we investigated the relationship between diffusion and magnetic susceptibility in the white matter. Experiments were conducted on phantoms and human brains in vivo. Diffusion properties were quantified with the diffusion <span class="hlt">tensor</span> model and also with the higher order <span class="hlt">tensor</span> model based on the cumulant expansion. Frequency shift and susceptibility <span class="hlt">tensor</span> were measured with quantitative susceptibility mapping and susceptibility <span class="hlt">tensor</span> imaging. These diffusion and susceptibility quantities were compared and correlated in regions of single fiber bundles and regions of multiple fiber orientations. Relationships were established with similarities and differences identified. It is believed that diffusion MRI and susceptibility MRI provide complementary information of the microstructure of white matter. Together, they allow a more complete assessment of healthy and diseased brains. PMID:23507987</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/scitech/biblio/1136377','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/1136377"><span>Effect of Multi-Axial Loading on Residual Strain <span class="hlt">Tensor</span> for 12L14 Steel Alloy</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Bunn, J. R.; Penumadu, Dayakar; Lou, Xin; Hubbard, Camden R</p> <p>2014-01-01</p> <p>Evaluating the state of residual strain or <span class="hlt">stress</span> is critically important for structural materials and for reliable design of complex shape components that need to function in extreme environment subjected to large thermo-mechanical loading. When residual <span class="hlt">stress</span> state is superposed to external loads, it can lead to reduction or increase in failure strength. Past diffraction studies for evaluating the residual strain state involved measuring lattice spacings in three orthogonal directions and do not often correspond to principal directions. To completely resolve the state of strain at a given location, a full strain <span class="hlt">tensor</span> must be determined. This is especially important when characterizing materials or metallic components exposed to biaxial or complex loading. Neutron diffraction at the second Generation Neutron Residual <span class="hlt">Stress</span> Facility (NRSF2) at Oak Ridge National Laboratory is used in this study to measure strain <span class="hlt">tensors</span> associated with different modes of <span class="hlt">stress</span> path. Hollow cylinder steel samples with 2 mm wall thickness are subjected to either pure axial extension or pure torsion to simulate multi-axial loading conditions. A virgin sample that is not subjected to any deformation, but subjected to identical manufacturing conditions and machining steps involved to obtain hollow cylinder geometry is used for obtaining reference d-spacing for given hkl planes at target spatial location(s). The two samples which are subjected to either pure tension or torsion are loaded to a deformation state that corresponded to equal amount of octahedral shear strain which is an invariant. This procedure is used so that a basis for comparison between the two samples can be made to isolate the <span class="hlt">stress</span> path effects. A 2-circle Huber orienter is used to obtain strain measurements on identical gauge volume at a series of chi and psi values. The residual state of <span class="hlt">stress</span> <span class="hlt">tensor</span> corresponding to ex situ (upon unloading) conditions is presented for three lattice planes (211, 110, 200) for</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017JHEP...03..044A','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017JHEP...03..044A"><span><span class="hlt">Quantum</span> information metric and Berry curvature from a Lagrangian approach</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Alvarez-Jimenez, Javier; Dector, Aldo; Vergara, J. David</p> <p>2017-03-01</p> <p>We take as a starting point an expression for the <span class="hlt">quantum</span> geometric <span class="hlt">tensor</span> recently derived in the context of the gauge/gravity duality. We proceed to generalize this formalism in such way it is possible to compute the geometrical phases of <span class="hlt">quantum</span> systems. Our scheme provides a conceptually complete description and introduces a different point of view of earlier works. Using our formalism, we show how this expression can be applied to well-known <span class="hlt">quantum</span> mechanical systems.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/26291919','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/26291919"><span>Arbuscular mycorrhizal symbiosis ameliorates the optimum <span class="hlt">quantum</span> yield of photosystem II and reduces non-photochemical quenching in rice plants subjected to salt <span class="hlt">stress</span>.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Porcel, Rosa; Redondo-Gómez, Susana; Mateos-Naranjo, Enrique; Aroca, Ricardo; Garcia, Rosalva; Ruiz-Lozano, Juan Manuel</p> <p>2015-08-01</p> <p>Rice is the most important food crop in the world and is a primary source of food for more than half of the world population. However, salinity is considered the most common abiotic <span class="hlt">stress</span> reducing its productivity. Soil salinity inhibits photosynthetic processes, which can induce an over-reduction of the reaction centres in photosystem II (PSII), damaging the photosynthetic machinery. The arbuscular mycorrhizal (AM) symbiosis may improve host plant tolerance to salinity, but it is not clear how the AM symbiosis affects the plant photosynthetic capacity, particularly the efficiency of PSII. This study aimed at determining the influence of the AM symbiosis on the performance of PSII in rice plants subjected to salinity. Photosynthetic activity, plant gas-exchange parameters, accumulation of photosynthetic pigments and rubisco activity and gene expression were also measured in order to analyse comprehensively the response of the photosynthetic processes to AM symbiosis and salinity. Results showed that the AM symbiosis enhanced the actual <span class="hlt">quantum</span> yield of PSII photochemistry and reduced the <span class="hlt">quantum</span> yield of non-photochemical quenching in rice plants subjected to salinity. AM rice plants maintained higher net photosynthetic rate, stomatal conductance and transpiration rate than nonAM plants. Thus, we propose that AM rice plants had a higher photochemical efficiency for CO2 fixation and solar energy utilization and this increases plant salt tolerance by preventing the injury to the photosystems reaction centres and by allowing a better utilization of light energy in photochemical processes. All these processes translated into higher photosynthetic and rubisco activities in AM rice plants and improved plant biomass production under salinity.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/scitech/biblio/21518407','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/21518407"><span>Strain balanced <span class="hlt">quantum</span> posts</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Alonso-Alvarez, D.; Alen, B.; Ripalda, J. M.; Llorens, J. M.; Taboada, A. G.; Briones, F.; Roldan, M. A.; Hernandez-Saz, J.; Hernandez-Maldonado, D.; Herrera, M.; Molina, S. I.</p> <p>2011-04-25</p> <p><span class="hlt">Quantum</span> posts are assembled by epitaxial growth of closely spaced <span class="hlt">quantum</span> dot layers, modulating the composition of a semiconductor alloy, typically InGaAs. In contrast with most self-assembled nanostructures, the height of <span class="hlt">quantum</span> posts can be controlled with nanometer precision, up to a maximum value limited by the accumulated <span class="hlt">stress</span> due to the lattice mismatch. Here, we present a strain compensation technique based on the controlled incorporation of phosphorous, which substantially increases the maximum attainable <span class="hlt">quantum</span> post height. The luminescence from the resulting nanostructures presents giant linear polarization anisotropy.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=4745859','PMC'); return false;" href="https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=4745859"><span>Cytotoxicity of CdTe <span class="hlt">quantum</span> dots in human umbilical vein endothelial cells: the involvement of cellular uptake and induction of pro-apoptotic endoplasmic reticulum <span class="hlt">stress</span></span></a></p> <p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pmc">PubMed Central</a></p> <p>Yan, Ming; Zhang, Yun; Qin, Haiyan; Liu, Kezhou; Guo, Miao; Ge, Yakun; Xu, Mingen; Sun, Yonghong; Zheng, Xiaoxiang</p> <p>2016-01-01</p> <p>Cadmium telluride <span class="hlt">quantum</span> dots (CdTe QDs) have been proposed to induce oxidative <span class="hlt">stress</span>, which plays a crucial role in CdTe QDs-mediated mitochondrial-dependent apoptosis in human umbilical vein endothelial cells (HUVECs). However, the direct interactions of CdTe QDs with HUVECs and their potential impairment of other organelles like endoplasmic reticulum (ER) in HUVECs are poorly understood. In this study, we reported that the negatively charged CdTe QDs (−21.63±0.91 mV), with good dispersity and fluorescence stability, were rapidly internalized via endocytosis by HUVECs, as the notable internalization could be inhibited up to 95.52% by energy depletion (NaN3/deoxyglucose or low temperature). The endocytosis inhibitors (methyl-β-cyclodextrin, genistein, sucrose, chlorpromazine, and colchicine) dramatically decreased the uptake of CdTe QDs by HUVECs, suggesting that both caveolae/raft- and clathrin-mediated endocytosis were involved in the endothelial uptake of CdTe QDs. Using immunocytochemistry, a striking overlap of the internalized CdTe QDs and ER marker was observed, which indicates that QDs may be transported to ER. The CdTe QDs also caused remarkable ER <span class="hlt">stress</span> responses in HUVECs, confirmed by significant dilatation of ER cisternae, upregulation of ER <span class="hlt">stress</span> markers GRP78/GRP94, and activation of protein kinase RNA-like ER kinase-eIF2α-activating transcription factor 4 pathway (including phosphorylation of both protein kinase RNA-like ER kinase and eIF2α and elevated level of activating transcription factor 4). CdTe QDs further promoted an increased C/EBP homologous protein expression, phosphorylation of c-JUN NH2-terminal kinase, and cleavage of ER-resident caspase-4, while the specific inhibitor (SP600125, Z-LEVD-fmk, or salubrinal) significantly attenuated QDs-triggered apoptosis, indicating that all three ER <span class="hlt">stress</span>-mediated apoptosis pathways were activated and the direct participation of ER in the CdTe QDs-caused apoptotic cell death in HUVECs</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2014JPhCS.543a2001K','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2014JPhCS.543a2001K"><span><span class="hlt">Tensor</span>-polarized structure functions: <span class="hlt">Tensor</span> structure of deuteron in 2020's</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Kumano, S.</p> <p>2014-10-01</p> <p>We explain spin structure for a spin-one hadron, in which there are new structure functions, in addition to the ones (F1, F2, g1, g2) which exist for the spin-1/2 nucleon, associated with its <span class="hlt">tensor</span> structure. The new structure functions are b1, b2, b3, and b4 in deep inelastic scattering of a charged-lepton from a spin-one hadron such as the deuteron. Among them, twist- two functions are related by the Callan-Gross type relation b2 = 2xb1 in the Bjorken scaling limit. First, these new structure functions are introduced, and useful formulae are derived for projection operators of b1-4 from a hadron <span class="hlt">tensor</span> Wμν. Second, a sum rule is explained for b1, and possible <span class="hlt">tensor</span>-polarized distributions are discussed by using HERMES data in order to propose future experimental measurements and to compare them with theoretical models. A proposal was approved to measure b1 at the Thomas Jefferson National Accelerator Facility (JLab), so that much progress is expected for b1 in the near future. Third, formalisms of polarized proton-deuteron Drell-Yan processes are explained for probing especially <span class="hlt">tensor</span>- polarized antiquark distributions, which were suggested by the HERMES data. The studies of the <span class="hlt">tensor</span>-polarized structure functions will open a new era in 2020's for <span class="hlt">tensor</span>-structure studies in terms of quark and gluon degrees of freedom, which are very different from ordinary descriptions in terms of nucleons and mesons.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2015JPhCS.626a2067M','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015JPhCS.626a2067M"><span><span class="hlt">Quantum</span> mechanics from invariance principles</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Moldoveanu, Florin</p> <p>2015-07-01</p> <p><span class="hlt">Quantum</span> mechanics is an extremely successful theory of nature and yet it lacks an intuitive axiomatization. In contrast, the special theory of relativity is well understood and is rooted into natural or experimentally justified postulates. Here we introduce an axiomatization approach to <span class="hlt">quantum</span> mechanics which is very similar to special theory of relativity derivation. The core idea is that a composed system obeys the same laws of nature as its components. This leads to a Jordan-Lie algebraic formulation of <span class="hlt">quantum</span> mechanics. The starting assumptions are minimal: the laws of nature are invariant under time evolution, the laws of nature are invariant under <span class="hlt">tensor</span> composition, the laws of nature are relational, together with the ability to define a physical state (positivity). <span class="hlt">Quantum</span> mechanics is singled out by a fifth experimentally justified postulate: nature violates Bell's inequalities.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/1274416','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/1274416"><span>Cross-scale Efficient <span class="hlt">Tensor</span> Contractions for Coupled Cluster Computations Through Multiple Programming Model Backends</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Ibrahim, Khaled Z.; Epifanovsky, Evgeny; Williams, Samuel W.; Krylov, Anna I.</p> <p>2016-07-26</p> <p>Coupled-cluster methods provide highly accurate models of molecular structure by explicit numerical calculation of <span class="hlt">tensors</span> representing the correlation between electrons. These calculations are dominated by a sequence of <span class="hlt">tensor</span> contractions, motivating the development of numerical libraries for such operations. While based on matrix-matrix multiplication, these libraries are specialized to exploit symmetries in the molecular structure and in electronic interactions, and thus reduce the size of the <span class="hlt">tensor</span> representation and the complexity of contractions. The resulting algorithms are irregular and their parallelization has been previously achieved via the use of dynamic scheduling or specialized data decompositions. We introduce our efforts to extend the Libtensor framework to work in the distributed memory environment in a scalable and energy efficient manner. We achieve up to 240 speedup compared with the best optimized shared memory implementation. We attain scalability to hundreds of thousands of compute cores on three distributed-memory architectures, (Cray XC30&XC40, BlueGene/Q), and on a heterogeneous GPU-CPU system (Cray XK7). As the bottlenecks shift from being compute-bound DGEMM's to communication-bound collectives as the size of the molecular system scales, we adopt two radically different parallelization approaches for handling load-imbalance. Nevertheless, we preserve a uni ed interface to both programming models to maintain the productivity of computational <span class="hlt">quantum</span> chemists.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/scitech/biblio/22436540','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/22436540"><span>Temperature effects in first-principles solid state calculations of the chemical shielding <span class="hlt">tensor</span> made simple</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Monserrat, Bartomeu Needs, Richard J.; Pickard, Chris J.</p> <p>2014-10-07</p> <p>We study the effects of atomic vibrations on the solid-state chemical shielding <span class="hlt">tensor</span> using first principles density functional theory calculations. At the harmonic level, we use a Monte Carlo method and a perturbative expansion. The Monte Carlo method is accurate but computationally expensive, while the perturbative method is computationally more efficient, but approximate. We find excellent agreement between the two methods for both the isotropic shift and the shielding anisotropy. The effects of zero-point <span class="hlt">quantum</span> mechanical nuclear motion are important up to relatively high temperatures: at 500 K they still represent about half of the overall vibrational contribution. We also investigate the effects of anharmonic vibrations, finding that their contribution to the zero-point correction to the chemical shielding <span class="hlt">tensor</span> is small. We exemplify these ideas using magnesium oxide and the molecular crystals L-alanine and β-aspartyl-L-alanine. We therefore propose as the method of choice to incorporate the effects of temperature in solid state chemical shielding <span class="hlt">tensor</span> calculations using the perturbative expansion within the harmonic approximation. This approach is accurate and requires a computational effort that is about an order of magnitude smaller than that of dynamical or Monte Carlo approaches, so these effects might be routinely accounted for.</p> </li> </ol> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_15");'>15</a></li> <li><a href="#" onclick='return showDiv("page_16");'>16</a></li> <li class="active"><span>17</span></li> <li><a href="#" onclick='return showDiv("page_18");'>18</a></li> <li><a href="#" onclick='return showDiv("page_19");'>19</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div><!-- col-sm-12 --> </div><!-- row --> </div><!-- page_17 --> <div id="page_18" class="hiddenDiv"> <div class="row"> <div class="col-sm-12"> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_16");'>16</a></li> <li><a href="#" onclick='return showDiv("page_17");'>17</a></li> <li class="active"><span>18</span></li> <li><a href="#" onclick='return showDiv("page_19");'>19</a></li> <li><a href="#" onclick='return showDiv("page_20");'>20</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div> </div> <div class="row"> <div class="col-sm-12"> <ol class="result-class" start="341"> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017PhRvD..95f6008C','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017PhRvD..95f6008C"><span>Equation of motion of canonical <span class="hlt">tensor</span> model and Hamilton-Jacobi equation of general relativity</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Chen, Hua; Sasakura, Naoki; Sato, Yuki</p> <p>2017-03-01</p> <p>The canonical <span class="hlt">tensor</span> model (CTM) is a rank-three <span class="hlt">tensor</span> model formulated as a totally constrained system in the canonical formalism. The constraint algebra of CTM has a similar structure as that of the Arnowitt-Deser-Misner formalism of general relativity, and it is studied as a discretized model for <span class="hlt">quantum</span> gravity. In this paper, we analyze the classical equation of motion (EOM) of CTM in a formal continuum limit through a derivative expansion of the <span class="hlt">tensor</span> of CTM up to the fourth order, and we show that it is the same as the EOM of a coupled system of gravity and a scalar field derived from the Hamilton-Jacobi equation with an appropriate choice of an action. The action contains a scalar field potential of an exponential form, and the system classically respects a dilatational symmetry. We find that the system has a critical dimension, given by six, over which it becomes unstable due to the wrong sign of the scalar kinetic term. In six dimensions, de Sitter spacetime becomes a solution to the EOM, signaling the emergence of a conformal symmetry, while the time evolution of the scale factor is a power law in dimensions below six.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/scitech/biblio/22454497','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/22454497"><span>More on loops in reheating: non-gaussianities and <span class="hlt">tensor</span> power spectrum</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Katırcı, Nihan; Kaya, Ali; Tarman, Merve</p> <p>2014-06-11</p> <p>We consider the single field chaotic m{sup 2}ϕ{sup 2} inflationary model with a period of preheating, where the inflaton decays to another scalar field χ in the parametric resonance regime. In a recent work, one of us has shown that the χ modes circulating in the loops during preheating notably modify the <ζζ> correlation function. We first rederive this result using a different gauge condition hence reconfirm that superhorizon ζ modes are affected by the loops in preheating. Further, we examine how χ loops give rise to non-gaussianity and affect the <span class="hlt">tensor</span> perturbations. For that, all cubic and some higher order interactions involving two χ fields are determined and their contribution to the non-gaussianity parameter f{sub NL} and the <span class="hlt">tensor</span> power spectrum are calculated at one loop. Our estimates for these corrections show that while a large amount of non-gaussianity can be produced during reheating, the <span class="hlt">tensor</span> power spectrum receive moderate corrections. We observe that the loop <span class="hlt">quantum</span> effects increase with more χ fields circulating in the loops indicating that the perturbation theory might be broken down. These findings demonstrate that the loop corrections during reheating are significant and they must be taken into account for precision inflationary cosmology.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2014JChPh.141m4113M','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2014JChPh.141m4113M"><span>Temperature effects in first-principles solid state calculations of the chemical shielding <span class="hlt">tensor</span> made simple</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Monserrat, Bartomeu; Needs, Richard J.; Pickard, Chris J.</p> <p>2014-10-01</p> <p>We study the effects of atomic vibrations on the solid-state chemical shielding <span class="hlt">tensor</span> using first principles density functional theory calculations. At the harmonic level, we use a Monte Carlo method and a perturbative expansion. The Monte Carlo method is accurate but computationally expensive, while the perturbative method is computationally more efficient, but approximate. We find excellent agreement between the two methods for both the isotropic shift and the shielding anisotropy. The effects of zero-point <span class="hlt">quantum</span> mechanical nuclear motion are important up to relatively high temperatures: at 500 K they still represent about half of the overall vibrational contribution. We also investigate the effects of anharmonic vibrations, finding that their contribution to the zero-point correction to the chemical shielding <span class="hlt">tensor</span> is small. We exemplify these ideas using magnesium oxide and the molecular crystals L-alanine and β-aspartyl-L-alanine. We therefore propose as the method of choice to incorporate the effects of temperature in solid state chemical shielding <span class="hlt">tensor</span> calculations using the perturbative expansion within the harmonic approximation. This approach is accurate and requires a computational effort that is about an order of magnitude smaller than that of dynamical or Monte Carlo approaches, so these effects might be routinely accounted for.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2015APS..DFDH28006B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015APS..DFDH28006B"><span>A control volume study of the pressure <span class="hlt">tensor</span> across a liquid-vapour interface</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Braga, Carlos; Yatsyshin, Petr; Smith, Edward; Nold, Andreas; Goddard, Benjamin; Savva, Nikos; Schmuck, Markus; Duncan, Andrew; Sibley, David; Kalliadasis, Serafim</p> <p>2015-11-01</p> <p>The presence of an interface renders the properties of the system position dependent. The pressure <span class="hlt">tensor</span> will no longer be uniform nor isotropic giving rise to the surface tension. The theory of Kirkwood-Buff gives a formal description of the surface tension based on the analysis of the local pressure <span class="hlt">tensor</span> while capillary wave theory assumes the existence of an instantaneous intrinsic surface separating the liquid and vapour. Analysis of its Fourier components gives both structural and dynamical routes to compute the surface based on hydrodynamic theory. The defining equation of a capillary surface is given by the <span class="hlt">stress</span> balance between the pressure <span class="hlt">tensors</span> and the surface tension. Here, we employ the instantaneous interface as a representative surface across which we compute the local pressures following the seminal work of Irving and Kirkwood. The control volume approach to the Irving-Kirkwood expressions provides an exact balance between the <span class="hlt">stress</span> and momentum transfer across the surface element allowing the study of the surface tension from a mechanical standpoint. We acknowledge financial support from European Research Council via Advanced Grant No. 247031.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/pages/biblio/1327290-chaos-quantum-channels','SCIGOV-DOEP'); return false;" href="https://www.osti.gov/pages/biblio/1327290-chaos-quantum-channels"><span>Chaos in <span class="hlt">quantum</span> channels</span></a></p> <p><a target="_blank" href="http://www.osti.gov/pages">DOE PAGES</a></p> <p>Hosur, Pavan; Qi, Xiao-Liang; Roberts, Daniel A.; ...</p> <p>2016-02-01</p> <p>For this research, we study chaos and scrambling in unitary channels by considering their entanglement properties as states. Using out-of-time-order correlation functions to diagnose chaos, we characterize the ability of a channel to process <span class="hlt">quantum</span> information. We show that the generic decay of such correlators implies that any input subsystem must have near vanishing mutual information with almost all partitions of the output. Additionally, we propose the negativity of the tripartite information of the channel as a general diagnostic of scrambling. This measures the delocalization of information and is closely related to the decay of out-of-time-order correlators. We back upmore » our results with numerics in two non-integrable models and analytic results in a perfect <span class="hlt">tensor</span> network model of chaotic time evolution. In conclusion, these results show that the butterfly effect in <span class="hlt">quantum</span> systems implies the information-theoretic definition of scrambling.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/1327290','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/1327290"><span>Chaos in <span class="hlt">quantum</span> channels</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Hosur, Pavan; Qi, Xiao-Liang; Roberts, Daniel A.; Yoshida, Beni</p> <p>2016-02-01</p> <p>For this research, we study chaos and scrambling in unitary channels by considering their entanglement properties as states. Using out-of-time-order correlation functions to diagnose chaos, we characterize the ability of a channel to process <span class="hlt">quantum</span> information. We show that the generic decay of such correlators implies that any input subsystem must have near vanishing mutual information with almost all partitions of the output. Additionally, we propose the negativity of the tripartite information of the channel as a general diagnostic of scrambling. This measures the delocalization of information and is closely related to the decay of out-of-time-order correlators. We back up our results with numerics in two non-integrable models and analytic results in a perfect <span class="hlt">tensor</span> network model of chaotic time evolution. In conclusion, these results show that the butterfly effect in <span class="hlt">quantum</span> systems implies the information-theoretic definition of scrambling.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017APS..APR.S6003O','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017APS..APR.S6003O"><span>Loop <span class="hlt">quantum</span> cosmology: confronting the hybrid quantization approach with observations</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Olmedo, Javier; Martin de Blas, Daniel</p> <p>2017-01-01</p> <p>In loop <span class="hlt">quantum</span> cosmology there are several approaches for the confrontation of the theory with observations. Here, we focus on the hybrid quantization approach. We provide an exhaustive analysis including scalar and <span class="hlt">tensor</span> perturbations on effective (<span class="hlt">quantum</span>-mechanically corrected) homogeneous and isotropic cosmologies coupled to a massive scalar field. We compute the primordial power spectrum of the perturbations at the end of inflation for a set of initial vacuum states defined at the deep <span class="hlt">quantum</span> regime of the cosmological model. We then analyze the <span class="hlt">tensor</span>-to-scalar ratio and the consistency relation between this quantity and the spectral index of the <span class="hlt">tensor</span> power spectrum. Eventually, we compute the temperature-temperature, electric-electric, temperature-electric and magnetic-magnetic correlation functions predicted by this approach and compare them with present observations.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016IJGMM..1350001B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016IJGMM..1350001B"><span>Construction of energy-momentum <span class="hlt">tensor</span> of gravitation</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Bamba, Kazuharu; Shimizu, Katsutaro</p> <p>2016-10-01</p> <p>We construct the gravitational energy-momentum <span class="hlt">tensor</span> in general relativity through the Noether theorem. In particular, we explicitly demonstrate that the constructed quantity can vary as a <span class="hlt">tensor</span> under the general coordinate transformation. Furthermore, we verify that the energy-momentum conservation is satisfied because one of the two indices of the energy-momentum <span class="hlt">tensor</span> should be in the local Lorentz frame. It is also shown that the gravitational energy and the matter one cancel out in certain space-times.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016NIMPA.813...62M','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016NIMPA.813...62M"><span>Irreducible Cartesian <span class="hlt">tensors</span> of highest weight, for arbitrary order</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Mane, S. R.</p> <p>2016-03-01</p> <p>A closed form expression is presented for the irreducible Cartesian <span class="hlt">tensor</span> of highest weight, for arbitrary order. Two proofs are offered, one employing bookkeeping of indices and, after establishing the connection with the so-called natural <span class="hlt">tensors</span> and their projection operators, the other one employing purely coordinate-free <span class="hlt">tensor</span> manipulations. Some theorems and formulas in the published literature are generalized from SO(3) to SO(n), for dimensions n ≥ 3.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.dtic.mil/docs/citations/ADA615943','DTIC-ST'); return false;" href="http://www.dtic.mil/docs/citations/ADA615943"><span>Square Deal: Lower Bounds and Improved Relaxations for <span class="hlt">Tensor</span> Recovery</span></a></p> <p><a target="_blank" href="https://publicaccess.dtic.mil/psm/api/service/search/search">DTIC Science & Technology</a></p> <p></p> <p>2013-08-16</p> <p>a low-rank <span class="hlt">tensor</span> from incomplete information is a recurring problem in signal processing and machine learning . The most popular convex relaxation of...is a recurring problem in signal processing and machine learning . The most popular convex relaxation of this problem minimizes the sum of the nuclear...results to low-rank <span class="hlt">tensors</span> is not obvious. The numerical algebra of <span class="hlt">tensors</span> is fraught with hardness results [HL09]. For example, even computing a</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2014PhRvD..90l3503R','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2014PhRvD..90l3503R"><span>Relativistic Lagrangian displacement field and <span class="hlt">tensor</span> perturbations</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Rampf, Cornelius; Wiegand, Alexander</p> <p>2014-12-01</p> <p>We investigate the purely spatial Lagrangian coordinate transformation from the Lagrangian to the basic Eulerian frame. We demonstrate three techniques for extracting the relativistic displacement field from a given solution in the Lagrangian frame. These techniques are (a) from defining a local set of Eulerian coordinates embedded into the Lagrangian frame; (b) from performing a specific gauge transformation; and (c) from a fully nonperturbative approach based on the Arnowitt-Deser-Misner (ADM) split. The latter approach shows that this decomposition is not tied to a specific perturbative formulation for the solution of the Einstein equations. Rather, it can be defined at the level of the nonperturbative coordinate change from the Lagrangian to the Eulerian description. Studying such different techniques is useful because it allows us to compare and develop further the various approximation techniques available in the Lagrangian formulation. We find that one has to solve the gravitational wave equation in the relativistic analysis, otherwise the corresponding Newtonian limit will necessarily contain spurious nonpropagating <span class="hlt">tensor</span> artifacts at second order in the Eulerian frame. We also derive the magnetic part of the Weyl <span class="hlt">tensor</span> in the Lagrangian frame, and find that it is not only excited by gravitational waves but also by <span class="hlt">tensor</span> perturbations which are induced through the nonlinear frame dragging. We apply our findings to calculate for the first time the relativistic displacement field, up to second order, for a Λ CDM Universe in the presence of a local primordial non-Gaussian component. Finally, we also comment on recent claims about whether mass conservation in the Lagrangian frame is violated.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2013CQGra..30p5014H','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2013CQGra..30p5014H"><span>Minimal <span class="hlt">tensors</span> and purely electric or magnetic spacetimes of arbitrary dimension</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Hervik, Sigbjørn; Ortaggio, Marcello; Wylleman, Lode</p> <p>2013-08-01</p> <p>We consider time reversal transformations to obtain twofold orthogonal splittings of any <span class="hlt">tensor</span> on a Lorentzian space of arbitrary dimension n. Applied to the Weyl <span class="hlt">tensor</span> of a spacetime, this leads to a definition of its electric and magnetic parts relative to an observer (defined by a unit timelike vector field u), in any dimension. We study the cases where one of these parts vanishes in detail, i.e., purely electric (PE) or magnetic (PM) spacetimes. We generalize several results from four to higher dimensions and discuss new features of higher dimensions. For instance, we prove that the only permitted Weyl types are G, Ii and D, and discuss the possible relation of u with the Weyl aligned null directions (WANDs); we provide invariant conditions that characterize PE/PM spacetimes, such as Bel-Debever-like criteria, or constraints on scalar invariants, and connect the PE/PM parts to the kinematic quantities of u; we present conditions under which direct product spacetimes (and certain warps) are PE/PM, which enables us to construct explicit examples. In particular, it is also shown that all static spacetimes are necessarily PE, while stationary spacetimes (such as spinning black holes) are in general neither PE nor PM. Whereas ample classes of PE spacetimes exist, PM solutions are elusive; specifically, we prove that PM Einstein spacetimes of type D do not exist, in any dimension. Finally, we derive corresponding results for the electric/magnetic parts of the Riemann <span class="hlt">tensor</span>, which is useful when considering spacetimes with matter fields, and moreover leads to first examples of PM spacetimes in higher dimensions. We also note in passing that PE/PM Weyl (or Riemann) <span class="hlt">tensors</span> provide examples of minimal <span class="hlt">tensors</span>, and we make the connection hereof with the recently proved alignment theorem (Hervik 2011 Class. <span class="hlt">Quantum</span> Grav. 28 215009). This in turn sheds new light on the classification of the Weyl <span class="hlt">tensors</span> based on null alignment, providing a further invariant</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.dtic.mil/docs/citations/ADA604494','DTIC-ST'); return false;" href="http://www.dtic.mil/docs/citations/ADA604494"><span><span class="hlt">Tensor</span> Decompositions for Learning Latent Variable Models</span></a></p> <p><a target="_blank" href="https://publicaccess.dtic.mil/psm/api/service/search/search">DTIC Science & Technology</a></p> <p></p> <p>2012-12-08</p> <p>of a <span class="hlt">tensor</span>, 2011. arXiv:1004.4953. [CSC+12] S. B. Cohen, K. Stratos, M. Collins, D. P. Foster, and L. Ungar . Spectral learning of latent-variable...12] P. S. Dhillon, J. Rodu, M. Collins, D. P. Foster, and L. H. Ungar . Spectral dependency parsing with latent variables. In EMNLP-CoNLL, 2012. [DS07...Foster, J. Rodu, and L. H. Ungar . Spectral dimensionality reduction for HMMs, 2012. arXiv:1203.6130. [GvL96] G. H. Golub and C. F. van Loan. Matrix</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016JHEP...11..009H','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016JHEP...11..009H"><span>Holographic duality from random <span class="hlt">tensor</span> networks</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Hayden, Patrick; Nezami, Sepehr; Qi, Xiao-Liang; Thomas, Nathaniel; Walter, Michael; Yang, Zhao</p> <p>2016-11-01</p> <p><span class="hlt">Tensor</span> networks provide a natural framework for exploring holographic duality because they obey entanglement area laws. They have been used to construct explicit toy models realizing many of the interesting structural features of the AdS/CFT correspondence, including the non-uniqueness of bulk operator reconstruction in the boundary theory. In this article, we explore the holographic properties of networks of random <span class="hlt">tensors</span>. We find that our models naturally incorporate many features that are analogous to those of the AdS/CFT correspondence. When the bond dimension of the <span class="hlt">tensors</span> is large, we show that the entanglement entropy of all boundary regions, whether connected or not, obey the Ryu-Takayanagi entropy formula, a fact closely related to known properties of the multipartite entanglement of assistance. We also discuss the behavior of Rényi entropies in our models and contrast it with AdS/CFT. Moreover, we find that each boundary region faithfully encodes the physics of the entire bulk entanglement wedge, i.e., the bulk region enclosed by the boundary region and the minimal surface. Our method is to interpret the average over random <span class="hlt">tensors</span> as the partition function of a classical ferromagnetic Ising model, so that the minimal surfaces of Ryu-Takayanagi appear as domain walls. Upon including the analog of a bulk field, we find that our model reproduces the expected corrections to the Ryu-Takayanagi formula: the bulk minimal surface is displaced and the entropy is augmented by the entanglement of the bulk field. Increasing the entanglement of the bulk field ultimately changes the minimal surface behavior topologically, in a way similar to the effect of creating a black hole. Extrapolating bulk correlation functions to the boundary permits the calculation of the scaling dimensions of boundary operators, which exhibit a large gap between a small number of low-dimension operators and the rest. While we are primarily motivated by the AdS/CFT duality, the main</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2015JPhCS.600a2003C','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015JPhCS.600a2003C"><span>Self tuning scalar <span class="hlt">tensor</span> black holes</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Charmousis, Christos; Iosifidis, Damianos</p> <p>2015-04-01</p> <p>Studying a certain sub class of higher order Horndeski (scalar-<span class="hlt">tensor</span>) theories we discuss a method discovered recently permitting analytic black hole solutions with a non trivial and regular scalar field. One of the solutions found has de Sitter asymptotics and self tunes the bulk cosmological constant. Using the aforementioned method we find and analyse new black hole solutions which can also have de Sitter asymptotics. By looking at small deviations of the integration constant responsible for self tuning we discuss the robustness of the self tuning mechanism. We find that neighboring solutions to the one previously found present also self tuning properties with unaltered effective cosmological constant.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017PhRvL.118c5502W','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017PhRvL.118c5502W"><span>Full Elasticity <span class="hlt">Tensor</span> from Thermal Diffuse Scattering</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Wehinger, Björn; Mirone, Alessandro; Krisch, Michael; Bosak, Alexeï</p> <p>2017-01-01</p> <p>We present a method for the precise determination of the full elasticity <span class="hlt">tensor</span> from a single crystal diffraction experiment using monochromatic x rays. For the two benchmark systems calcite and magnesium oxide, we show that the measurement of thermal diffuse scattering in the proximity of Bragg reflections provides accurate values of the complete set of elastic constants. This approach allows for a reliable and model-free determination of the elastic properties and can be performed together with crystal structure investigation in the same experiment.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/20000012389','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20000012389"><span>The Topology of Three-Dimensional Symmetric <span class="hlt">Tensor</span> Fields</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Lavin, Yingmei; Levy, Yuval; Hesselink, Lambertus</p> <p>1994-01-01</p> <p>We study the topology of 3-D symmetric <span class="hlt">tensor</span> fields. The goal is to represent their complex structure by a simple set of carefully chosen points and lines analogous to vector field topology. The basic constituents of <span class="hlt">tensor</span> topology are the degenerate points, or points where eigenvalues are equal to each other. First, we introduce a new method for locating 3-D degenerate points. We then extract the topological skeletons of the eigenvector fields and use them for a compact, comprehensive description of the <span class="hlt">tensor</span> field. Finally, we demonstrate the use of <span class="hlt">tensor</span> field topology for the interpretation of the two-force Boussinesq problem.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2010AIPC.1309....1A','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2010AIPC.1309....1A"><span>Conharmonic <span class="hlt">Tensor</span> of Certain Classes of Almost Hermitian Manifold</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Abood, Habeeb Mtashar; Lafta, Gassan Irhaim</p> <p>2010-11-01</p> <p>Most of the conharmonic <span class="hlt">tensor</span> studies are applied on Riemannian space. In this work we investigated the conharmonic curvature <span class="hlt">tensor</span> of some more specific important classes, In particular, the nearly Kahler and almost Kahler manifolds. Firstly, three special classes of almost Hermitian manifold depending on conharmonic <span class="hlt">tensor</span> have been defined. We found the relation between these classes and the class nearly Kahler manifold. The conharmonic recurrent of nearly Kahler manifold has been studied. Secondly, we found the necessary condition where an almost Kahler manifold is a manifold of a pointwise holomrphic conharmonic <span class="hlt">tensor</span>.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016ISPAr49B3..283L','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016ISPAr49B3..283L"><span><span class="hlt">Tensor</span> Modeling Based for Airborne LiDAR Data Classification</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Li, N.; Liu, C.; Pfeifer, N.; Yin, J. F.; Liao, Z. Y.; Zhou, Y.</p> <p>2016-06-01</p> <p>Feature selection and description is a key factor in classification of Earth observation data. In this paper a classification method based on <span class="hlt">tensor</span> decomposition is proposed. First, multiple features are extracted from raw LiDAR point cloud, and raster LiDAR images are derived by accumulating features or the "raw" data attributes. Then, the feature rasters of LiDAR data are stored as a <span class="hlt">tensor</span>, and <span class="hlt">tensor</span> decomposition is used to select component features. This <span class="hlt">tensor</span> representation could keep the initial spatial structure and insure the consideration of the neighborhood. Based on a small number of component features a k nearest neighborhood classification is applied.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016CRMec.344..402D','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016CRMec.344..402D"><span>3D extension of Tensorial Polar Decomposition. Application to (photo-)elasticity <span class="hlt">tensors</span></span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Desmorat, Rodrigue; Desmorat, Boris</p> <p>2016-06-01</p> <p>The orthogonalized harmonic decomposition of symmetric fourth-order <span class="hlt">tensors</span> (i.e. having major and minor indicial symmetries, such as elasticity <span class="hlt">tensors</span>) is completed by a representation of harmonic fourth-order <span class="hlt">tensors</span> H by means of two second-order harmonic (symmetric deviatoric) <span class="hlt">tensors</span> only. A similar decomposition is obtained for non-symmetric <span class="hlt">tensors</span> (i.e. having minor indicial symmetry only, such as photo-elasticity <span class="hlt">tensors</span> or elasto-plasticity tangent operators) introducing a fourth-order major antisymmetric traceless <span class="hlt">tensor</span> Z. The <span class="hlt">tensor</span> Z is represented by means of one harmonic second-order <span class="hlt">tensor</span> and one antisymmetric second-order <span class="hlt">tensor</span> only. Representations of totally symmetric (rari-constant), symmetric and major antisymmetric fourth-order <span class="hlt">tensors</span> are simple particular cases of the proposed general representation. Closed-form expressions for <span class="hlt">tensor</span> decomposition are given in the monoclinic case. Practical applications to elasticity and photo-elasticity monoclinic <span class="hlt">tensors</span> are finally presented. xml:lang="fr"</p> </li> </ol> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_16");'>16</a></li> <li><a href="#" onclick='return showDiv("page_17");'>17</a></li> <li class="active"><span>18</span></li> <li><a href="#" onclick='return showDiv("page_19");'>19</a></li> <li><a href="#" onclick='return showDiv("page_20");'>20</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div><!-- col-sm-12 --> </div><!-- row --> </div><!-- page_18 --> <div id="page_19" class="hiddenDiv"> <div class="row"> <div class="col-sm-12"> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_17");'>17</a></li> <li><a href="#" onclick='return showDiv("page_18");'>18</a></li> <li class="active"><span>19</span></li> <li><a href="#" onclick='return showDiv("page_20");'>20</a></li> <li><a href="#" onclick='return showDiv("page_21");'>21</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div> </div> <div class="row"> <div class="col-sm-12"> <ol class="result-class" start="361"> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017PhRvD..95f6004M','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017PhRvD..95f6004M"><span>From path integrals to <span class="hlt">tensor</span> networks for the AdS /CFT correspondence</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Miyaji, Masamichi; Takayanagi, Tadashi; Watanabe, Kento</p> <p>2017-03-01</p> <p>In this paper, we discuss <span class="hlt">tensor</span> network descriptions of AdS /CFT from two different viewpoints. First, we start with a Euclidean path-integral computation of ground state wave functions with a UV cutoff. We consider its efficient optimization by making its UV cutoff position dependent and define a <span class="hlt">quantum</span> state at each length scale. We conjecture that this path integral corresponds to a time slice of anti-de Sitter (AdS) spacetime. Next, we derive a flow of <span class="hlt">quantum</span> states by rewriting the action of Killing vectors of AdS3 in terms of the dual two-dimensional conformal field theory (CFT). Both approaches support a correspondence between the hyperbolic time slice H2 in AdS3 and a version of continuous multiscale entanglement renormalization ansatz. We also give a heuristic argument about why we can expect a sub-AdS scale bulk locality for holographic CFTs.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/23467780','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/23467780"><span>A symmetry invariant formulation of the relationship between the elasticity <span class="hlt">tensor</span> and the fabric <span class="hlt">tensor</span>.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Moesen, Maarten; Cardoso, Luis; Cowin, Stephen C</p> <p>2012-11-01</p> <p>The fabric <span class="hlt">tensor</span> is employed as a quantitative stereological measure of the structural anisotropy in the pore architecture of a porous medium. Earlier work showed that the fabric <span class="hlt">tensor</span> can be used additionally to the porosity to describe the anisotropy in the elastic constants of the porous medium. This contribution presents a reformulation of the relationship between fabric <span class="hlt">tensor</span> and anisotropic elastic constants that is approximation free and symmetry-invariant. From specific data on the elastic constants and the fabric, the parameters in the reformulated relationship can be evaluated individually and efficiently using a simplified method that works independent of the material symmetry. The well-behavedness of the parameters and the accuracy of the method was analyzed using the Mori-Tanaka model for aligned ellipsoidal inclusions and using Buckminster Fuller's octet-truss lattice. Application of the method to a cancellous bone data set revealed that employing the fabric <span class="hlt">tensor</span> allowed explaining 75-90% of the total variance. An implementation of the proposed methods was made publicly available.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=3953644','PMC'); return false;" href="https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=3953644"><span>Direct Solution of the Chemical Master Equation Using Quantized <span class="hlt">Tensor</span> Trains</span></a></p> <p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pmc">PubMed Central</a></p> <p>Kazeev, Vladimir; Khammash, Mustafa; Nip, Michael; Schwab, Christoph</p> <p>2014-01-01</p> <p>The Chemical Master Equation (CME) is a cornerstone of stochastic analysis and simulation of models of biochemical reaction networks. Yet direct solutions of the CME have remained elusive. Although several approaches overcome the infinite dimensional nature of the CME through projections or other means, a common feature of proposed approaches is their susceptibility to the curse of dimensionality, i.e. the exponential growth in memory and computational requirements in the number of problem dimensions. We present a novel approach that has the potential to “lift” this curse of dimensionality. The approach is based on the use of the recently proposed Quantized <span class="hlt">Tensor</span> Train (QTT) formatted numerical linear algebra for the low parametric, numerical representation of <span class="hlt">tensors</span>. The QTT decomposition admits both, algorithms for basic <span class="hlt">tensor</span> arithmetics with complexity scaling linearly in the dimension (number of species) and sub-linearly in the mode size (maximum copy number), and a numerical <span class="hlt">tensor</span> rounding procedure which is stable and quasi-optimal. We show how the CME can be represented in QTT format, then use the exponentially-converging -discontinuous Galerkin discretization in time to reduce the CME evolution problem to a set of QTT-structured linear equations to be solved at each time step using an algorithm based on Density Matrix Renormalization Group (DMRG) methods from <span class="hlt">quantum</span> chemistry. Our method automatically adapts the “basis” of the solution at every time step guaranteeing that it is large enough to capture the dynamics of interest but no larger than necessary, as this would increase the computational complexity. Our approach is demonstrated by applying it to three different examples from systems biology: independent birth-death process, an example of enzymatic futile cycle, and a stochastic switch model. The numerical results on these examples demonstrate that the proposed QTT method achieves dramatic speedups and several orders of magnitude</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/24626049','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/24626049"><span>Direct solution of the Chemical Master Equation using quantized <span class="hlt">tensor</span> trains.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Kazeev, Vladimir; Khammash, Mustafa; Nip, Michael; Schwab, Christoph</p> <p>2014-03-01</p> <p>The Chemical Master Equation (CME) is a cornerstone of stochastic analysis and simulation of models of biochemical reaction networks. Yet direct solutions of the CME have remained elusive. Although several approaches overcome the infinite dimensional nature of the CME through projections or other means, a common feature of proposed approaches is their susceptibility to the curse of dimensionality, i.e. the exponential growth in memory and computational requirements in the number of problem dimensions. We present a novel approach that has the potential to "lift" this curse of dimensionality. The approach is based on the use of the recently proposed Quantized <span class="hlt">Tensor</span> Train (QTT) formatted numerical linear algebra for the low parametric, numerical representation of <span class="hlt">tensors</span>. The QTT decomposition admits both, algorithms for basic <span class="hlt">tensor</span> arithmetics with complexity scaling linearly in the dimension (number of species) and sub-linearly in the mode size (maximum copy number), and a numerical <span class="hlt">tensor</span> rounding procedure which is stable and quasi-optimal. We show how the CME can be represented in QTT format, then use the exponentially-converging hp-discontinuous Galerkin discretization in time to reduce the CME evolution problem to a set of QTT-structured linear equations to be solved at each time step using an algorithm based on Density Matrix Renormalization Group (DMRG) methods from <span class="hlt">quantum</span> chemistry. Our method automatically adapts the "basis" of the solution at every time step guaranteeing that it is large enough to capture the dynamics of interest but no larger than necessary, as this would increase the computational complexity. Our approach is demonstrated by applying it to three different examples from systems biology: independent birth-death process, an example of enzymatic futile cycle, and a stochastic switch model. The numerical results on these examples demonstrate that the proposed QTT method achieves dramatic speedups and several orders of magnitude storage</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/25749731','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/25749731"><span>Using the <span class="hlt">quantum</span> yields of photosystem II and the rate of net photosynthesis to monitor high irradiance and temperature <span class="hlt">stress</span> in chrysanthemum (Dendranthema grandiflora).</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Janka, Eshetu; Körner, Oliver; Rosenqvist, Eva; Ottosen, Carl-Otto</p> <p>2015-05-01</p> <p>Under a dynamic greenhouse climate control regime, temperature is adjusted to optimise plant physiological responses to prevailing irradiance levels; thus, both temperature and irradiance are used by the plant to maximise the rate of photosynthesis, assuming other factors are not limiting. The control regime may be optimised by monitoring plant responses, and may be promptly adjusted when plant performance is affected by extreme microclimatic conditions, such as high irradiance or temperature. To determine the <span class="hlt">stress</span> indicators of plants based on their physiological responses, net photosynthesis (Pn) and four chlorophyll-a fluorescence parameters: maximum photochemical efficiency of PSII [Fv/Fm], electron transport rate [ETR], PSII operating efficiency [F'q/F'm], and non-photochemical quenching [NPQ] were assessed for potted chrysanthemum (Dendranthema grandiflora Tzvelev) 'Coral Charm' under different temperature (20, 24, 28, 32, 36 °C) and daily light integrals (DLI; 11, 20, 31, and 43 mol m(-2) created by a PAR of 171, 311, 485 and 667 μmol m(-2) s(-1) for 16 h). High irradiance (667 μmol m(-2) s(-1)) combined with high temperature (>32 °C) significantly (p < 0.05) decreased Fv/Fm. Under high irradiance, the maximum Pn and ETR were reached at 24 °C. Increased irradiance decreased the PSII operating efficiency and increased NPQ, while both high irradiance and temperature had a significant effect on the PSII operating efficiency at temperatures >28 °C. Under high irradiance and temperature, changes in the NPQ determined the PSII operating efficiency, with no major change in the fraction of open PSII centres (qL) (indicating a QA redox state). We conclude that 1) chrysanthemum plants cope with excess irradiance by non-radiative dissipation or a reversible <span class="hlt">stress</span> response, with the effect on the Pn and <span class="hlt">quantum</span> yield of PSII remaining low until the temperature reaches 28 °C and 2) the integration of online measurements to monitor photosynthesis and PSII</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017JPhCS.795a2031A','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017JPhCS.795a2031A"><span>Solution of generalized Dirac equation for Eckart plus Hulthen central potential combined with modified Hylleraas like <span class="hlt">tensor</span> potential using Romanovski polynomial method</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Ayu Dianawati, Dyah; Suparmi, A.; Cari, C.</p> <p>2017-01-01</p> <p>Romanovski Polynomial method was used to analyze of Dirac equation with Eckart plus Hulthen central potential combined with modified Hylleraas like <span class="hlt">tensor</span> potential on spin symmetry case. By using parameter and variable substitution, the Dirac equation was reduced into one dimensional Schrodinger like equation with centrifugal approximation that can be solved using Romanovski polynomial. The relativistic energy spectra is obtained from the relativistic energy equation by using Matlab R2008b software. The relativistic energy with <span class="hlt">quantum</span> number and spin orbit <span class="hlt">quantum</span> number variations were obtained. By using matlab R2008b software, visualisasion of the relativistic energy spectra with <span class="hlt">quantum</span> number variasion were obtained.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/scitech/biblio/22525725','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/22525725"><span>Energy-momentum <span class="hlt">tensor</span> of bouncing gravitons</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Iofa, Mikhail Z.</p> <p>2015-07-01</p> <p>In models of the Universe with extra dimensions gravity propagates in the whole space-time. Graviton production by matter on the brane is significant in the early hot Universe. In a model of 3-brane with matter embedded in 5D space-time conditions for gravitons emitted from the brane to the bulk to return back to the brane are found. For a given 5-momentum of graviton falling back to the brane the interval between the times of emission and return to the brane is calculated. A method to calculate contribution to the energy-momentum <span class="hlt">tensor</span> from multiple graviton bouncings is developed. Explicit expressions for contributions to the energy-momentum <span class="hlt">tensor</span> of gravitons which have made one, two and three bounces are obtained and their magnitudes are numerically calculated. These expressions are used to solve the evolution equation for dark radiation. A relation connecting reheating temperature and the scale of extra dimension is obtained. For the reheating temperature T{sub R}∼ 10{sup 6} GeV we estimate the scale of extra dimension μ to be of order 10{sup −9} GeV (μ{sup −1}∼ 10{sup −5} cm)</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/scitech/biblio/22454569','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/22454569"><span>Energy-momentum <span class="hlt">tensor</span> of bouncing gravitons</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Iofa, Mikhail Z.</p> <p>2015-07-14</p> <p>In models of the Universe with extra dimensions gravity propagates in the whole space-time. Graviton production by matter on the brane is significant in the early hot Universe. In a model of 3-brane with matter embedded in 5D space-time conditions for gravitons emitted from the brane to the bulk to return back to the brane are found. For a given 5-momentum of graviton falling back to the brane the interval between the times of emission and return to the brane is calculated. A method to calculate contribution to the energy-momentum <span class="hlt">tensor</span> from multiple graviton bouncings is developed. Explicit expressions for contributions to the energy-momentum <span class="hlt">tensor</span> of gravitons which have made one, two and three bounces are obtained and their magnitudes are numerically calculated. These expressions are used to solve the evolution equation for dark radiation. A relation connecting reheating temperature and the scale of extra dimension is obtained. For the reheating temperature T{sub R}∼10{sup 6} GeV we estimate the scale of extra dimension μ to be of order 10{sup −9} GeV (μ{sup −1}∼10{sup −5} cm)</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/scitech/biblio/22369955','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/22369955"><span>Stability of Horndeski vector-<span class="hlt">tensor</span> interactions</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Jiménez, Jose Beltrán; Durrer, Ruth; Heisenberg, Lavinia; Thorsrud, Mikjel E-mail: ruth.durrer@unige.ch E-mail: mikjel.thorsrud@astro.uio.no</p> <p>2013-10-01</p> <p>We study the Horndeski vector-<span class="hlt">tensor</span> theory that leads to second order equations of motion and contains a non-minimally coupled abelian gauge vector field. This theory is remarkably simple and consists of only 2 terms for the vector field, namely: the standard Maxwell kinetic term and a coupling to the dual Riemann <span class="hlt">tensor</span>. Furthermore, the vector sector respects the U(1) gauge symmetry and the theory contains only one free parameter, M{sup 2}, that controls the strength of the non-minimal coupling. We explore the theory in a de Sitter spacetime and study the presence of instabilities and show that it corresponds to an attractor solution in the presence of the vector field. We also investigate the cosmological evolution and stability of perturbations in a general FLRW spacetime. We find that a sufficient condition for the absence of ghosts is M{sup 2} > 0. Moreover, we study further constraints coming from imposing the absence of Laplacian instabilities. Finally, we study the stability of the theory in static and spherically symmetric backgrounds (in particular, Schwarzschild and Reissner-Nordström-de Sitter). We find that the theory, quite generally, do have ghosts or Laplacian instabilities in regions of spacetime where the non-minimal interaction dominates over the Maxwell term. We also calculate the propagation speed in these spacetimes and show that superluminality is a quite generic phenomenon in this theory.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2015JCAP...07..021I','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015JCAP...07..021I"><span>Energy-momentum <span class="hlt">tensor</span> of bouncing gravitons</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Iofa, Mikhail Z.</p> <p>2015-07-01</p> <p>In models of the Universe with extra dimensions gravity propagates in the whole space-time. Graviton production by matter on the brane is significant in the early hot Universe. In a model of 3-brane with matter embedded in 5D space-time conditions for gravitons emitted from the brane to the bulk to return back to the brane are found. For a given 5-momentum of graviton falling back to the brane the interval between the times of emission and return to the brane is calculated. A method to calculate contribution to the energy-momentum <span class="hlt">tensor</span> from multiple graviton bouncings is developed. Explicit expressions for contributions to the energy-momentum <span class="hlt">tensor</span> of gravitons which have made one, two and three bounces are obtained and their magnitudes are numerically calculated. These expressions are used to solve the evolution equation for dark radiation. A relation connecting reheating temperature and the scale of extra dimension is obtained. For the reheating temperature TR~ 106 GeV we estimate the scale of extra dimension μ to be of order 10-9 GeV (μ-1~ 10-5 cm).</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/971192','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/971192"><span>Interactive Volume Rendering of Diffusion <span class="hlt">Tensor</span> Data</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Hlawitschka, Mario; Weber, Gunther; Anwander, Alfred; Carmichael, Owen; Hamann, Bernd; Scheuermann, Gerik</p> <p>2007-03-30</p> <p>As 3D volumetric images of the human body become an increasingly crucial source of information for the diagnosis and treatment of a broad variety of medical conditions, advanced techniques that allow clinicians to efficiently and clearly visualize volumetric images become increasingly important. Interaction has proven to be a key concept in analysis of medical images because static images of 3D data are prone to artifacts and misunderstanding of depth. Furthermore, fading out clinically irrelevant aspects of the image while preserving contextual anatomical landmarks helps medical doctors to focus on important parts of the images without becoming disoriented. Our goal was to develop a tool that unifies interactive manipulation and context preserving visualization of medical images with a special focus on diffusion <span class="hlt">tensor</span> imaging (DTI) data. At each image voxel, DTI provides a 3 x 3 <span class="hlt">tensor</span> whose entries represent the 3D statistical properties of water diffusion locally. Water motion that is preferential to specific spatial directions suggests structural organization of the underlying biological tissue; in particular, in the human brain, the naturally occuring diffusion of water in the axon portion of neurons is predominantly anisotropic along the longitudinal direction of the elongated, fiber-like axons [MMM+02]. This property has made DTI an emerging source of information about the structural integrity of axons and axonal connectivity between brain regions, both of which are thought to be disrupted in a broad range of medical disorders including multiple sclerosis, cerebrovascular disease, and autism [Mos02, FCI+01, JLH+99, BGKM+04, BJB+03].</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/scitech/biblio/22525481','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/22525481"><span>Consistent cosmic microwave background spectra from <span class="hlt">quantum</span> depletion</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Casadio, Roberto; Orlandi, Alessio; Kühnel, Florian E-mail: florian.kuhnel@fysik.su.se</p> <p>2015-09-01</p> <p>Following a new <span class="hlt">quantum</span> cosmological model proposed by Dvali and Gomez, we quantitatively investigate possible modifications to the Hubble parameter and following corrections to the cosmic microwave background spectrum. In this model, scalar and <span class="hlt">tensor</span> perturbations are generated by the <span class="hlt">quantum</span> depletion of the background inflaton and graviton condensate respectively. We show how the inflaton mass affects the power spectra and the <span class="hlt">tensor</span>-to-scalar ratio. Masses approaching the Planck scale would lead to strong deviations, while standard spectra are recovered for an inflaton mass much smaller than the Planck mass.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://pubs.er.usgs.gov/publication/70029131','USGSPUBS'); return false;" href="http://pubs.er.usgs.gov/publication/70029131"><span>Moment <span class="hlt">tensor</span> inversion of ground motion from mining-induced earthquakes, Trail Mountain, Utah</span></a></p> <p><a target="_blank" href="http://pubs.er.usgs.gov/pubs/index.jsp?view=adv">USGS Publications Warehouse</a></p> <p>Fletcher, Joe B.; McGarr, A.</p> <p>2005-01-01</p> <p>A seismic network was operated in the vicinity of the Trail Mountain mine, central Utah, from the summer of 2000 to the spring of 2001 to investigate the seismic hazard to a local dam from mining-induced events that we expect to be triggered by future coal mining in this area. In support of efforts to develop groundmotion prediction relations for this situation, we inverted ground-motion recordings for six mining-induced events to determine seismic moment <span class="hlt">tensors</span> and then to estimate moment magnitudes M for comparison with the network coda magnitudes Mc. Six components of the <span class="hlt">tensor</span> were determined, for an assumed point source, following the inversion method of McGarr (1992a), which uses key measurements of amplitude from obvious features of the displacement waveforms. When the resulting moment <span class="hlt">tensors</span> were decomposed into implosive and deviatoric components, we found that four of the six events showed a substantial volume reduction, presumably due to coseismic closure of the adjacent mine openings. For these four events, the volume reduction ranges from 27% to 55% of the shear component (fault area times average slip). Radiated seismic energy, computed from attenuation-corrected body-wave spectra, ranged from 2.4 ?? 105 to 2.4 ?? 106 J for events with M from 1.3 to 1.8, yielding apparent <span class="hlt">stresses</span> from 0.02 to 0.06 MPa. The energy released for each event, approximated as the product of volume reduction and overburden <span class="hlt">stress</span>, when compared with the corresponding seismic energies, revealed seismic efficiencies ranging from 0.5% to 7%. The low apparent <span class="hlt">stresses</span> are consistent with the shallow focal depths of 0.2 to 0.6 km and rupture in a low <span class="hlt">stress</span>/low strength regime compared with typical earthquake source regions at midcrustal depths.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2015IJMPA..3050197B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015IJMPA..3050197B"><span>Relativistic geometric <span class="hlt">quantum</span> phases from the Lorentz symmetry violation effects in the CPT-even gauge sector of Standard Model Extension</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Bakke, K.; Belich, H.</p> <p>2015-11-01</p> <p>We discuss the appearance of geometric <span class="hlt">quantum</span> phases for a Dirac neutral particle in the context of relativistic <span class="hlt">quantum</span> mechanics based on possible scenarios of the Lorentz symmetry violation <span class="hlt">tensor</span> background in the CPT-even gauge sector of Standard Model Extension. We assume that the Lorentz symmetry breaking is determined by a <span class="hlt">tensor</span> background given by (KF)μναβ, then, relativistic analogues of the Anandan <span class="hlt">quantum</span> phase [J. Anandan, Phys. Lett. A 138, 347 (1989)] are obtained based on the parity-even and parity-odd sectors of the <span class="hlt">tensor</span> (KF)μναβ.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016PhRvD..93e4015L','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016PhRvD..93e4015L"><span>Central exclusive diffractive production of the π+π- continuum, scalar, and <span class="hlt">tensor</span> resonances in p p and p p ¯ scattering within the <span class="hlt">tensor</span> Pomeron approach</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Lebiedowicz, Piotr; Nachtmann, Otto; Szczurek, Antoni</p> <p>2016-03-01</p> <p>We consider central exclusive diffractive dipion production in the reactions p p →p p π+π- and p p ¯ →p p ¯ π+π- at high energies. We include the dipion continuum, the dominant scalar f0(500 ), f0(980 ) , and <span class="hlt">tensor</span> f2(1270 ) resonances decaying into the π+π- pairs. The calculation is based on a <span class="hlt">tensor</span> Pomeron model and the amplitudes for the processes are formulated in terms of vertices respecting the standard crossing and charge-conjugation relations of <span class="hlt">quantum</span> field theory. The formulas for the dipion continuum and <span class="hlt">tensor</span> meson production are given here for the first time. The theoretical results are compared with existing STAR, CDF, CMS experimental data and predictions for planned or current experiments (ALICE, ATLAS) are presented. We show the influence of the experimental cuts on the integrated cross section and on various differential distributions for outgoing particles. Distributions in rapidities and transverse momenta of outgoing protons and pions as well as correlations in azimuthal angle between them are presented. We find that the relative contribution of the resonant f2(1270 ) and dipion continuum strongly depends on the cut on proton transverse momenta or four-momentum transfer squared t1 ,2 which may explain some controversial observations made by different ISR experiments in the past. The cuts may play then the role of a π π resonance filter. We suggest some experimental analyses to fix model parameters related to the Pomeron-Pomeron-f2 coupling.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2010APS..MARZ42001V','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2010APS..MARZ42001V"><span>Continuum mechanics for <span class="hlt">quantum</span> many-body systems</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Vignale, Giovanni; Tao, Jianmin; Gao, Xianlong; Tokatly, Ilya</p> <p>2010-03-01</p> <p>Continuum mechanics is a theory of the dynamics of classical liquids and solids in which the state of the body is described by a small set of collective, such as density and current. A similar description is possible for <span class="hlt">quantum</span> many-body systems, and indeed its existence is guaranteed by the basic theorems of time-dependent current density functional theory. In this paper we show how the exact Heisenberg equation of motion for the current density of a many-body system can be closed by expressing the <span class="hlt">quantum</span> <span class="hlt">stress</span> <span class="hlt">tensor</span> as a functional of the current density. Several approximation schemes for this functional are discussed. The simplest scheme allows us to bypass the solution of the time-dependent Schr"odinger equation, resulting in an equation of motion for the current that requires only ground-state properties as an input. We illustrate the formalism by applying it to the calculation of excitation energies in simple one- and two-electron systems.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/23822257','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/23822257"><span>A constitutive framework for the non-Newtonian pressure <span class="hlt">tensor</span> of a simple fluid under planar flows.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Hartkamp, Remco; Todd, B D; Luding, Stefan</p> <p>2013-06-28</p> <p>Non-equilibrium molecular dynamics simulations of an atomic fluid under shear flow, planar elongational flow, and a combination of shear and elongational flow are unified consistently with a tensorial model over a wide range of strain rates. A model is presented that predicts the pressure <span class="hlt">tensor</span> for a non-Newtonian bulk fluid under a homogeneous planar flow field. The model provides a quantitative description of the strain-thinning viscosity, pressure dilatancy, deviatoric viscoelastic lagging, and out-of-flow-plane pressure anisotropy. The non-equilibrium pressure <span class="hlt">tensor</span> is completely described through these four quantities and can be calculated as a function of the equilibrium material constants and the velocity gradient. This constitutive framework in terms of invariants of the pressure <span class="hlt">tensor</span> departs from the conventional description that deals with an orientation-dependent description of shear <span class="hlt">stresses</span> and normal <span class="hlt">stresses</span>. The present model makes it possible to predict the full pressure <span class="hlt">tensor</span> for a simple fluid under various types of flows without having to produce these flow types explicitly in a simulation or experiment.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2008CG.....34..738P','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2008CG.....34..738P"><span><span class="hlt">Tensor</span>3D: A computer graphics program to simulate 3D real-time deformation and visualization of geometric bodies</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Pallozzi Lavorante, Luca; Dirk Ebert, Hans</p> <p>2008-07-01</p> <p><span class="hlt">Tensor</span>3D is a geometric modeling program with the capacity to simulate and visualize in real-time the deformation, specified through a <span class="hlt">tensor</span> matrix and applied to triangulated models representing geological bodies. 3D visualization allows the study of deformational processes that are traditionally conducted in 2D, such as simple and pure shears. Besides geometric objects that are immediately available in the program window, the program can read other models from disk, thus being able to import objects created with different open-source or proprietary programs. A strain ellipsoid and a bounding box are simultaneously shown and instantly deformed with the main object. The principal axes of strain are visualized as well to provide graphical information about the orientation of the <span class="hlt">tensor</span>'s normal components. The deformed models can also be saved, retrieved later and deformed again, in order to study different steps of progressive strain, or to make this data available to other programs. The shape of <span class="hlt">stress</span> ellipsoids and the corresponding Mohr circles defined by any <span class="hlt">stress</span> <span class="hlt">tensor</span> can also be represented. The application was written using the Visualization ToolKit, a powerful scientific visualization library in the public domain. This development choice, allied to the use of the Tcl/Tk programming language, which is independent on the host computational platform, makes the program a useful tool for the study of geometric deformations directly in three dimensions in teaching as well as research activities.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/24074068','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/24074068"><span>Black holes with surrounding matter in scalar-<span class="hlt">tensor</span> theories.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Cardoso, Vitor; Carucci, Isabella P; Pani, Paolo; Sotiriou, Thomas P</p> <p>2013-09-13</p> <p>We uncover two mechanisms that can render Kerr black holes unstable in scalar-<span class="hlt">tensor</span> gravity, both associated with the presence of matter in the vicinity of the black hole and the fact that this introduces an effective mass for the scalar. Our results highlight the importance of understanding the structure of spacetime in realistic, astrophysical black holes in scalar-<span class="hlt">tensor</span> theories.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2014JPhCS.543a1001.','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2014JPhCS.543a1001."><span>PREFACE: 1st <span class="hlt">Tensor</span> Polarized Solid Target Workshop</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p></p> <p>2014-10-01</p> <p>These are the proceedings of the first <span class="hlt">Tensor</span> Spin Observables Workshop that was held in March 2014 at the Thomas Jefferson National Accelerator Facility in Newport News, Virginia. The conference was convened to study the physics that can be done with the recently approved E12-13-011 polarized target. A <span class="hlt">tensor</span> polarized target holds the potential of initiating a new generation of <span class="hlt">tensor</span> spin physics at Jefferson Lab. Experiments which utilize <span class="hlt">tensor</span> polarized targets can help clarify how nuclear properties arise from partonic degrees of freedom, provide unique insight into short-range correlations and quark angular momentum, and also help pin down the polarization of the quark sea with a future Electron Ion Collider. This three day workshop was focused on <span class="hlt">tensor</span> spin observables and the associated <span class="hlt">tensor</span> target development. The workshop goals were to stimulate progress in the theoretical treatment of polarized spin-1 systems, foster the development of new proposals, and to reach a consensus on the optimal polarized target configuration for the <span class="hlt">tensor</span> spin program. The workshop was sponsored by the University of New Hampshire, the Jefferson Science Associates, Florida International University, and Jefferson Lab. It was organized by Karl Slifer (chair), Patricia Solvignon, and Elena Long of the University of New Hampshire, Douglas Higinbotham and Christopher Keith of Jefferson Lab, and Misak Sargsian of the Florida International University. These proceedings represent the effort put forth by the community to begin exploring the possibilities that a high-luminosity, high-<span class="hlt">tensor</span> polarized solid target can offer.</p> </li> </ol> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_17");'>17</a></li> <li><a href="#" onclick='return showDiv("page_18");'>18</a></li> <li class="active"><span>19</span></li> <li><a href="#" onclick='return showDiv("page_20");'>20</a></li> <li><a href="#" onclick='return showDiv("page_21");'>21</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div><!-- col-sm-12 --> </div><!-- row --> </div><!-- page_19 --> <div id="page_20" class="hiddenDiv"> <div class="row"> <div class="col-sm-12"> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_18");'>18</a></li> <li><a href="#" onclick='return showDiv("page_19");'>19</a></li> <li class="active"><span>20</span></li> <li><a href="#" onclick='return showDiv("page_21");'>21</a></li> <li><a href="#" onclick='return showDiv("page_22");'>22</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div> </div> <div class="row"> <div class="col-sm-12"> <ol class="result-class" start="381"> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016JHEP...08..086B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016JHEP...08..086B"><span>Exploring the <span class="hlt">tensor</span> networks/AdS correspondence</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Bhattacharyya, Arpan; Gao, Zhe-Shen; Hung, Ling-Yan; Liu, Si-Nong</p> <p>2016-08-01</p> <p>In this paper we study the recently proposed <span class="hlt">tensor</span> networks/AdS correspondence. We found that the Coxeter group is a useful tool to describe <span class="hlt">tensor</span> networks in a negatively curved space. Studying generic <span class="hlt">tensor</span> network populated by perfect <span class="hlt">tensors</span>, we find that the physical wave function generically do not admit any connected correlation functions of local operators. To remedy the problem, we assume that wavefunctions admitting such semi-classical gravitational interpretation are composed of <span class="hlt">tensors</span> close to, but not exactly perfect <span class="hlt">tensors</span>. Computing corrections to the connected two point correlation functions, we find that the leading contribution is given by structures related to geodesics connecting the operators inserted at the boundary physical dofs. Such considerations admit generalizations at least to three point functions. This is highly suggestive of the emergence of the analogues of Witten diagrams in the <span class="hlt">tensor</span> network. The perturbations alone however do not give the right entanglement spectrum. Using the Coxeter construction, we also constructed the <span class="hlt">tensor</span> network counterpart of the BTZ black hole, by orbifolding the discrete lattice on which the network resides. We found that the construction naturally reproduces some of the salient features of the BTZ black hole, such as the appearance of RT surfaces that could wrap the horizon, depending on the size of the entanglement region A.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/scitech/biblio/22403415','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/22403415"><span>The Kummer <span class="hlt">tensor</span> density in electrodynamics and in gravity</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Baekler, Peter; Favaro, Alberto; Itin, Yakov; Hehl, Friedrich W.</p> <p>2014-10-15</p> <p>Guided by results in the premetric electrodynamics of local and linear media, we introduce on 4-dimensional spacetime the new abstract notion of a Kummer <span class="hlt">tensor</span> density of rank four, K{sup ijkl}. This <span class="hlt">tensor</span> density is, by definition, a cubic algebraic functional of a <span class="hlt">tensor</span> density of rank four T{sup ijkl}, which is antisymmetric in its first two and its last two indices: T{sup ijkl}=−T{sup jikl}=−T{sup ijlk}. Thus, K∼T{sup 3}, see Eq. (46). (i) If T is identified with the electromagnetic response <span class="hlt">tensor</span> of local and linear media, the Kummer <span class="hlt">tensor</span> density encompasses the generalized Fresnel wave surfaces for propagating light. In the reversible case, the wave surfaces turn out to be Kummer surfaces as defined in algebraic geometry (Bateman 1910). (ii) If T is identified with the curvature <span class="hlt">tensor</span> R{sup ijkl} of a Riemann–Cartan spacetime, then K∼R{sup 3} and, in the special case of general relativity, K reduces to the Kummer <span class="hlt">tensor</span> of Zund (1969). This K is related to the principal null directions of the curvature. We discuss the properties of the general Kummer <span class="hlt">tensor</span> density. In particular, we decompose K irreducibly under the 4-dimensional linear group GL(4,R) and, subsequently, under the Lorentz group SO(1,3)</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/974874','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/974874"><span>MATLAB <span class="hlt">tensor</span> classes for fast algorithm prototyping : source code.</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Bader, Brett William; Kolda, Tamara Gibson</p> <p>2004-10-01</p> <p>We present the source code for three MATLAB classes for manipulating <span class="hlt">tensors</span> in order to allow fast algorithm prototyping. A <span class="hlt">tensor</span> is a multidimensional or Nway array. This is a supplementary report; details on using this code are provided separately in SAND-XXXX.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2014AnPhy.349..297B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2014AnPhy.349..297B"><span>The Kummer <span class="hlt">tensor</span> density in electrodynamics and in gravity</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Baekler, Peter; Favaro, Alberto; Itin, Yakov; Hehl, Friedrich W.</p> <p>2014-10-01</p> <p>Guided by results in the premetric electrodynamics of local and linear media, we introduce on 4-dimensional spacetime the new abstract notion of a Kummer <span class="hlt">tensor</span> density of rank four, K. This <span class="hlt">tensor</span> density is, by definition, a cubic algebraic functional of a <span class="hlt">tensor</span> density of rank four T, which is antisymmetric in its first two and its last two indices: T=-T=-T. Thus, K∼T3, see Eq. (46). (i) If T is identified with the electromagnetic response <span class="hlt">tensor</span> of local and linear media, the Kummer <span class="hlt">tensor</span> density encompasses the generalized Fresnel wave surfaces for propagating light. In the reversible case, the wave surfaces turn out to be Kummer surfaces as defined in algebraic geometry (Bateman 1910). (ii) If T is identified with the curvature <span class="hlt">tensor</span> R of a Riemann-Cartan spacetime, then K∼R3 and, in the special case of general relativity, K reduces to the Kummer <span class="hlt">tensor</span> of Zund (1969). This K is related to the principal null directions of the curvature. We discuss the properties of the general Kummer <span class="hlt">tensor</span> density. In particular, we decompose K irreducibly under the 4-dimensional linear group GL(4,R) and, subsequently, under the Lorentz group SO(1,3).</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/scitech/biblio/1208022','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/1208022"><span><span class="hlt">Tensor</span> spin observables and spin stucture at low Q2</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Slifer, Karl J.</p> <p>2015-04-01</p> <p>We discuss recent spin structure results from Jefferson Lab, and outline an emerging program to study <span class="hlt">tensor</span> spin observables using solid deuteron targets. These new experiments open the potential to study hidden color, the <span class="hlt">tensor</span> nature of short range correlations, and to probe for exotic gluonic states.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016REDS..171...13R','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016REDS..171...13R"><span>Self-consistency conditions for elementary Reynolds <span class="hlt">stress</span> closures</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Rubinstein, Robert</p> <p>2016-02-01</p> <p>This paper summarizes the analytical representation of the correlation <span class="hlt">tensor</span> in homogeneous anisotropic turbulence and sketches an application to Reynolds <span class="hlt">stress</span> transport turbulence models. It is shown that the analytical approach can address some of the limitations of conventional modeling.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/1221372','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/1221372"><span>On the energy-momentum <span class="hlt">tensor</span> in Moyal space</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Balasin, Herbert; Blaschke, Daniel N.; Gieres, François; Schweda, Manfred</p> <p>2015-06-26</p> <p>We study the properties of the energy-momentum <span class="hlt">tensor</span> of gauge fields coupled to matter in non-commutative (Moyal) space. In general, the non-commutativity affects the usual conservation law of the <span class="hlt">tensor</span> as well as its transformation properties (gauge covariance instead of gauge invariance). It is known that the conservation of the energy-momentum <span class="hlt">tensor</span> can be achieved by a redefinition involving another starproduct. Furthermore, for a pure gauge theory it is always possible to define a gauge invariant energy-momentum <span class="hlt">tensor</span> by means of a Wilson line. We show that the latter two procedures are incompatible with each other if couplings of gauge fields to matter fields (scalars or fermions) are considered: The gauge invariant <span class="hlt">tensor</span> (constructed via Wilson line) does not allow for a redefinition assuring its conservation, and vice-versa the introduction of another star-product does not allow for gauge invariance by means of a Wilson line.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/20593175','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/20593175"><span>Diffusion <span class="hlt">tensor</span> imaging of peripheral nerves.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Jambawalikar, Sachin; Baum, Jeremy; Button, Terry; Li, Haifang; Geronimo, Veronica; Gould, Elaine S</p> <p>2010-11-01</p> <p>Magnetic resonance diffusion <span class="hlt">tensor</span> imaging (DTI) allows the directional dependence of water diffusion to be studied. Analysis of the resulting image data allows for the determination of fractional anisotropy (FA), apparent diffusion coefficient (ADC), as well as allowing three-dimensional visualization of the fiber tract (tractography). We visualized the ulnar nerve of ten healthy volunteers with DTI. We found FA to be 0.752 ± 0.067 and the ADC to be 0.96 ± 0.13 × 10(-3) mm(2)/s. A nuts-and-bolts description of the physical aspects of DTI is provided as an educational process for readers.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016CQGra..33g5012P','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016CQGra..33g5012P"><span>f(R)-gravity from Killing <span class="hlt">tensors</span></span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Paliathanasis, Andronikos</p> <p>2016-04-01</p> <p>We consider f(R)-gravity in a Friedmann-Lemaître-Robertson-Walker spacetime with zero spatial curvature. We apply the Killing <span class="hlt">tensors</span> of the minisuperspace in order to specify the functional form of f(R) and for the field equations to be invariant under Lie-Bäcklund transformations, which are linear in momentum (contact symmetries). Consequently, the field equations to admit quadratic conservation laws given by Noether’s theorem. We find three new integrable f(R)-models, for which, with the application of the conservation laws, we reduce the field equations to a system of two first-order ordinary differential equations. For each model we study the evolution of the cosmological fluid. We find that for each integrable model the cosmological fluid has an equation of state parameter, in which there is linear behavior in terms of the scale factor which describes the Chevallier, Polarski and Linder parametric dark energy model.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016EPJWC.13005021X','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016EPJWC.13005021X"><span>Photo-production of <span class="hlt">tensor</span> mesons</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Xie, Ju-Jun; Geng, Li-Sheng; Oset, Eulogio</p> <p>2016-11-01</p> <p>Assuming that the f2(1270), f'2(1525), a2(1320), and K*2(1430) resonances are dynamically generated states from the vector meson-vector meson interactions in L = 0 and spin 2, we study the γp → f2(1270)[f'2(1525)]p, γp → a02 (1320)p, and γp → K*2(1430)Λ(Σ) reactions. For the γp → f2(1270)p reaction, we find that the theoretical results for the differential cross sections are in good agreement with the experimental measurements and provide support for the molecular picture of the f2(1270) in the first baryonic reaction where it has been tested. Furthermore, we predict also the total and differential cross sections for other reactions. The results can be tested in future experiments and therefore offer new clues on the nature of these <span class="hlt">tensor</span> states.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/scitech/biblio/21503600','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/21503600"><span>Bounds on <span class="hlt">tensor</span> wave and twisted inflation</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Panda, Sudhakar; Sami, M.; Ward, John</p> <p>2010-11-15</p> <p>We study the bounds on <span class="hlt">tensor</span> wave in a class of twisted inflation models, where D(4+2k)-branes are wrapped on cycles in the compact manifold and wrap the Kaluza-Klein direction in the corresponding effective field theory. While the lower bound is found to be analogous to that in type IIB models of brane inflation, the upper bound turns out to be significantly different. This is argued for a range of values for the parameter g{sub s}M satisfying the self-consistency relation and the WMAP data. Further, we observe that the wrapped D8-brane appears to be the most attractive from a cosmological perspective.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/16342152','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/16342152"><span>Diffusion <span class="hlt">tensor</span> spectroscopy (DTS) of human brain.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Ellegood, Jacob; Hanstock, Chris C; Beaulieu, Christian</p> <p>2006-01-01</p> <p>The diffusion <span class="hlt">tensor</span> of N-acetyl aspartate (NAA), creatine and phosphocreatine (tCr), and choline (Cho) was measured at 3T using a diffusion weighted STEAM (1)H-MRS sequence in the healthy human brain in 6 distinct regions (4 white matter and 2 cortical gray matter). The Trace/3 apparent diffusion coefficient (ADC) of each metabolite was significantly greater in white matter than gray matter. The Trace/3 ADC values of tCr and Cho were found to be significantly greater than NAA in white matter, whereas all 3 metabolites had similar Trace/3 ADC in cortical gray matter. Fractional anisotropy (FA) values for all 3 metabolites were consistent with water FA values in the 4 white matter regions; however, metabolite FA values were found to be higher than expected in the cortical gray matter. The principal diffusion direction derived for NAA was in good agreement with expected anatomic tract directions in the white matter.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/scitech/biblio/22392517','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/22392517"><span>Development of a vector-<span class="hlt">tensor</span> system to measure the absolute magnetic flux density and its gradient in magnetically shielded rooms</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Voigt, J.; Knappe-Grüneberg, S.; Gutkelch, D.; Neuber, S.; Schnabel, A.; Burghoff, M.; Haueisen, J.</p> <p>2015-05-15</p> <p>Several experiments in fundamental physics demand an environment of very low, homogeneous, and stable magnetic fields. For the magnetic characterization of such environments, we present a portable SQUID system that measures the absolute magnetic flux density vector and the gradient <span class="hlt">tensor</span>. This vector-<span class="hlt">tensor</span> system contains 13 integrated low-critical temperature (LTc) superconducting <span class="hlt">quantum</span> interference devices (SQUIDs) inside a small cylindrical liquid helium Dewar with a height of 31 cm and 37 cm in diameter. The achievable resolution depends on the flux density of the field under investigation and its temporal drift. Inside a seven-layer mu-metal shield, an accuracy better than ±23 pT for the components of the static magnetic field vector and ±2 pT/cm for each of the nine components of the gradient <span class="hlt">tensor</span> is reached by using the shifting method.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/22392704','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/22392704"><span>Affinity learning with diffusion on <span class="hlt">tensor</span> product graph.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Yang, Xingwei; Prasad, Lakshman; Latecki, Longin Jan</p> <p>2013-01-01</p> <p>In many applications, we are given a finite set of data points sampled from a data manifold and represented as a graph with edge weights determined by pairwise similarities of the samples. Often the pairwise similarities (which are also called affinities) are unreliable due to noise or due to intrinsic difficulties in estimating similarity values of the samples. As observed in several recent approaches, more reliable similarities can be obtained if the original similarities are diffused in the context of other data points, where the context of each point is a set of points most similar to it. Compared to the existing methods, our approach differs in two main aspects. First, instead of diffusing the similarity information on the original graph, we propose to utilize the <span class="hlt">tensor</span> product graph (TPG) obtained by the <span class="hlt">tensor</span> product of the original graph with itself. Since TPG takes into account higher order information, it is not a surprise that we obtain more reliable similarities. However, it comes at the price of higher order computational complexity and storage requirement. The key contribution of the proposed approach is that the information propagation on TPG can be computed with the same computational complexity and the same amount of storage as the propagation on the original graph. We prove that a graph diffusion process on TPG is equivalent to a novel iterative algorithm on the original graph, which is guaranteed to converge. After its convergence we obtain new edge weights that can be interpreted as new, learned affinities. We <span class="hlt">stress</span> that the affinities are learned in an unsupervised setting. We illustrate the benefits of the proposed approach for data manifolds composed of shapes, images, and image patches on two very different tasks of image retrieval and image segmentation. With learned affinities, we achieve the bull's eye retrieval score of 99.99 percent on the MPEG-7 shape dataset, which is much higher than the state-of-the-art algorithms. When the data</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2015PhyS...90i5101N','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015PhyS...90i5101N"><span>Non-classical conditional probability and the <span class="hlt">quantum</span> no-cloning theorem</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Niestegge, Gerd</p> <p>2015-09-01</p> <p>The <span class="hlt">quantum</span> mechanical no-cloning theorem for pure states is generalized and transfered to the <span class="hlt">quantum</span> logics with a conditional probability calculus in a rather abstract, though simple and basic fashion without relying on a <span class="hlt">tensor</span> product construction or finite dimension as required in other generalizations.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016MTDM..tmp...36S','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016MTDM..tmp...36S"><span>A viscoelastic Unitary Crack-Opening strain <span class="hlt">tensor</span> for crack width assessment in fractured concrete structures</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Sciumè, Giuseppe; Benboudjema, Farid</p> <p>2016-09-01</p> <p>A post-processing technique which allows computing crack width in concrete is proposed for a viscoelastic damage model. Concrete creep is modeled by means of a Kelvin-Voight cell while the damage model is that of Mazars in its local form. Due to the local damage approach, the constitutive model is regularized with respect to finite element mesh to avoid mesh dependency in the computed solution (regularization is based on fracture energy). The presented method is an extension to viscoelasticity of the approach proposed by Matallah et al. (Int. J. Numer. Anal. Methods Geomech. 34(15):1615-1633, 2010) for a purely elastic damage model. The viscoelastic Unitary Crack-Opening (UCO) strain <span class="hlt">tensor</span> is computed accounting for evolution with time of surplus of <span class="hlt">stress</span> related to damage; this <span class="hlt">stress</span> is obtained from decomposition of the effective <span class="hlt">stress</span> <span class="hlt">tensor</span>. From UCO the normal crack width is then derived accounting for finite element characteristic length in the direction orthogonal to crack. This extension is quite natural and allows for accounting of creep impact on opening/closing of cracks in time dependent problems. A graphical interpretation of the viscoelastic UCO using Mohr's circles is proposed and application cases together with a theoretical validation are presented to show physical consistency of computed viscoelastic UCO.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/scitech/biblio/22525199','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/22525199"><span>The <span class="hlt">tensor</span> bi-spectrum in a matter bounce</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Chowdhury, Debika; Sreenath, V.; Sriramkumar, L. E-mail: sreenath@lsu.edu</p> <p>2015-11-01</p> <p>Matter bounces are bouncing scenarios wherein the universe contracts as in a matter dominated phase at early times. Such scenarios are known to lead to a scale invariant spectrum of <span class="hlt">tensor</span> perturbations, just as de Sitter inflation does. In this work, we examine if the <span class="hlt">tensor</span> bi-spectrum can discriminate between the inflationary and the bouncing scenarios. Using the Maldacena formalism, we analytically evaluate the <span class="hlt">tensor</span> bi-spectrum in a matter bounce for an arbitrary triangular configuration of the wavevectors. We show that, over scales of cosmological interest, the non-Gaussianity parameter h{sub NL} that characterizes the amplitude of the <span class="hlt">tensor</span> bi-spectrum is quite small when compared to the corresponding values in de Sitter inflation. During inflation, the amplitude of the <span class="hlt">tensor</span> perturbations freeze on super-Hubble scales, a behavior that results in the so-called consistency condition relating the <span class="hlt">tensor</span> bi-spectrum and the power spectrum in the squeezed limit. In contrast, in the bouncing scenarios, the amplitude of the <span class="hlt">tensor</span> perturbations grow strongly as one approaches the bounce, which suggests that the consistency condition will not be valid in such situations. We explicitly show that the consistency relation is indeed violated in the matter bounce. We discuss the implications of the results.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016APS..APRR12007S','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016APS..APRR12007S"><span>The <span class="hlt">tensor</span> bi-spectrum in a matter bounce</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Sreenath, V.; Chowdhury, Debika; Sriramkumar, L.</p> <p>2016-03-01</p> <p>Matter bounces are bouncing scenarios wherein the universe contracts as in a matter dominated phase at early times. Such scenarios are known to lead to a scale invariant spectrum of <span class="hlt">tensor</span> perturbations, just as de Sitter inflation does. In this work, we examine if the <span class="hlt">tensor</span> bi-spectrum can discriminate between the inflationary and the bouncing scenarios. Using the Maldacena formalism, we analytically evaluate the <span class="hlt">tensor</span> bi-spectrum in a matter bounce for an arbitrary triangular configuration of the wavevectors. We show that, over scales of cosmological interest, the non-Gaussianity parameter hNL that characterizes the amplitude of the <span class="hlt">tensor</span> bi-spectrum is quite small when compared to the corresponding values in de Sitter inflation. During inflation, the amplitude of the <span class="hlt">tensor</span> perturbations freeze on super-Hubble scales, a behavior that results in the so-called consistency condition relating the <span class="hlt">tensor</span> bi-spectrum and the power spectrum in the squeezed limit. In contrast, in the bouncing scenarios, the amplitude of the <span class="hlt">tensor</span> perturbations grow strongly as one approaches the bounce, which suggests that the consistency condition will not be valid in such situations. We explicitly show that the consistency relation is indeed violated in the matter bounce.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2015JCAP...11..002C','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015JCAP...11..002C"><span>The <span class="hlt">tensor</span> bi-spectrum in a matter bounce</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Chowdhury, Debika; Sreenath, V.; Sriramkumar, L.</p> <p>2015-11-01</p> <p>Matter bounces are bouncing scenarios wherein the universe contracts as in a matter dominated phase at early times. Such scenarios are known to lead to a scale invariant spectrum of <span class="hlt">tensor</span> perturbations, just as de Sitter inflation does. In this work, we examine if the <span class="hlt">tensor</span> bi-spectrum can discriminate between the inflationary and the bouncing scenarios. Using the Maldacena formalism, we analytically evaluate the <span class="hlt">tensor</span> bi-spectrum in a matter bounce for an arbitrary triangular configuration of the wavevectors. We show that, over scales of cosmological interest, the non-Gaussianity parameter hNL that characterizes the amplitude of the <span class="hlt">tensor</span> bi-spectrum is quite small when compared to the corresponding values in de Sitter inflation. During inflation, the amplitude of the <span class="hlt">tensor</span> perturbations freeze on super-Hubble scales, a behavior that results in the so-called consistency condition relating the <span class="hlt">tensor</span> bi-spectrum and the power spectrum in the squeezed limit. In contrast, in the bouncing scenarios, the amplitude of the <span class="hlt">tensor</span> perturbations grow strongly as one approaches the bounce, which suggests that the consistency condition will not be valid in such situations. We explicitly show that the consistency relation is indeed violated in the matter bounce. We discuss the implications of the results.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=5217756','PMC'); return false;" href="https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=5217756"><span><span class="hlt">Tensor</span>-based Dictionary Learning for Spectral CT Reconstruction</span></a></p> <p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pmc">PubMed Central</a></p> <p>Zhang, Yanbo; Wang, Ge</p> <p>2016-01-01</p> <p>Spectral computed tomography (CT) produces an energy-discriminative attenuation map of an object, extending a conventional image volume with a spectral dimension. In spectral CT, an image can be sparsely represented in each of multiple energy channels, and are highly correlated among energy channels. According to this characteristics, we propose a <span class="hlt">tensor</span>-based dictionary learning method for spectral CT reconstruction. In our method, <span class="hlt">tensor</span> patches are extracted from an image <span class="hlt">tensor</span>, which is reconstructed using the filtered backprojection (FBP), to form a training dataset. With the Candecomp/Parafac decomposition, a <span class="hlt">tensor</span>-based dictionary is trained, in which each atom is a rank-one <span class="hlt">tensor</span>. Then, the trained dictionary is used to sparsely represent image <span class="hlt">tensor</span> patches during an iterative reconstruction process, and the alternating minimization scheme is adapted for optimization. The effectiveness of our proposed method is validated with both numerically simulated and real preclinical mouse datasets. The results demonstrate that the proposed <span class="hlt">tensor</span>-based method generally produces superior image quality, and leads to more accurate material decomposition than the currently popular popular methods. PMID:27541628</p> </li> </ol> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_18");'>18</a></li> <li><a href="#" onclick='return showDiv("page_19");'>19</a></li> <li class="active"><span>20</span></li> <li><a href="#" onclick='return showDiv("page_21");'>21</a></li> <li><a href="#" onclick='return showDiv("page_22");'>22</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div><!-- col-sm-12 --> </div><!-- row --> </div><!-- page_20 --> <div id="page_21" class="hiddenDiv"> <div class="row"> <div class="col-sm-12"> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_19");'>19</a></li> <li><a href="#" onclick='return showDiv("page_20");'>20</a></li> <li class="active"><span>21</span></li> <li><a href="#" onclick='return showDiv("page_22");'>22</a></li> <li><a href="#" onclick='return showDiv("page_23");'>23</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div> </div> <div class="row"> <div class="col-sm-12"> <ol class="result-class" start="401"> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016MNRAS.457.2501F','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016MNRAS.457.2501F"><span><span class="hlt">Tensor</span> classification of structure in smoothed particle hydrodynamics density fields</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Forgan, Duncan; Bonnell, Ian; Lucas, William; Rice, Ken</p> <p>2016-04-01</p> <p>As hydrodynamic simulations increase in scale and resolution, identifying structures with non-trivial geometries or regions of general interest becomes increasingly challenging. There is a growing need for algorithms that identify a variety of different features in a simulation without requiring a `by eye' search. We present <span class="hlt">tensor</span> classification as such a technique for smoothed particle hydrodynamics (SPH). These methods have already been used to great effect in N-Body cosmological simulations, which require smoothing defined as an input free parameter. We show that <span class="hlt">tensor</span> classification successfully identifies a wide range of structures in SPH density fields using its native smoothing, removing a free parameter from the analysis and preventing the need for tessellation of the density field, as required by some classification algorithms. As examples, we show that <span class="hlt">tensor</span> classification using the tidal <span class="hlt">tensor</span> and the velocity shear <span class="hlt">tensor</span> successfully identifies filaments, shells and sheet structures in giant molecular cloud simulations, as well as spiral arms in discs. The relationship between structures identified using different <span class="hlt">tensors</span> illustrates how different forces compete and co-operate to produce the observed density field. We therefore advocate the use of multiple <span class="hlt">tensors</span> to classify structure in SPH simulations, to shed light on the interplay of multiple physical processes.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016SIGMA..12..073B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016SIGMA..12..073B"><span>Large N Limits in <span class="hlt">Tensor</span> Models: Towards More Universality Classes of Colored Triangulations in Dimension d≥2</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Bonzom, Valentin</p> <p>2016-07-01</p> <p>We review an approach which aims at studying discrete (pseudo-)manifolds in dimension d≥ 2 and called random <span class="hlt">tensor</span> models. More specifically, we insist on generalizing the two-dimensional notion of p-angulations to higher dimensions. To do so, we consider families of triangulations built out of simplices with colored faces. Those simplices can be glued to form new building blocks, called bubbles which are pseudo-manifolds with boundaries. Bubbles can in turn be glued together to form triangulations. The main challenge is to classify the triangulations built from a given set of bubbles with respect to their numbers of bubbles and simplices of codimension two. While the colored triangulations which maximize the number of simplices of codimension two at fixed number of simplices are series-parallel objects called melonic triangulations, this is not always true anymore when restricting attention to colored triangulations built from specific bubbles. This opens up the possibility of new universality classes of colored triangulations. We present three existing strategies to find those universality classes. The first two strategies consist in building new bubbles from old ones for which the problem can be solved. The third strategy is a bijection between those colored triangulations and stuffed, edge-colored maps, which are some sort of hypermaps whose hyperedges are replaced with edge-colored maps. We then show that the present approach can lead to enumeration results and identification of universality classes, by working out the example of quartic <span class="hlt">tensor</span> models. They feature a tree-like phase, a planar phase similar to two-dimensional <span class="hlt">quantum</span> gravity and a phase transition between them which is interpreted as a proliferation of baby universes. While this work is written in the context of random <span class="hlt">tensors</span>, it is almost exclusively of combinatorial nature and we hope it is accessible to interested readers who are not familiar with random matrices, <span class="hlt">tensors</span> and <span class="hlt">quantum</span></p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017MeScT..28c5403L','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017MeScT..28c5403L"><span><span class="hlt">Tensor</span>-based dynamic reconstruction method for electrical capacitance tomography</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Lei, J.; Mu, H. P.; Liu, Q. B.; Li, Z. H.; Liu, S.; Wang, X. Y.</p> <p>2017-03-01</p> <p>Electrical capacitance tomography (ECT) is an attractive visualization measurement method, in which the acquisition of high-quality images is beneficial for the understanding of the underlying physical or chemical mechanisms of the dynamic behaviors of the measurement objects. In real-world measurement environments, imaging objects are often in a dynamic process, and the exploitation of the spatial-temporal correlations related to the dynamic nature will contribute to improving the imaging quality. Different from existing imaging methods that are often used in ECT measurements, in this paper a dynamic image sequence is stacked into a third-order <span class="hlt">tensor</span> that consists of a low rank <span class="hlt">tensor</span> and a sparse <span class="hlt">tensor</span> within the framework of the multiple measurement vectors model and the multi-way data analysis method. The low rank <span class="hlt">tensor</span> models the similar spatial distribution information among frames, which is slowly changing over time, and the sparse <span class="hlt">tensor</span> captures the perturbations or differences introduced in each frame, which is rapidly changing over time. With the assistance of the Tikhonov regularization theory and the <span class="hlt">tensor</span>-based multi-way data analysis method, a new cost function, with the considerations of the multi-frames measurement data, the dynamic evolution information of a time-varying imaging object and the characteristics of the low rank <span class="hlt">tensor</span> and the sparse <span class="hlt">tensor</span>, is proposed to convert the imaging task in the ECT measurement into a reconstruction problem of a third-order image <span class="hlt">tensor</span>. An effective algorithm is developed to search for the optimal solution of the proposed cost function, and the images are reconstructed via a batching pattern. The feasibility and effectiveness of the developed reconstruction method are numerically validated.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016EPJC...76..420L','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016EPJC...76..420L"><span>Cosmological implications of modified gravity induced by <span class="hlt">quantum</span> metric fluctuations</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Liu, Xing; Harko, Tiberiu; Liang, Shi-Dong</p> <p>2016-08-01</p> <p>We investigate the cosmological implications of modified gravities induced by the <span class="hlt">quantum</span> fluctuations of the gravitational metric. If the metric can be decomposed as the sum of the classical and of a fluctuating part, of <span class="hlt">quantum</span> origin, then the corresponding Einstein <span class="hlt">quantum</span> gravity generates at the classical level modified gravity models with a non-minimal coupling between geometry and matter. As a first step in our study, after assuming that the expectation value of the <span class="hlt">quantum</span> correction can be generally expressed in terms of an arbitrary second order <span class="hlt">tensor</span> constructed from the metric and from the thermodynamic quantities characterizing the matter content of the Universe, we derive the (classical) gravitational field equations in their general form. We analyze in detail the cosmological models obtained by assuming that the <span class="hlt">quantum</span> correction <span class="hlt">tensor</span> is given by the coupling of a scalar field and of a scalar function to the metric <span class="hlt">tensor</span>, and by a term proportional to the matter energy-momentum <span class="hlt">tensor</span>. For each considered model we obtain the gravitational field equations, and the generalized Friedmann equations for the case of a flat homogeneous and isotropic geometry. In some of these models the divergence of the matter energy-momentum <span class="hlt">tensor</span> is non-zero, indicating a process of matter creation, which corresponds to an irreversible energy flow from the gravitational field to the matter fluid, and which is direct consequence of the non-minimal curvature-matter coupling. The cosmological evolution equations of these modified gravity models induced by the <span class="hlt">quantum</span> fluctuations of the metric are investigated in detail by using both analytical and numerical methods, and it is shown that a large variety of cosmological models can be constructed, which, depending on the numerical values of the model parameters, can exhibit both accelerating and decelerating behaviors.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016JHEP...09..148A','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016JHEP...09..148A"><span>Abelian <span class="hlt">tensor</span> hierarchy in 4D N = 1 conformal supergravity</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Aoki, Shuntaro; Higaki, Tetsutaro; Yamada, Yusuke; Yokokura, Ryo</p> <p>2016-09-01</p> <p>We consider Abelian <span class="hlt">tensor</span> hierarchy in four-dimensional N = 1 supergravity in the conformal superspace formalism, where the so-called covariant approach is used to antisymmetric <span class="hlt">tensor</span> fields. We introduce p-form gauge superfields as superforms in the conformal superspace. We solve the Bianchi identities under the constraints for the super-forms. As a result, each of form fields is expressed by a single gauge invariant superfield. We also show the relation between the superspace formalism and the superconformal <span class="hlt">tensor</span> calculus.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/scitech/biblio/22415451','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/22415451"><span>Extracting the diffusion <span class="hlt">tensor</span> from molecular dynamics simulation with Milestoning</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Mugnai, Mauro L.; Elber, Ron</p> <p>2015-01-07</p> <p>We propose an algorithm to extract the diffusion <span class="hlt">tensor</span> from Molecular Dynamics simulations with Milestoning. A Kramers-Moyal expansion of a discrete master equation, which is the Markovian limit of the Milestoning theory, determines the diffusion <span class="hlt">tensor</span>. To test the algorithm, we analyze overdamped Langevin trajectories and recover a multidimensional Fokker-Planck equation. The recovery process determines the flux through a mesh and estimates local kinetic parameters. Rate coefficients are converted to the derivatives of the potential of mean force and to coordinate dependent diffusion <span class="hlt">tensor</span>. We illustrate the computation on simple models and on an atomically detailed system—the diffusion along the backbone torsions of a solvated alanine dipeptide.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2015JChPh.142a4105M','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015JChPh.142a4105M"><span>Extracting the diffusion <span class="hlt">tensor</span> from molecular dynamics simulation with Milestoning</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Mugnai, Mauro L.; Elber, Ron</p> <p>2015-01-01</p> <p>We propose an algorithm to extract the diffusion <span class="hlt">tensor</span> from Molecular Dynamics simulations with Milestoning. A Kramers-Moyal expansion of a discrete master equation, which is the Markovian limit of the Milestoning theory, determines the diffusion <span class="hlt">tensor</span>. To test the algorithm, we analyze overdamped Langevin trajectories and recover a multidimensional Fokker-Planck equation. The recovery process determines the flux through a mesh and estimates local kinetic parameters. Rate coefficients are converted to the derivatives of the potential of mean force and to coordinate dependent diffusion <span class="hlt">tensor</span>. We illustrate the computation on simple models and on an atomically detailed system—the diffusion along the backbone torsions of a solvated alanine dipeptide.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/1986PhRvL..57..803S','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/1986PhRvL..57..803S"><span><span class="hlt">Tensor</span> analyzing power in πd elastic scattering</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Smith, G. R.; Altman, A.; Delheij, P.; Gill, D. R.; Healey, D.; Johnson, R. R.; Jones, G.; Ottewell, D.; Rozon, F. M.; Sevior, M. E.; Tervisidis, F.; Trelle, R. P.; Wait, G. D.; Walden, P.; Mathie, E. L.; Lolos, G. J.; Naqvi, S. I.; Boschitz, E. T.; Ottermann, C. R.; Kyle, G. S.; Amaudruz, P. A.</p> <p>1986-08-01</p> <p>A <span class="hlt">tensor</span>-polarized deuteron target has been employed for the first measurements of the <span class="hlt">tensor</span> analyzing power, T20, in πd elastic scattering. Data at six angles were measured at pion bombarding energies of 133.8 and 150.9 MeV. The results settle a long-standing controversy over conflicting measurements of the <span class="hlt">tensor</span> polarization t20, and dispute evidence for dibaryon resonances predicated on one of these t20 measurements. The data are shown to be in reasonable agreement with recent Faddeev calculations which have reduced contributions from pion absorption.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016PhPl...23f2108G','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016PhPl...23f2108G"><span>The general dielectric <span class="hlt">tensor</span> for bi-kappa magnetized plasmas</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Gaelzer, R.; Ziebell, L. F.; Meneses, A. R.</p> <p>2016-06-01</p> <p>In this paper, we derive the dielectric <span class="hlt">tensor</span> for a plasma containing particles described by an anisotropic superthermal (bi-kappa) velocity distribution function. The <span class="hlt">tensor</span> components are written in terms of the two-variables kappa plasma special functions, recently defined by Gaelzer and Ziebell [Phys. Plasmas 23, 022110 (2016)]. We also obtain various new mathematical properties for these functions, which are useful for the analytical treatment, numerical implementation, and evaluation of the functions and, consequently, of the dielectric <span class="hlt">tensor</span>. The formalism developed here and in the previous paper provides a mathematical framework for the study of electromagnetic waves propagating at arbitrary angles and polarizations in a superthermal plasma.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/25573551','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/25573551"><span>Extracting the diffusion <span class="hlt">tensor</span> from molecular dynamics simulation with Milestoning.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Mugnai, Mauro L; Elber, Ron</p> <p>2015-01-07</p> <p>We propose an algorithm to extract the diffusion <span class="hlt">tensor</span> from Molecular Dynamics simulations with Milestoning. A Kramers-Moyal expansion of a discrete master equation, which is the Markovian limit of the Milestoning theory, determines the diffusion <span class="hlt">tensor</span>. To test the algorithm, we analyze overdamped Langevin trajectories and recover a multidimensional Fokker-Planck equation. The recovery process determines the flux through a mesh and estimates local kinetic parameters. Rate coefficients are converted to the derivatives of the potential of mean force and to coordinate dependent diffusion <span class="hlt">tensor</span>. We illustrate the computation on simple models and on an atomically detailed system-the diffusion along the backbone torsions of a solvated alanine dipeptide.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/scitech/biblio/20782903','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/20782903"><span>Trace anomaly on a <span class="hlt">quantum</span> spacetime manifold</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Spallucci, Euro; Smailagic, Anais; Nicolini, Piero</p> <p>2006-04-15</p> <p>In this paper we investigate the trace anomaly in a space-time where single events are delocalized as a consequence of short distance <span class="hlt">quantum</span> coordinate fluctuations. We obtain a modified form of heat kernel asymptotic expansion which does not suffer from short distance divergences. Calculation of the trace anomaly is performed using an IR regulator in order to circumvent the absence of UV infinities. The explicit form of the trace anomaly is presented and the corresponding 2D Polyakov effective action and energy-momentum <span class="hlt">tensor</span> are obtained. The vacuum expectation value of the energy-momentum <span class="hlt">tensor</span> in the Boulware, Hartle-Hawking and Unruh vacua is explicitly calculated in a rt section of a recently found, noncommutative inspired, Schwarzschild-like solution of the Einstein equations. The standard short distance divergences in the vacuum expectation values are regularized in agreement with the absence of UV infinities removed by <span class="hlt">quantum</span> coordinate fluctuations.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2011PhTea..49..434H','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2011PhTea..49..434H"><span>Teaching <span class="hlt">Quantum</span> Uncertainty1</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Hobson, Art</p> <p>2011-10-01</p> <p>An earlier paper2 introduces <span class="hlt">quantum</span> physics by means of four experiments: Youngs double-slit interference experiment using (1) a light beam, (2) a low-intensity light beam with time-lapse photography, (3) an electron beam, and (4) a low-intensity electron beam with time-lapse photography. It's ironic that, although these experiments demonstrate most of the <span class="hlt">quantum</span> fundamentals, conventional pedagogy <span class="hlt">stresses</span> their difficult and paradoxical nature. These paradoxes (i.e., logical contradictions) vanish, and understanding becomes simpler, if one takes seriously the fact that <span class="hlt">quantum</span> mechanics is the nonrelativistic limit of our most accurate physical theory, namely <span class="hlt">quantum</span> field theory, and treats the Schroedinger wave function, as well as the electromagnetic field, as quantized fields.2 Both the Schroedinger field, or "matter field," and the EM field are made of "quanta"—spatially extended but energetically discrete chunks or bundles of energy. Each <span class="hlt">quantum</span> comes nonlocally from the entire space-filling field and interacts with macroscopic systems such as the viewing screen by collapsing into an atom instantaneously and randomly in accordance with the probability amplitude specified by the field. Thus, uncertainty and nonlocality are inherent in <span class="hlt">quantum</span> physics. This paper is about <span class="hlt">quantum</span> uncertainty. A planned later paper will take up <span class="hlt">quantum</span> nonlocality.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2013AGUFMNS34A..02Q','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2013AGUFMNS34A..02Q"><span>Airborne full <span class="hlt">tensor</span> magnetic gradiometry surveys in the Thuringian basin, Germany</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Queitsch, M.; Schiffler, M.; Goepel, A.; Stolz, R.; Meyer, M.; Meyer, H.; Kukowski, N.</p> <p>2013-12-01</p> <p>In this contribution we introduce a newly developed fully operational full <span class="hlt">tensor</span> magnetic gradiometer (FTMG) instrument based on Superconducting <span class="hlt">Quantum</span> Interference Devices (SQUIDs) and show example data acquired in 2012 within the framework of the INFLUINS (Integrated Fluid Dynamics in Sedimentary basins) project. This multidisciplinary project aims for a better understanding of movements and interaction between shallow and deep fluids in the Thuringian Basin in the center of Germany. In contrast to mapping total magnetic field intensity (TMI) in conventional airborne magnetic surveys for industrial exploration of mineral deposits and sedimentary basins, our instrument measures all components of the magnetic field gradient <span class="hlt">tensor</span> using highly sensitive SQUID gradiometers. This significantly constrains the solutions of the inverse problem. Furthermore, information on the ratio between induced and remanent magnetization is obtained. Special care has been taken to reduce motion noise while acquiring data in airborne operation. Therefore, the sensors are mounted in a nonmagnetic and aerodynamically shaped bird made of fiberglas with a high drag tail which stabilizes the bird even at low velocities. The system is towed by a helicopter and kept at 30m above ground during data acquisition. Additionally, the system in the bird incorporates an inertial unit for geo-referencing and enhanced motion noise compensation, a radar altimeter for topographic correction and a GPS system for high precision positioning. Advanced data processing techniques using reference magnetometer and inertial unit data result in a very low system noise of less than 60 pT/m peak to peak in airborne operation. To show the performance of the system we present example results from survey areas within the Thuringian basin and along its bordering highlands. The mapped gradient <span class="hlt">tensor</span> components show a high correlation to existing geologic maps. Furthermore, the measured gradient components indicate</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/6086624','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/6086624"><span>PHYSLIB: A C++ <span class="hlt">tensor</span> class library</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Budge, K.G.</p> <p>1991-10-09</p> <p>C++ is the first object-oriented programming language which produces sufficiently efficient code for consideration in computation-intensive physics and engineering applications. In addition, the increasing availability of massively parallel architectures requires novel programming techniques which may prove to be relatively easy to implement in C++. For these reasons, Division 1541 at Sandia National Laboratories is devoting considerable resources to the development of C++ libraries. This document describes the first of these libraries to be released, PHYSLIB, which defines classes representing Cartesian vectors and (second-order) <span class="hlt">tensors</span>. This library consists of the header file physlib.h, the inline code file physlib.inl, and the source file physlib.C. The library is applicable to both three-dimensional and two-dimensional problems; the user selects the 2-D version of the library by defining the symbol TWO D in the header file physlib.h and recompiling physlib.C and his own code. Alternately, system managers may wish to provide duplicate header and object modules of each dimensionality. This code was produced under the auspices of Sandia National Laboratories, a federally-funded research center administered for the United States Department of Energy on a non-profit basis by AT T. This code is available to US citizens, and institutions under research, government use and/or commercial license agreements.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/pages/biblio/1343854-moment-tensor-analysis-very-shallow-sources','SCIGOV-DOEP'); return false;" href="https://www.osti.gov/pages/biblio/1343854-moment-tensor-analysis-very-shallow-sources"><span>Moment <span class="hlt">tensor</span> analysis of very shallow sources</span></a></p> <p><a target="_blank" href="http://www.osti.gov/pages">DOE PAGES</a></p> <p>Chiang, Andrea; Dreger, Douglas S.; Ford, Sean R.; ...</p> <p>2016-10-11</p> <p>An issue for moment <span class="hlt">tensor</span> (MT) inversion of shallow seismic sources is that some components of the Green’s functions have vanishing amplitudes at the free surface, which can result in bias in the MT solution. The effects of the free surface on the stability of the MT method become important as we continue to investigate and improve the capabilities of regional full MT inversion for source–type identification and discrimination. It is important to understand free–surface effects on discriminating shallow explosive sources for nuclear monitoring purposes. It may also be important in natural systems that have very shallow seismicity, such asmore » volcanic and geothermal systems. We examine the effects of the free surface on the MT via synthetic testing and apply the MT–based discrimination method to three quarry blasts from the HUMMING ALBATROSS experiment. These shallow chemical explosions at ~10 m depth and recorded up to several kilometers distance represent rather severe source–station geometry in terms of free–surface effects. We show that the method is capable of recovering a predominantly explosive source mechanism, and the combined waveform and first–motion method enables the unique discrimination of these events. Furthermore, recovering the design yield using seismic moment estimates from MT inversion remains challenging, but we can begin to put error bounds on our moment estimates using the network sensitivity solution technique.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=4631675','PMC'); return false;" href="https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=4631675"><span>Diffusion <span class="hlt">Tensor</span> Imaging in Hemorrhagic Stroke</span></a></p> <p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pmc">PubMed Central</a></p> <p>Chaudhary, Neeraj; Pandey, Aditya S; Gemmete, Joseph J; Hua, Ya; Huang, Yining; Gu, Yuxiang; Xi, Guohua</p> <p>2015-01-01</p> <p>Diffusion <span class="hlt">Tensor</span> Imaging (DTI) has evolved considerably over the last decade to now be knocking on the doors of wider clinical applications. There have been several efforts over the last decade to seek valuable and reliable application of DTI in different neurological disorders. The role of DTI in predicting outcomes in patients with brain tumors has been extensively studied and has become a fairly established clinical tool in this scenario. More recently DTI has been applied in mild traumatic brain injury to predict clinical outcomes based on DTI of the white matter tracts. The resolution of white matter fiber tractography based on DTI has improved over the years with increased magnet strength and better tractography post processing. The role of DTI in hemorrhagic stroke has been studied preliminarily in the scientific literature. There is some evidence that DTI may be efficacious in predicting outcomes of motor function in animal models of intracranial hemorrhage. Only a handful of studies of DTI have been performed in subarachnoid hemorrhage or intraventricular hemorrhage scenarios. In this manuscript we will review the evolution of DTI, the existing evidence for its role in hemorrhagic stroke and discuss possible application of this non-invasive evaluation technique of human cerebral white matter tracts in the future. PMID:26015333</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/scitech/biblio/1343854','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/1343854"><span>Moment <span class="hlt">tensor</span> analysis of very shallow sources</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Chiang, Andrea; Dreger, Douglas S.; Ford, Sean R.; Walter, William R.; Yoo, Seung -Hoon</p> <p>2016-10-11</p> <p>An issue for moment <span class="hlt">tensor</span> (MT) inversion of shallow seismic sources is that some components of the Green’s functions have vanishing amplitudes at the free surface, which can result in bias in the MT solution. The effects of the free surface on the stability of the MT method become important as we continue to investigate and improve the capabilities of regional full MT inversion for source–type identification and discrimination. It is important to understand free–surface effects on discriminating shallow explosive sources for nuclear monitoring purposes. It may also be important in natural systems that have very shallow seismicity, such as volcanic and geothermal systems. We examine the effects of the free surface on the MT via synthetic testing and apply the MT–based discrimination method to three quarry blasts from the HUMMING ALBATROSS experiment. These shallow chemical explosions at ~10 m depth and recorded up to several kilometers distance represent rather severe source–station geometry in terms of free–surface effects. We show that the method is capable of recovering a predominantly explosive source mechanism, and the combined waveform and first–motion method enables the unique discrimination of these events. Furthermore, recovering the design yield using seismic moment estimates from MT inversion remains challenging, but we can begin to put error bounds on our moment estimates using the network sensitivity solution technique.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/555532','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/555532"><span>A new two-dimensional, limited, zone-centered <span class="hlt">tensor</span> artificial viscosity</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Clover, M.; Cranfill, C.</p> <p>1997-12-01</p> <p>It is the goal of this paper to describe a fully multidimensional, limited discretization viscosity. The authors prefer discretization to artificial because it arises naturally from discretizing the momentum equation of fluid dynamics. By this is meant that the velocity-dependent <span class="hlt">stress</span> <span class="hlt">tensor</span> is not arbitrary, as has been assumed since von Neumann`s paper of 1952, but unavoidable, if a method of weak solution is used to solve the Euler equations. This weak solution method--due to Harten, Lax and van Leer [1985]--shows that Q arises in order to numerically conserve momentum, when the equation is integrated over a finite space and time interval. Understanding the ramifications of this insight lead to the construction of a <span class="hlt">tensor</span> Q that is the sum of a number of dyadic terms (one per dimension). Thus, the k- and l-directed viscosities of k-l mesh codes is to be understood as the two dyadic terms corresponding to the two eigenvalues of the strain-rate <span class="hlt">tensor</span> in 2-D (where the assumption had not been explicitly stated that the faces of the control volume--on which the <span class="hlt">stresses</span> push--are orthogonal or parallel to the eigenvectors of the strain-rate). Calculating velocity jumps within zones to higher order and using limiters is done with the same degree of ad hoc rigor as in Godunov codes. The structure of this paper is to reprise certain results from 1-d analysis of a momentum equation, in order to highlight certain lessons that, when understood, enable one to easily generalize to higher dimension. The authors will also present some results on analytic test problems that this Q produces in a Free-Lagrange hydro code.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=5354362','PMC'); return false;" href="https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=5354362"><span>Non-convex Statistical Optimization for Sparse <span class="hlt">Tensor</span> Graphical Model</span></a></p> <p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pmc">PubMed Central</a></p> <p>Sun, Wei; Wang, Zhaoran; Liu, Han; Cheng, Guang</p> <p>2016-01-01</p> <p>We consider the estimation of sparse graphical models that characterize the dependency structure of high-dimensional <span class="hlt">tensor</span>-valued data. To facilitate the estimation of the precision matrix corresponding to each way of the <span class="hlt">tensor</span>, we assume the data follow a <span class="hlt">tensor</span> normal distribution whose covariance has a Kronecker product structure. The penalized maximum likelihood estimation of this model involves minimizing a non-convex objective function. In spite of the non-convexity of this estimation problem, we prove that an alternating minimization algorithm, which iteratively estimates each sparse precision matrix while fixing the others, attains an estimator with the optimal statistical rate of convergence as well as consistent graph recovery. Notably, such an estimator achieves estimation consistency with only one <span class="hlt">tensor</span> sample, which is unobserved in previous work. Our theoretical results are backed by thorough numerical studies.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017JHEP...03..090C','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017JHEP...03..090C"><span>A defect in holographic interpretations of <span class="hlt">tensor</span> networks</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Czech, Bartlomiej; Nguyen, Phuc H.; Swaminathan, Sivaramakrishnan</p> <p>2017-03-01</p> <p>We initiate the study of how <span class="hlt">tensor</span> networks reproduce properties of static holographic space-times, which are not locally pure anti-de Sitter. We consider geometries that are holographically dual to ground states of defect, interface and boundary CFTs and compare them to the structure of the requisite MERA networks predicted by the theory of minimal updates. When the CFT is deformed, certain <span class="hlt">tensors</span> require updating. On the other hand, even identical <span class="hlt">tensors</span> can contribute differently to estimates of entanglement entropies. We interpret these facts holographically by associating <span class="hlt">tensor</span> updates to turning on non-normalizable modes in the bulk. In passing, we also clarify and complement existing arguments in support of the theory of minimal updates, propose a novel ansatz called rayed MERA that applies to a class of generalized interface CFTs, and analyze the kinematic spaces of the thin wall and AdS3-Janus geometries.</p> </li> </ol> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_19");'>19</a></li> <li><a href="#" onclick='return showDiv("page_20");'>20</a></li> <li class="active"><span>21</span></li> <li><a href="#" onclick='return showDiv("page_22");'>22</a></li> <li><a href="#" onclick='return showDiv("page_23");'>23</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div><!-- col-sm-12 --> </div><!-- row --> </div><!-- page_21 --> <div id="page_22" class="hiddenDiv"> <div class="row"> <div class="col-sm-12"> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_20");'>20</a></li> <li><a href="#" onclick='return showDiv("page_21");'>21</a></li> <li class="active"><span>22</span></li> <li><a href="#" onclick='return showDiv("page_23");'>23</a></li> <li><a href="#" onclick='return showDiv("page_24");'>24</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div> </div> <div class="row"> <div class="col-sm-12"> <ol class="result-class" start="421"> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016JHEP...10..098A','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016JHEP...10..098A"><span>The <span class="hlt">tensor</span> hierarchy of 8-dimensional field theories</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Andino, Óscar Lasso; Ortín, Tomás</p> <p>2016-10-01</p> <p>We construct the <span class="hlt">tensor</span> hierarchy of generic, bosonic, 8-dimensional field theories. We first study the form of the most general 8-dimensional bosonic theory with Abelian gauge symmetries only and no massive deformations. This study determines the <span class="hlt">tensors</span> that occur in the Chern-Simons terms of the (electric and magnetic) field strengths and the action for the electric fields, which we determine. Having constructed the most general Abelian theory we study the most general gaugings of its global symmetries and the possible massive deformations using the embedding <span class="hlt">tensor</span> formalism, constructing the complete <span class="hlt">tensor</span> hierarchy using the Bianchi identities. We find the explicit form of all the field strengths of the gauged theory up to the 6-forms. Finally, we find the equations of motion comparing the Noether identities with the identities satisfied by the Bianchi identities themselves. We find that some equations of motion are not simply the Bianchi identities of the dual fields, but combinations of them.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://pubs.usgs.gov/sir/2005/5046/','USGSPUBS'); return false;" href="https://pubs.usgs.gov/sir/2005/5046/"><span>Reducing <span class="hlt">tensor</span> magnetic gradiometer data for unexploded ordnance detection</span></a></p> <p><a target="_blank" href="http://pubs.er.usgs.gov/pubs/index.jsp?view=adv">USGS Publications Warehouse</a></p> <p>Bracken, Robert E.; Brown, Philip J.</p> <p>2005-01-01</p> <p>We performed a survey to demonstrate the effectiveness of a prototype <span class="hlt">tensor</span> magnetic gradiometer system (TMGS) for detection of buried unexploded ordnance (UXO). In order to achieve a useful result, we designed a data-reduction procedure that resulted in a realistic magnetic gradient <span class="hlt">tensor</span> and devised a simple way of viewing complicated <span class="hlt">tensor</span> data, not only to assess the validity of the final resulting <span class="hlt">tensor</span>, but also to preview the data at interim stages of processing. The final processed map of the surveyed area clearly shows a sharp anomaly that peaks almost directly over the target UXO. This map agrees well with a modeled map derived from dipolar sources near the known target locations. From this agreement, it can be deduced that the reduction process is valid, making the prototype TMGS a foundation for development of future systems and processes.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/scitech/biblio/21426647','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/21426647"><span>Hidden symmetries and killing <span class="hlt">tensors</span> on curved spaces</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Ianus, S.; Visinescu, M.; Vilcu, G. E.</p> <p>2010-11-15</p> <p>Higher-order symmetries corresponding to Killing <span class="hlt">tensors</span> are investigated. The intimate relation between Killing-Yano <span class="hlt">tensors</span> and nonstandard supersymmetries is pointed out. In the Dirac theory on curved spaces, Killing-Yano <span class="hlt">tensors</span> generate Dirac-type operators involved in interesting algebraic structures as dynamical algebras or even infinite dimensional algebras or superalgebras. The general results are applied to space-times which appear in modern studies. One presents the infinite dimensional superalgebra of Dirac type operators on the 4-dimensional Euclidean Taub-NUT space that can be seen as a twisted loop algebra. The existence of the conformal Killing-Yano <span class="hlt">tensors</span> is investigated for some spaces with mixed 3-Sasakian structures.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/scitech/biblio/21003506','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/21003506"><span><span class="hlt">Tensor</span> interaction and short range correlations in relativistic nuclear models</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Panda, Prafulla K.; Providencia, C.; Providencia, J. da</p> <p>2007-06-15</p> <p>Short range correlations are introduced using a Jastrow factor in a relativistic approach to the equation of state of the infinite nuclear matter in the framework of the Hartree-Fock approximation. The pion exchange, including the <span class="hlt">tensor</span> contribution, is taken into account. It is shown that both the <span class="hlt">tensor</span> contribution of pion exchange and short range correlations soften the equation of state. Neutron matter with correlations presents no minimum at low densities.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=2639875','PMC'); return false;" href="https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=2639875"><span><span class="hlt">Tensor</span> veli palatini electromyography with surface electrode applied transnasally</span></a></p> <p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pmc">PubMed Central</a></p> <p>Picciotti, PM; Della Marca, G; Restuccia, D; Rigante, M; Di Nardo, W; Scarano, E</p> <p>2005-01-01</p> <p>Summary A new technique is proposed for paratubal electromyography, using a surface, non-invasive, electrode applied transnasally under nasopharyngoscope guidance. This electrode records activity of the <span class="hlt">tensor</span> veli palatini muscle during swallowing. This technique is of interest for two reasons: endoscopic guid-ance offers the possibility to check correct positioning of the electrode recording at <span class="hlt">tensor</span> veli palatini muscle level. Introduction of the non-invasive surface electrode is simple and not painful. PMID:16116836</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016PhRvD..93j5012D','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016PhRvD..93j5012D"><span>Higher rank antisymmetric <span class="hlt">tensor</span> fields in Klebanov-Strassler geometry</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Das, Ashmita; SenGupta, Soumitra</p> <p>2016-05-01</p> <p>In string theory, higher rank antisymmetric <span class="hlt">tensor</span> fields appear as massless excitations of closed strings. To date, there is no experimental support in favor of their existence. In a stringy framework, starting from a warped throatlike Klebanov-Strassler geometry, we show that all the massless higher rank antisymmetric <span class="hlt">tensor</span> fields are heavily suppressed due to the background fluxes leading to their invisibility in our Universe.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016APS..DMP.H7009Y','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016APS..DMP.H7009Y"><span>Contact <span class="hlt">Tensor</span> in a p-Wave Fermi Gas with Anisotropic Feshbach Resonances</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Yoshida, Shuhei M.; Ueda, Masahito</p> <p>2016-05-01</p> <p>Recent theoretical and experimental investigations have revealed that a Fermi gas with a p-wave Feshbach resonance has universal relations between the system's high-momentum behavior and thermodynamics. A new feature introduced by the p-wave interaction is anisotropy in the Feshbach resonances; three degenerate p-wave resonances split according to the magnetic <span class="hlt">quantum</span> number of the closed-channel molecules | m | due to the magnetic dipole-dipole interaction. Here, we investigate the consequences of the anisotropy. We show that the momentum distribution has a high-momentum asymptote nk ~k-2 ∑ m, m' = - 1 1 >Cm, m'Y1m * (\\kcirc)Y1m' (\\kcirc) , in which we introduce the p-wave contact <span class="hlt">tensor</span> Cm ,m'. In contrast to the previous studies, it has nine components. We identify them as the number, angular momentum, and nematicity of the closed-channel molecules. We also discuss two examples, the anisotropic p-wave superfluid and a gas confined in a cigar-shaped trap, which exhibit a nematicity component in the p-wave contact <span class="hlt">tensor</span>.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/17121407','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/17121407"><span>Hyperfine coupling <span class="hlt">tensors</span> of the benzosemiquinone radical anion from Car-Parrinello molecular dynamics.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Asher, James R; Kaupp, Martin</p> <p>2007-01-08</p> <p>Based on Car-Parrinello ab initio molecular dynamics simulations of the benzosemiquinone radical anion in both aqueous solution and the gas phase, density functional calculations provide the currently most refined EPR hyperfine coupling (HFC) <span class="hlt">tensors</span> of semiquinone nuclei and solvent protons. For snapshots taken at regular intervals from the molecular dynamics trajectories, cluster models with different criteria for inclusion of water molecules and an additional continuum solvent model are used to analyse the HFCs. These models provide a detailed picture of the effects of dynamics and of different intermolecular interactions on the spin-density distribution and HFC <span class="hlt">tensors</span>. Comparison with static calculations allows an assessment of the importance of dynamical effects, and of error compensation in static DFT calculations. Solvent proton HFCs depend characteristically on the position relative to the semiquinone radical anion. A point-dipolar model works well for in-plane hydrogen-bonded protons but deviates from the <span class="hlt">quantum</span> chemical values for out-of-plane hydrogen bonding.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2014GeoJI.196.1813C','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2014GeoJI.196.1813C"><span>Seismicity monitoring by cluster analysis of moment <span class="hlt">tensors</span></span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Cesca, Simone; Şen, Ali Tolga; Dahm, Torsten</p> <p>2014-03-01</p> <p>We suggest a new clustering approach to classify focal mechanisms from large moment <span class="hlt">tensor</span> catalogues, with the purpose of automatically identify families of earthquakes with similar source geometry, recognize the orientation of most active faults, and detect temporal variations of the rupture processes. The approach differs in comparison to waveform similarity methods since clusters are detected even if they occur in large spatial distances. This approach is particularly helpful to analyse large moment <span class="hlt">tensor</span> catalogues, as in microseismicity applications, where a manual analysis and classification is not feasible. A flexible algorithm is here proposed: it can handle different metrics, norms, and focal mechanism representations. In particular, the method can handle full moment <span class="hlt">tensor</span> or constrained source model catalogues, for which different metrics are suggested. The method can account for variable uncertainties of different moment <span class="hlt">tensor</span> components. We verify the method with synthetic catalogues. An application to real data from mining induced seismicity illustrates possible applications of the method and demonstrate the cluster detection and event classification performance with different moment <span class="hlt">tensor</span> catalogues. Results proof that main earthquake source types occur on spatially separated faults, and that temporal changes in the number and characterization of focal mechanism clusters are detected. We suggest that moment <span class="hlt">tensor</span> clustering can help assessing time dependent hazard in mines.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2013ApGeo..10..241Y','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2013ApGeo..10..241Y"><span>Noise filtering of full-gravity gradient <span class="hlt">tensor</span> data</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Yuan, Yuan; Huang, Da-Nian; Yu, Qing-Lu; Geng, Mei-Xia</p> <p>2013-06-01</p> <p>In oil and mineral exploration, gravity gradient <span class="hlt">tensor</span> data include higher-frequency signals than gravity data, which can be used to delineate small-scale anomalies. However, full-<span class="hlt">tensor</span> gradiometry (FTG) data are contaminated by high-frequency random noise. The separation of noise from high-frequency signals is one of the most challenging tasks in processing of gravity gradient <span class="hlt">tensor</span> data. We first derive the Cartesian equations of gravity gradient <span class="hlt">tensors</span> under the constraint of the Laplace equation and the expression for the gravitational potential, and then we use the Cartesian equations to fit the measured gradient <span class="hlt">tensor</span> data by using optimal linear inversion and remove the noise from the measured data. Based on model tests, we confirm that not only this method removes the high-frequency random noise but also enhances the weak anomaly signals masked by the noise. Compared with traditional low-pass filtering methods, this method avoids removing noise by sacrificing resolution. Finally, we apply our method to real gravity gradient <span class="hlt">tensor</span> data acquired by Bell Geospace for the Vinton Dome at the Texas-Louisiana border.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/20020083040','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20020083040"><span>An Introduction to <span class="hlt">Tensors</span> for Students of Physics and Engineering</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Kolecki, Joseph C.</p> <p>2002-01-01</p> <p><span class="hlt">Tensor</span> analysis is the type of subject that can make even the best of students shudder. My own post-graduate instructor in the subject took away much of the fear by speaking of an implicit rhythm in the peculiar notation traditionally used, and helped us to see how this rhythm plays its way throughout the various formalisms. Prior to taking that class, I had spent many years "playing" on my own with <span class="hlt">tensors</span>. I found the going to be tremendously difficult but was able, over time, to back out some physical and geometrical considerations that helped to make the subject a little more transparent. Today, it is sometimes hard not to think in terms of <span class="hlt">tensors</span> and their associated concepts. This article, prompted and greatly enhanced by Marlos Jacob, whom I've met only by e-mail, is an attempt to record those early notions concerning <span class="hlt">tensors</span>. It is intended to serve as a bridge from the point where most undergraduate students "leave off" in their studies of mathematics to the place where most texts on <span class="hlt">tensor</span> analysis begin. A basic knowledge of vectors, matrices, and physics is assumed. A semi-intuitive approach to those notions underlying <span class="hlt">tensor</span> analysis is given via scalars, vectors, dyads, triads, and higher vector products. The reader must be prepared to do some mathematics and to think. For those students who wish to go beyond this humble start, I can only recommend my professor's wisdom: find the rhythm in the mathematics and you will fare pretty well.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2007SPIE.6511E..18S','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2007SPIE.6511E..18S"><span>Diffusion <span class="hlt">tensor</span> imaging of the lower leg musculature during exercise</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Schick, Fritz; Steidle, Guenter</p> <p>2007-03-01</p> <p>Echoplanar diffusion <span class="hlt">tensor</span> imaging of musculature was performed using an adapted sequence with stimulated echo preparation and eddy current compensation. Reliable diffusion <span class="hlt">tensor</span> data were obtained in short measuring time of 2 minutes. Image distortion problems due to eddy currents arising from long lasting diffusion sensitizing gradients could be overcome by insertion of additional gradient pulses in the TM interval of the stimulated echo preparation. In addition, a T II-weighted multi-contrast spin-echo sequence with seven echoes was applied for assessment of changes in T2 during exercise. The diffusion <span class="hlt">tensor</span> and T2 in the musculature of the lower leg was investigated in 4 healthy subjects and maps of the trace and the three eigenvalues of the diffusion <span class="hlt">tensor</span>, fractional anisotropy maps, and angle maps were calculated from examinations before and after 90 seconds of exhausting tiptoe exercises. For both fractional anisotropy and muscle fibre orientation obvious differences for the miscellaneous muscle groups could be observed, whereas the eigenvalues of the diffusion <span class="hlt">tensor</span> were found rather homogenous in the whole calf musculature. All eigenvalues of the diffusion <span class="hlt">tensor</span> of loaded muscles were significantly increased by 7-17% immediately after the exercise. Maximum increase (14-17%) was found in the smallest eigenvalue in gastrocnemius lateralis and soleus muscle.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/scitech/biblio/21420950','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/21420950"><span><span class="hlt">Quantum</span> gravitational correction to the Hawking temperature from the Lemaitre-Tolman-Bondi model</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Banerjee, Rabin; Majhi, Bibhas Ranjan; Kiefer, Claus</p> <p>2010-08-15</p> <p>We solve the <span class="hlt">quantum</span> constraint equations of the Lemaitre-Tolman-Bondi model in a semiclassical approximation in which an expansion is performed with respect to the Planck length. We recover in this way the standard expression for the Hawking temperature as well as its first <span class="hlt">quantum</span> gravitational correction. We then interpret this correction in terms of the one-loop trace anomaly of the energy-momentum <span class="hlt">tensor</span> and thereby make contact with earlier work on <span class="hlt">quantum</span> black holes.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/5217350','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/5217350"><span>Application of the implicit <span class="hlt">TENSOR</span> code to studies of containment of undergound nuclear tests</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Burton, D. E.; Bryan, J. B.; Lettis, Jr., L. A.; Rambo, J. T.</p> <p>1982-02-01</p> <p>The <span class="hlt">TENSOR</span> code, a two-dimensional finite-difference code, has been used extensively for the solution of <span class="hlt">stress</span> wave propagation problems in materials, particularly those associated with the containment of underground nuclear test. These problems are typically characterized by shock waves at early times and by nearly incompressible flow at later times. To address this type of problem more economically, an implicit Newmark time integration has been implemented. Implicit differencing requires the solution of a coupled system of equations, by either direct or interative methods. An iterative technique has been selected to reduce the impact of the algorithm on the code structure and because it is the more economical method when only modest increases in timestep are desired. Although the algorithm is similar in some respects to the ICE method of Harlow and Amsden, substantial differences are required by the involvement of a complete <span class="hlt">stress</span> <span class="hlt">tensor</span> (instead of a scalar pressure) and by the highly nonlinear nature of the earth material constitutive relations.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016JGRB..121..972Z','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016JGRB..121..972Z"><span>Discriminating induced seismicity from natural earthquakes using moment <span class="hlt">tensors</span> and source spectra</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Zhang, Hongliang; Eaton, David W.; Li, Ge; Liu, Yajing; Harrington, Rebecca M.</p> <p>2016-02-01</p> <p>Earthquake source mechanisms and spectra can provide important clues to aid in discriminating between natural and induced events. In this study, we calculate moment <span class="hlt">tensors</span> and <span class="hlt">stress</span> drop values for eight recent induced earthquakes in the Western Canadian Sedimentary Basin with magnitudes between 3.2 and 4.4, as well as a nearby magnitude 5.3 event that is interpreted as a natural earthquake. We calculate full moment <span class="hlt">tensor</span> solutions by performing a waveform-fitting procedure based on a 1-D transversely isotropic velocity model. In addition to a dominant double-couple (DC) signature that is common to nearly all events, most induced events exhibit significant non-double-couple components. A parameter sensitivity analysis indicates that spurious non-DC components are negligible if the signal to noise ratio (SNR) exceeds 10 and if the 1-D model differs from the true velocity structure by less than 5%. Estimated focal depths of induced events are significantly shallower than the typical range of focal depths for intraplate earthquakes in the Canadian Shield. <span class="hlt">Stress</span> drops of the eight induced events were estimated using a generalized spectral-fitting method and fall within the typical range of 2 to 90 MPa for tectonic earthquakes. Elastic moduli changes due to the brittle damage production at the source, presence of multiple intersecting fractures, dilatant jogs created at the overlapping areas of multiple fractures, or non-planar pre-existing faults may explain the non-DC components for induced events.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/20160006095','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20160006095"><span>Representing Matrix Cracks Through Decomposition of the Deformation Gradient <span class="hlt">Tensor</span> in Continuum Damage Mechanics Methods</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Leone, Frank A., Jr.</p> <p>2015-01-01</p> <p>A method is presented to represent the large-deformation kinematics of intraply matrix cracks and delaminations in continuum damage mechanics (CDM) constitutive material models. The method involves the additive decomposition of the deformation gradient <span class="hlt">tensor</span> into 'crack' and 'bulk material' components. The response of the intact bulk material is represented by a reduced deformation gradient <span class="hlt">tensor</span>, and the opening of an embedded cohesive interface is represented by a normalized cohesive displacement-jump vector. The rotation of the embedded interface is tracked as the material deforms and as the crack opens. The distribution of the total local deformation between the bulk material and the cohesive interface components is determined by minimizing the difference between the cohesive <span class="hlt">stress</span> and the bulk material <span class="hlt">stress</span> projected onto the cohesive interface. The improvements to the accuracy of CDM models that incorporate the presented method over existing approaches are demonstrated for a single element subjected to simple shear deformation and for a finite element model of a unidirectional open-hole tension specimen. The material model is implemented as a VUMAT user subroutine for the Abaqus/Explicit finite element software. The presented deformation gradient decomposition method reduces the artificial load transfer across matrix cracks subjected to large shearing deformations, and avoids the spurious secondary failure modes that often occur in analyses based on conventional progressive damage models.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2001JMP....42.2293M','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2001JMP....42.2293M"><span><span class="hlt">Quantum</span> toroidal algebra Uq(sl2,tor) and R matrices</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Miki, Kei</p> <p>2001-05-01</p> <p>We show the existence of R matrices acting on the <span class="hlt">tensor</span> product of a certain class of representations of the <span class="hlt">quantum</span> toroidal algebra Uq(sl2,tor). In particular, the explicit expressions of R matrices acting on the <span class="hlt">tensor</span> product of level 1 integrable highest weight representations of Uq(sl2∧) are obtained. Our approach is based on the work of Chari and Pressley.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/22181869','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/22181869"><span>Observational constraints on loop <span class="hlt">quantum</span> cosmology.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Bojowald, Martin; Calcagni, Gianluca; Tsujikawa, Shinji</p> <p>2011-11-18</p> <p>In the inflationary scenario of loop <span class="hlt">quantum</span> cosmology in the presence of inverse-volume corrections, we give analytic formulas for the power spectra of scalar and <span class="hlt">tensor</span> perturbations convenient to compare with observations. Since inverse-volume corrections can provide strong contributions to the running spectral indices, inclusion of terms higher than the second-order runnings in the power spectra is crucially important. Using the recent data of cosmic microwave background and other cosmological experiments, we place bounds on the <span class="hlt">quantum</span> corrections.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/scitech/biblio/20698021','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/20698021"><span>Exactly soluble <span class="hlt">quantum</span> wormhole in two dimensions</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Kim, Won Tae; Son, Edwin J.; Yoon, Myung Seok</p> <p>2004-11-15</p> <p>We are presenting a <span class="hlt">quantum</span> traversable wormhole in an exactly soluble two-dimensional model. This is different from previous works since the exotic negative energy that supports the wormhole is generated from the quantization of classical energy-momentum <span class="hlt">tensors</span>. This explicit illustration shows the <span class="hlt">quantum</span>-mechanical energy can be used as a candidate for the exotic source. As for the traversability, after a particle travels through the wormhole, the static initial wormhole geometry gets a back reaction which spoils the wormhole structure. However, it may still maintain the initial structure along with the appropriate boundary condition.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2015PhRvE..92e3010A','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015PhRvE..92e3010A"><span>Turbulence constitutive modeling of the square root of the Reynolds <span class="hlt">stress</span></span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Ariki, Taketo</p> <p>2015-11-01</p> <p>A methodology for turbulence constitutive modeling is discussed on the basis of the square-root <span class="hlt">tensor</span> of the Reynolds <span class="hlt">stress</span>. The present methodology can satisfy the realizability condition for the Reynolds <span class="hlt">stress</span> proposed by Schumann [Phys. Fluids 20, 721 (1977)], 10.1063/1.861942 in a more general manner than the conventional methodologies. The definition and uniqueness of the square-root <span class="hlt">tensor</span> have been discussed, and its boundary condition has been properly obtained consistently with that of the Reynolds <span class="hlt">stress</span>. Examples of possible constitutive models of both <span class="hlt">tensor</span>-expansion and transport-equation types have been proposed.</p> </li> </ol> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_20");'>20</a></li> <li><a href="#" onclick='return showDiv("page_21");'>21</a></li> <li class="active"><span>22</span></li> <li><a href="#" onclick='return showDiv("page_23");'>23</a></li> <li><a href="#" onclick='return showDiv("page_24");'>24</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div><!-- col-sm-12 --> </div><!-- row --> </div><!-- page_22 --> <div id="page_23" class="hiddenDiv"> <div class="row"> <div class="col-sm-12"> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_21");'>21</a></li> <li><a href="#" onclick='return showDiv("page_22");'>22</a></li> <li class="active"><span>23</span></li> <li><a href="#" onclick='return showDiv("page_24");'>24</a></li> <li><a href="#" onclick='return showDiv("page_25");'>25</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div> </div> <div class="row"> <div class="col-sm-12"> <ol class="result-class" start="441"> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2013ApPhL.102j2602D','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2013ApPhL.102j2602D"><span>Ultra-low field magnetic resonance imaging detection with gradient <span class="hlt">tensor</span> compensation in urban unshielded environment</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Dong, Hui; Qiu, Longqing; Shi, Wen; Chang, Baolin; Qiu, Yang; Xu, Lu; Liu, Chao; Zhang, Yi; Krause, Hans-Joachim; Offenhäusser, Andreas; Xie, Xiaoming</p> <p>2013-03-01</p> <p>An ultra-low field (ULF) magnetic resonance imaging (MRI) system was set up in an urban laboratory without magnetic shielding. The measured environmental gradient fields of 1 ˜ 5 μT/m caused image distortion. We designed a gradient detection and compensation system to effectively balance the gradient <span class="hlt">tensor</span> components. The free induction decay signal duration of tap water was thus extended from 0.3 s to 2.5 s, providing the possibility for high-resolution imaging. Two-dimensional MRI images were then obtained at 130 μT with a helium-cooled second-order superconducting <span class="hlt">quantum</span> interference device gradiometer. This result allows us to develop an inexpensive ULF MRI system for biological studies.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2014MPLA...2950134H','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2014MPLA...2950134H"><span>Connection dynamics of higher-dimensional scalar-<span class="hlt">tensor</span> theories of gravity</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Han, Yu; Ma, Yongge; Zhang, Xiangdong</p> <p>2014-09-01</p> <p>The scalar-<span class="hlt">tensor</span> theories (STTs) of gravity in spacetime dimensions (D+1)>2 are studied. By performing Hamiltonian analysis, we obtain the geometrical dynamics of the theories from their Lagrangian. The Hamiltonian formalism indicates that the theories are naturally divided into two sectors by the coupling parameter ω. The Hamiltonian structures in both sectors are similar to the corresponding structures of four-dimensional cases. It turns out that, similar to the case of general relativity (GR), there is also a symplectic reduction from the canonical structure of so(D+1) Yang-Mills theories coupled to the scalar field to the canonical structure of the geometrical STTs. Therefore, the non-perturbative loop <span class="hlt">quantum</span> (LQG) gravity techniques can also be applied to the STTs in D+1 dimensions based on their connection-dynamical formalism.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017PhRvA..95a2112B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017PhRvA..95a2112B"><span><span class="hlt">Tensor</span> power of dynamical maps and positive versus completely positive divisibility</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Benatti, Fabio; Chruściński, Dariusz; Filippov, Sergey</p> <p>2017-01-01</p> <p>The are several nonequivalent notions of Markovian <span class="hlt">quantum</span> evolution. In this paper we show that the one based on the so-called CP divisibility of the corresponding dynamical map enjoys the following stability property: the dynamical map Λt is CP divisible if and only if the second <span class="hlt">tensor</span> power Λt⊗Λt is CP divisible as well. Moreover, the P divisibility of the map Λt⊗Λt is equivalent to the CP divisibility of the map Λt. Interestingly, the latter property is no longer true if we replace the P divisibility of Λt⊗Λt by simple positivity and the CP divisibility of Λt by complete positivity. That is, unlike when Λt has a time-independent generator, positivity of Λt⊗Λt does not imply complete positivity of Λt.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19920012845','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19920012845"><span>The Hamiltonian structure of Dirac's equation in <span class="hlt">tensor</span> form and its Fermi quantization</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Reifler, Frank; Morris, Randall</p> <p>1992-01-01</p> <p>Currently, there is some interest in studying the <span class="hlt">tensor</span> forms of the Dirac equation to elucidate the possibility of the constrained <span class="hlt">tensor</span> fields admitting Fermi quantization. We demonstrate that the bispinor and <span class="hlt">tensor</span> Hamiltonian systems have equivalent Fermi quantizations. Although the <span class="hlt">tensor</span> Hamiltonian system is noncanonical, representing the <span class="hlt">tensor</span> Poisson brackets as commutators for the Heisenberg operators directly leads to Fermi quantization without the use of bispinors.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016CMaPh.tmp..250H','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016CMaPh.tmp..250H"><span>The Asymptotics of <span class="hlt">Quantum</span> Max-Flow Min-Cut</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Hastings, Matthew B.</p> <p>2016-11-01</p> <p>The <span class="hlt">quantum</span> max-flow min-cut conjecture relates the rank of a <span class="hlt">tensor</span> network to the minimum cut in the case that all <span class="hlt">tensors</span> in the network are identical in Calegari et al. (J Am Math Soc 23(1):107-188, 2010). This conjecture was shown to be false in Cui et al. (J Math Phys 57:062206, 2016) by an explicit counter-example. Here, we show that the conjecture is almost true, in that the ratio of the <span class="hlt">quantum</span> max-flow to the <span class="hlt">quantum</span> min-cut converges to 1 as the dimension N of the degrees of freedom on the edges of the network tends to infinity. The proof is based on estimating moments of the singular values of the network. We introduce a generalization of "rainbow diagrams" to <span class="hlt">tensor</span> networks to estimate the dominant diagrams. A direct comparison of second and fourth moments lower bounds the ratio of the <span class="hlt">quantum</span> max-flow to the <span class="hlt">quantum</span> min-cut by a constant. To show the tighter bound that the ratio tends to 1, we consider higher moments. In addition, we show that the limiting moments as N → ∞ agree with that in a different ensemble where <span class="hlt">tensors</span> in the network are chosen independently; this is used to show that the distributions of singular values in the two different ensembles weakly converge to the same limiting distribution. We present also a numerical study of one particular <span class="hlt">tensor</span> network, which shows a surprising dependence of the rank deficit on N mod 4 and suggests further conjecture on the limiting behavior of the rank.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017CMaPh.351..387H','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017CMaPh.351..387H"><span>The Asymptotics of <span class="hlt">Quantum</span> Max-Flow Min-Cut</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Hastings, Matthew B.</p> <p>2017-04-01</p> <p>The <span class="hlt">quantum</span> max-flow min-cut conjecture relates the rank of a <span class="hlt">tensor</span> network to the minimum cut in the case that all <span class="hlt">tensors</span> in the network are identical in Calegari et al. (J Am Math Soc 23(1):107-188, 2010). This conjecture was shown to be false in Cui et al. (J Math Phys 57:062206, 2016) by an explicit counter-example. Here, we show that the conjecture is almost true, in that the ratio of the <span class="hlt">quantum</span> max-flow to the <span class="hlt">quantum</span> min-cut converges to 1 as the dimension N of the degrees of freedom on the edges of the network tends to infinity. The proof is based on estimating moments of the singular values of the network. We introduce a generalization of "rainbow diagrams" to <span class="hlt">tensor</span> networks to estimate the dominant diagrams. A direct comparison of second and fourth moments lower bounds the ratio of the <span class="hlt">quantum</span> max-flow to the <span class="hlt">quantum</span> min-cut by a constant. To show the tighter bound that the ratio tends to 1, we consider higher moments. In addition, we show that the limiting moments as N → ∞ agree with that in a different ensemble where <span class="hlt">tensors</span> in the network are chosen independently; this is used to show that the distributions of singular values in the two different ensembles weakly converge to the same limiting distribution. We present also a numerical study of one particular <span class="hlt">tensor</span> network, which shows a surprising dependence of the rank deficit on N mod 4 and suggests further conjecture on the limiting behavior of the rank.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016PhRvB..94k5125H','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016PhRvB..94k5125H"><span>Topological conformal defects with <span class="hlt">tensor</span> networks</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Hauru, Markus; Evenbly, Glen; Ho, Wen Wei; Gaiotto, Davide; Vidal, Guifre</p> <p>2016-09-01</p> <p>The critical two-dimensional classical Ising model on the square lattice has two topological conformal defects: the Z2 symmetry defect Dɛ and the Kramers-Wannier duality defect Dσ. These two defects implement antiperiodic boundary conditions and a more exotic form of twisted boundary conditions, respectively. On the torus, the partition function ZD of the critical Ising model in the presence of a topological conformal defect D is expressed in terms of the scaling dimensions Δα and conformal spins sα of a distinct set of primary fields (and their descendants, or conformal towers) of the Ising conformal field theory. This characteristic conformal data {Δα,sα}D can be extracted from the eigenvalue spectrum of a transfer matrix MD for the partition function ZD. In this paper, we investigate the use of <span class="hlt">tensor</span> network techniques to both represent and coarse grain the partition functions ZDɛand ZD σ of the critical Ising model with either a symmetry defect Dɛ or a duality defect Dσ. We also explain how to coarse grain the corresponding transfer matrices MDɛand MD σ, from which we can extract accurate numerical estimates of {Δα,sα}Dɛ and {Δα,sα}Dσ. Two key ingredients of our approach are (i) coarse graining of the defect D , which applies to any (i.e., not just topological) conformal defect and yields a set of associated scaling dimensions Δα, and (ii) construction and coarse graining of a generalized translation operator using a local unitary transformation that moves the defect, which only exist for topological conformal defects and yields the corresponding conformal spins sα.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=4305215','PMC'); return false;" href="https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=4305215"><span>Longitudinal Diffusion <span class="hlt">Tensor</span> Imaging in Frontotemporal Dementia</span></a></p> <p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pmc">PubMed Central</a></p> <p>Mahoney, Colin J; Simpson, Ivor J A; Nicholas, Jennifer M; Fletcher, Phillip D; Downey, Laura E; Golden, Hannah L; Clark, Camilla N; Schmitz, Nicole; Rohrer, Jonathan D; Schott, Jonathan M; Zhang, Hui; Ourselin, Sebastian; Warren, Jason D; Fox, Nick C</p> <p>2015-01-01</p> <p>Objective Novel biomarkers for monitoring progression in neurodegenerative conditions are needed. Measurement of microstructural changes in white matter (WM) using diffusion <span class="hlt">tensor</span> imaging (DTI) may be a useful outcome measure. Here we report trajectories of WM change using serial DTI in a cohort with behavioral variant frontotemporal dementia (bvFTD). Methods Twenty-three patients with bvFTD (12 having genetic mutations), and 18 age-matched control participants were assessed using DTI and neuropsychological batteries at baseline and ∼1.3 years later. Baseline and follow-up DTI scans were registered using a groupwise approach. Annualized rates of change for DTI metrics, neuropsychological measures, and whole brain volume were calculated. DTI metric performances were compared, and sample sizes for potential clinical trials were calculated. Results In the bvFTD group as a whole, rates of change in fractional anisotropy (FA) and mean diffusivity (MD) within the right paracallosal cingulum were greatest (FA: −6.8%/yr, p < 0.001; MD: 2.9%/yr, p = 0.01). MAPT carriers had the greatest change within left uncinate fasciculus (FA: −7.9%/yr, p < 0.001; MD: 10.9%/yr, p < 0.001); sporadic bvFTD and C9ORF72 carriers had the greatest change within right paracallosal cingulum (sporadic bvFTD, FA: −6.7%/yr, p < 0.001; MD: 3.8%/yr, p = 0.001; C9ORF72, FA: −6.8%/yr, p = 0.004). Sample size estimates using FA change were substantially lower than neuropsychological or whole brain measures of change. Interpretation Serial DTI scans may be useful for measuring disease progression in bvFTD, with particular trajectories of WM damage emerging. Sample size calculations suggest that longitudinal DTI may be a useful biomarker in future clinical trials. PMID:25363208</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016JPhCS.701a2017E','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016JPhCS.701a2017E"><span><span class="hlt">Quantum</span> features of natural cellular automata</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Elze, Hans-Thomas</p> <p>2016-03-01</p> <p>Cellular automata can show well known features of <span class="hlt">quantum</span> mechanics, such as a linear rule according to which they evolve and which resembles a discretized version of the Schrödinger equation. This includes corresponding conservation laws. The class of “natural” Hamiltonian cellular automata is based exclusively on integer-valued variables and couplings and their dynamics derives from an Action Principle. They can be mapped reversibly to continuum models by applying Sampling Theory. Thus, “deformed” <span class="hlt">quantum</span> mechanical models with a finite discreteness scale l are obtained, which for l → 0 reproduce familiar continuum results. We have recently demonstrated that such automata can form “multipartite” systems consistently with the <span class="hlt">tensor</span> product structures of nonrelativistic many-body <span class="hlt">quantum</span> mechanics, while interacting and maintaining the linear evolution. Consequently, the Superposition Principle fully applies for such primitive discrete deterministic automata and their composites and can produce the essential <span class="hlt">quantum</span> effects of interference and entanglement.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016JMP....57b2203M','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016JMP....57b2203M"><span>Entropy production of doubly stochastic <span class="hlt">quantum</span> channels</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Müller-Hermes, Alexander; Stilck França, Daniel; Wolf, Michael M.</p> <p>2016-02-01</p> <p>We study the entropy increase of <span class="hlt">quantum</span> systems evolving under primitive, doubly stochastic Markovian noise and thus converging to the maximally mixed state. This entropy increase can be quantified by a logarithmic-Sobolev constant of the Liouvillian generating the noise. We prove a universal lower bound on this constant that stays invariant under taking <span class="hlt">tensor</span>-powers. Our methods involve a new comparison method to relate logarithmic-Sobolev constants of different Liouvillians and a technique to compute logarithmic-Sobolev inequalities of Liouvillians with eigenvectors forming a projective representation of a finite abelian group. Our bounds improve upon similar results established before and as an application we prove an upper bound on continuous-time <span class="hlt">quantum</span> capacities. In the last part of this work we study entropy production estimates of discrete-time doubly stochastic <span class="hlt">quantum</span> channels by extending the framework of discrete-time logarithmic-Sobolev inequalities to the <span class="hlt">quantum</span> case.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/scitech/biblio/22479629','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/22479629"><span>Entropy production of doubly stochastic <span class="hlt">quantum</span> channels</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Müller-Hermes, Alexander; Stilck França, Daniel Wolf, Michael M.</p> <p>2016-02-15</p> <p>We study the entropy increase of <span class="hlt">quantum</span> systems evolving under primitive, doubly stochastic Markovian noise and thus converging to the maximally mixed state. This entropy increase can be quantified by a logarithmic-Sobolev constant of the Liouvillian generating the noise. We prove a universal lower bound on this constant that stays invariant under taking <span class="hlt">tensor</span>-powers. Our methods involve a new comparison method to relate logarithmic-Sobolev constants of different Liouvillians and a technique to compute logarithmic-Sobolev inequalities of Liouvillians with eigenvectors forming a projective representation of a finite abelian group. Our bounds improve upon similar results established before and as an application we prove an upper bound on continuous-time <span class="hlt">quantum</span> capacities. In the last part of this work we study entropy production estimates of discrete-time doubly stochastic <span class="hlt">quantum</span> channels by extending the framework of discrete-time logarithmic-Sobolev inequalities to the <span class="hlt">quantum</span> case.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/26296104','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/26296104"><span>Time-Delayed <span class="hlt">Quantum</span> Feedback Control.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Grimsmo, Arne L</p> <p>2015-08-07</p> <p>A theory of time-delayed coherent <span class="hlt">quantum</span> feedback is developed. More specifically, we consider a <span class="hlt">quantum</span> system coupled to a bosonic reservoir creating a unidirectional feedback loop. It is shown that the dynamics can be mapped onto a fictitious series of cascaded <span class="hlt">quantum</span> systems, where the system is driven by past versions of itself. The derivation of this model relies on a <span class="hlt">tensor</span> network representation of the system-reservoir time propagator. For concreteness, this general theory is applied to a driven two-level atom scattering into a coherent feedback loop. We demonstrate how delay effects can qualitatively change the dynamics of the atom and how <span class="hlt">quantum</span> control can be implemented in the presence of time delays.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016cosp...41E1682S','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016cosp...41E1682S"><span>Vacuum expectation values of the current density and energy-momentum <span class="hlt">tensor</span> for a charged scalar field in curved spacetime with toroidally compactified spatial dimensions</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Saharian, Aram; Kotanjyan, Anna; Sargsyan, Hayk; Simonyan, David</p> <p>2016-07-01</p> <p>The models with compact spatial dimensions appear in a number of fundamental physical theories. In particular, the idea of compactified dimensions has been extensively used in supergravity and superstring theories. In <span class="hlt">quantum</span> field theory, the modification of the vacuum fluctuations spectrum by the periodicity conditions imposed on the field operator along compact dimensions leads to a number of interesting physical effects. A well known example of this kind, demonstrating the close relation between <span class="hlt">quantum</span> phenomena and global geometry, is the topological Casimir effect. In models with extra compact dimensions, the Casimir energy creates a nontrivial potential for the compactification radius. This can serve as a stabilization mechanism for moduli fields and for the effective gauge couplings. The Casimir effect has also been considered as a possible origin for the dark energy in Kaluza-Klein-type and braneworld models. In the resent presentation we investigate the effects of the gravity and topology on the local properties of the <span class="hlt">quantum</span> vacuum for a charged scalar field in the presence of a classical gauge field. Vacuum expectation value of the energy-momentum <span class="hlt">tensor</span> and current density are investigated for a charged scalar field in dS spacetime with toroidally compact spatial dimensions in the presence of a classical constant gauge field. Due to the nontrivial topology, the latter gives rise to Aharonov-Bohm-like effect on the vacuum characteristics. The vacuum current density, energy density and <span class="hlt">stresses</span> are even periodic functions of the magnetic flux enclosed by compact dimensions. For small values of the comoving lengths of compact dimensions, compared with the dS curvature radius, the effects of gravity on the topological contributions are small and the expectation values are expressed in terms of the corresponding quantities in the Minkowski bulk by the standard conformal relation. For large values of the comoving lengths, depending on the field mass, two</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/21038400','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/21038400"><span>Applications of the Cartesian coordinate <span class="hlt">tensor</span> transfer technique in the simulations of vibrational circular dichroism spectra of oligonucleotides.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Andrushchenko, Valery; Bouř, Petr</p> <p>2010-01-01</p> <p>The application of the Cartesian coordinate <span class="hlt">tensor</span> transfer (CCT) technique for simulations of the IR absorption and vibrational circular dichroism (VCD) spectra of relatively large nucleic acid fragments is demonstrated on several case studies. The approach is based on direct ab initio calculations of atomic <span class="hlt">tensors</span>, determining molecular properties, for relatively small fragments, and subsequent transfer of these <span class="hlt">tensors</span> to the larger systems in Cartesian coordinates. This procedure enables precise computations of vibrational spectra for large biomolecular systems, currently with up to several thousands of atoms. The versatile ability of the CCT methods is emphasized on the examples of VCD and IR absorption spectra calculations for B- and Z-forms of DNA, single-, double-, and triple-stranded RNA helices and DNA structures with different base content and sequences. The development and recent improvements of the methodology are followed, including utilization of the constrained normal mode optimization (NMO) strategy and combined <span class="hlt">quantum</span> mechanics and molecular dynamics simulations. Advantages, drawbacks, and recommendations for future improvements of the CCT method as applied to nucleic acid spectra calculations are discussed.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/21394333','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/21394333"><span>Ab initio and DFT studies of the spin-orbit and spin-spin contributions to the zero-field splitting <span class="hlt">tensors</span> of triplet nitrenes with aryl scaffolds.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Sugisaki, Kenji; Toyota, Kazuo; Sato, Kazunobu; Shiomi, Daisuke; Kitagawa, Masahiro; Takui, Takeji</p> <p>2011-04-21</p> <p>Spin-orbit and spin-spin contributions to the zero-field splitting (ZFS) <span class="hlt">tensors</span> (D <span class="hlt">tensors</span>) of spin-triplet phenyl-, naphthyl-, and anthryl-nitrenes in their ground state are investigated by <span class="hlt">quantum</span> chemical calculations, focusing on the effects of the ring size and substituted position of nitrene on the D <span class="hlt">tensor</span>. A hybrid CASSCF/MRMP2 approach to the spin-orbit term of the D <span class="hlt">tensor</span> (D(SO) <span class="hlt">tensor</span>), which was recently proposed by us, has shown that the spin-orbit contribution to the entire D value, termed the ZFS parameter or fine-structure constant, is about 10% in all the arylnitrenes under study and less depends on the size and connectivity of the aryl groups. Order of the absolute values for D(SO) can be explained by the perturbation on the energy level and spatial distributions of π-SOMO through the orbital interaction between SOMO of the nitrene moiety and frontier orbitals of the aryl scaffolds. Spin-spin contribution to the D <span class="hlt">tensor</span> (D(SS) <span class="hlt">tensor</span>) has been calculated in terms of the McWeeny-Mizuno equation with the DFT/EPR-II spin densities. The D(SS) value calculated with the RO-B3LYP spin density agrees well with the D(Exptl) -D(SO) reference value in phenylnitrene, but agreement with the reference value gradually becomes worse as the D value decreases. Exchange-correlation functional dependence on the D(SS) <span class="hlt">tensor</span> has been explored with standard 23 exchange-correlation functionals in both RO- and U-DFT methodologies, and the RO-HCTH/407 method gives the best agreement with the D(Exptl) -D(SO) reference value. Significant exchange-correlation functional dependence is observed in spin-delocalized systems such as 9-anthrylnitrene (6). By employing the hybrid CASSCF/MRMP2 approach and the McWeeny-Mizuno equation combined with the RO-HCTH/407/EPR-II//U-HCTH/407/6-31G* spin densities for D(SO) and D(SS), respectively, a quantitative agreement with the experiment is achieved with errors less than 10% in all the arylnitrenes under study. Guidelines to the</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/6357068','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/6357068"><span><span class="hlt">Quantum</span> ontologies</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Stapp, H.P.</p> <p>1988-12-01</p> <p><span class="hlt">Quantum</span> ontologies are conceptions of the constitution of the universe that are compatible with <span class="hlt">quantum</span> theory. The ontological orientation is contrasted to the pragmatic orientation of science, and reasons are given for considering <span class="hlt">quantum</span> ontologies both within science, and in broader contexts. The principal <span class="hlt">quantum</span> ontologies are described and evaluated. Invited paper at conference: Bell's Theorem, <span class="hlt">Quantum</span> Theory, and Conceptions of the Universe, George Mason University, October 20-21, 1988. 16 refs.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2015PTEP.2015b3A01S','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015PTEP.2015b3A01S"><span>Radiation reaction in <span class="hlt">quantum</span> vacuum</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Seto, Keita</p> <p>2015-02-01</p> <p>Since the development of the radiating electron theory by P. A. M. Dirac in 1938 [P. A. M. Dirac, Proc. R. Soc. Lond. A 167, 148 (1938)], many authors have tried to reformulate this model, called the "radiation reaction". Recently, this equation has become important for ultra-intense laser-electron (plasma) interactions. In our recent research, we found a stabilized model of the radiation reaction in <span class="hlt">quantum</span> vacuum [K. Seto et al., Prog. Theor. Exp. Phys. 2014, 043A01 (2014)]. It led us to an updated Fletcher-Millikan charge-to-mass ratio including radiation. In this paper, I will discuss the generalization of our previous model and the new equation of motion with the radiation reaction in <span class="hlt">quantum</span> vacuum via photon-photon scatterings and also introduce the new <span class="hlt">tensor</span> d{E}^{μ ν α β }/dm, as the anisotropy of the charge-to-mass ratio.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2009PhDT........49L','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2009PhDT........49L"><span>Topics in <span class="hlt">quantum</span> cryptography, <span class="hlt">quantum</span> error correction, and channel simulation</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Luo, Zhicheng</p> <p></p> <p>In this thesis, we mainly investigate four different topics: efficiently implementable codes for <span class="hlt">quantum</span> key expansion [51], <span class="hlt">quantum</span> error-correcting codes based on privacy amplification [48], private classical capacity of <span class="hlt">quantum</span> channels [44], and classical channel simulation with <span class="hlt">quantum</span> side information [49, 50]. For the first topic, we propose an efficiently implementable <span class="hlt">quantum</span> key expansion protocol, capable of increasing the size of a pre-shared secret key by a constant factor. Previously, the Shor-Preskill proof [64] of the security of the Bennett-Brassard 1984 (BB84) [6] <span class="hlt">quantum</span> key distribution protocol relied on the theoretical existence of good classical error-correcting codes with the "dual-containing" property. But the explicit and efficiently decodable construction of such codes is unknown. We show that we can lift the dual-containing constraint by employing the non-dual-containing codes with excellent performance and efficient decoding algorithms. For the second topic, we propose a construction of Calderbank-Shor-Steane (CSS) [19, 68] <span class="hlt">quantum</span> error-correcting codes, which are originally based on pairs of mutually dual-containing classical codes, by combining a classical code with a two-universal hash function. We show, using the results of Renner and Koenig [57], that the communication rates of such codes approach the hashing bound on <span class="hlt">tensor</span> powers of Pauli channels in the limit of large block-length. For the third topic, we prove a regularized formula for the secret key assisted capacity region of a <span class="hlt">quantum</span> channel for transmitting private classical information. This result parallels the work of Devetak on entanglement assisted <span class="hlt">quantum</span> communication capacity. This formula provides a new family protocol, the private father protocol, under the resource inequality framework that includes the private classical communication without the assisted secret keys as a child protocol. For the fourth topic, we study and solve the problem of classical channel</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://eric.ed.gov/?q=quantum&pg=3&id=EJ930496','ERIC'); return false;" href="http://eric.ed.gov/?q=quantum&pg=3&id=EJ930496"><span><span class="hlt">Quantum</span> Computer Games: <span class="hlt">Quantum</span> Minesweeper</span></a></p> <p><a target="_blank" href="http://www.eric.ed.gov/ERICWebPortal/search/extended.jsp?_pageLabel=advanced">ERIC Educational Resources Information Center</a></p> <p>Gordon, Michal; Gordon, Goren</p> <p>2010-01-01</p> <p>The computer game of <span class="hlt">quantum</span> minesweeper is introduced as a <span class="hlt">quantum</span> extension of the well-known classical minesweeper. Its main objective is to teach the unique concepts of <span class="hlt">quantum</span> mechanics in a fun way. <span class="hlt">Quantum</span> minesweeper demonstrates the effects of superposition, entanglement and their non-local characteristics. While in the classical…</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017LaPhy..27d5203M','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017LaPhy..27d5203M"><span>Classical and <span class="hlt">quantum</span> emitters near a metal surface</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Mohammadi, Zahra; Kheirandish, Fardin</p> <p>2017-04-01</p> <p>The propagation of surface plasmon polaritons in an attenuating medium is investigated. The analytical calculations of the total electric-field Green’s <span class="hlt">tensor</span> of a metal–dielectric interface structure are provided and novel explicit expressions for the Green’s <span class="hlt">tensor</span> of a metal–dielectric interface are presented. The contribution of plasmons is obtained by evaluating the poles of the reflection coefficient for p-polarized waves incident on the metal interface. The emission pattern of a classical dipole located above the air/silver interface is studied. The relative intensity of the field to the field intensity in free space is studied for both normal and parallel orientations of the dipole. The <span class="hlt">quantum</span> optical properties of a <span class="hlt">quantum</span> emitter coupled to a metal surface are studied. Single photon emission is demonstrated for a <span class="hlt">quantum</span> dot near a metal surface using second-order correlation functions.</p> </li> </ol> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_21");'>21</a></li> <li><a href="#" onclick='return showDiv("page_22");'>22</a></li> <li class="active"><span>23</span></li> <li><a href="#" onclick='return showDiv("page_24");'>24</a></li> <li><a href="#" onclick='return showDiv("page_25");'>25</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div><!-- col-sm-12 --> </div><!-- row --> </div><!-- page_23 --> <div id="page_24" class="hiddenDiv"> <div class="row"> <div class="col-sm-12"> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_21");'>21</a></li> <li><a href="#" onclick='return showDiv("page_22");'>22</a></li> <li><a href="#" onclick='return showDiv("page_23");'>23</a></li> <li class="active"><span>24</span></li> <li><a href="#" onclick='return showDiv("page_25");'>25</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div> </div> <div class="row"> <div class="col-sm-12"> <ol class="result-class" start="461"> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/22271823','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/22271823"><span><span class="hlt">Tensor</span> completion for estimating missing values in visual data.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Liu, Ji; Musialski, Przemyslaw; Wonka, Peter; Ye, Jieping</p> <p>2013-01-01</p> <p>In this paper, we propose an algorithm to estimate missing values in <span class="hlt">tensors</span> of visual data. The values can be missing due to problems in the acquisition process or because the user manually identified unwanted outliers. Our algorithm works even with a small amount of samples and it can propagate structure to fill larger missing regions. Our methodology is built on recent studies about matrix completion using the matrix trace norm. The contribution of our paper is to extend the matrix case to the <span class="hlt">tensor</span> case by proposing the first definition of the trace norm for <span class="hlt">tensors</span> and then by building a working algorithm. First, we propose a definition for the <span class="hlt">tensor</span> trace norm that generalizes the established definition of the matrix trace norm. Second, similarly to matrix completion, the <span class="hlt">tensor</span> completion is formulated as a convex optimization problem. Unfortunately, the straightforward problem extension is significantly harder to solve than the matrix case because of the dependency among multiple constraints. To tackle this problem, we developed three algorithms: simple low rank <span class="hlt">tensor</span> completion (SiLRTC), fast low rank <span class="hlt">tensor</span> completion (FaLRTC), and high accuracy low rank <span class="hlt">tensor</span> completion (HaLRTC). The SiLRTC algorithm is simple to implement and employs a relaxation technique to separate the dependent relationships and uses the block coordinate descent (BCD) method to achieve a globally optimal solution; the FaLRTC algorithm utilizes a smoothing scheme to transform the original nonsmooth problem into a smooth one and can be used to solve a general <span class="hlt">tensor</span> trace norm minimization problem; the HaLRTC algorithm applies the alternating direction method of multipliers (ADMMs) to our problem. Our experiments show potential applications of our algorithms and the quantitative evaluation indicates that our methods are more accurate and robust than heuristic approaches. The efficiency comparison indicates that FaLTRC and HaLRTC are more efficient than SiLRTC and between FaLRTC an</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2010APS..DMP.W2001A','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2010APS..DMP.W2001A"><span><span class="hlt">Quantum</span> computation for <span class="hlt">quantum</span> chemistry</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Aspuru-Guzik, Alan</p> <p>2010-03-01</p> <p>Numerically exact simulation of <span class="hlt">quantum</span> systems on classical computers is in general, an intractable computational problem. Computational chemists have made progress in the development of approximate methods to tackle complex chemical problems. The downside of these approximate methods is that their failure for certain important cases such as long-range charge transfer states in the case of traditional density functional theory. In 1982, Richard Feynman suggested that a <span class="hlt">quantum</span> device should be able to simulate <span class="hlt">quantum</span> systems (in our case, molecules) exactly using <span class="hlt">quantum</span> computers in a tractable fashion. Our group has been working in the development of <span class="hlt">quantum</span> chemistry algorithms for <span class="hlt">quantum</span> devices. In this talk, I will describe how <span class="hlt">quantum</span> computers can be employed to carry out numerically exact <span class="hlt">quantum</span> chemistry and chemical reaction dynamics calculations, as well as molecular properties. Finally, I will describe our recent experimental <span class="hlt">quantum</span> computation of the energy of the hydrogen molecule using an optical <span class="hlt">quantum</span> computer.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/scitech/biblio/21537124','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/21537124"><span>Automated searching for <span class="hlt">quantum</span> subsystem codes</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Crosswhite, Gregory M.; Bacon, Dave</p> <p>2011-02-15</p> <p><span class="hlt">Quantum</span> error correction allows for faulty <span class="hlt">quantum</span> systems to behave in an effectively error-free manner. One important class of techniques for <span class="hlt">quantum</span> error correction is the class of <span class="hlt">quantum</span> subsystem codes, which are relevant both to active <span class="hlt">quantum</span> error-correcting schemes as well as to the design of self-correcting <span class="hlt">quantum</span> memories. Previous approaches for investigating these codes have focused on applying theoretical analysis to look for interesting codes and to investigate their properties. In this paper we present an alternative approach that uses computational analysis to accomplish the same goals. Specifically, we present an algorithm that computes the optimal <span class="hlt">quantum</span> subsystem code that can be implemented given an arbitrary set of measurement operators that are <span class="hlt">tensor</span> products of Pauli operators. We then demonstrate the utility of this algorithm by performing a systematic investigation of the <span class="hlt">quantum</span> subsystem codes that exist in the setting where the interactions are limited to two-body interactions between neighbors on lattices derived from the convex uniform tilings of the plane.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/pages/biblio/1221372-energy-momentum-tensor-moyal-space','SCIGOV-DOEP'); return false;" href="https://www.osti.gov/pages/biblio/1221372-energy-momentum-tensor-moyal-space"><span>On the energy-momentum <span class="hlt">tensor</span> in Moyal space</span></a></p> <p><a target="_blank" href="http://www.osti.gov/pages">DOE PAGES</a></p> <p>Balasin, Herbert; Blaschke, Daniel N.; Gieres, François; ...</p> <p>2015-06-26</p> <p>We study the properties of the energy-momentum <span class="hlt">tensor</span> of gauge fields coupled to matter in non-commutative (Moyal) space. In general, the non-commutativity affects the usual conservation law of the <span class="hlt">tensor</span> as well as its transformation properties (gauge covariance instead of gauge invariance). It is known that the conservation of the energy-momentum <span class="hlt">tensor</span> can be achieved by a redefinition involving another starproduct. Furthermore, for a pure gauge theory it is always possible to define a gauge invariant energy-momentum <span class="hlt">tensor</span> by means of a Wilson line. We show that the latter two procedures are incompatible with each other if couplings of gaugemore » fields to matter fields (scalars or fermions) are considered: The gauge invariant <span class="hlt">tensor</span> (constructed via Wilson line) does not allow for a redefinition assuring its conservation, and vice-versa the introduction of another star-product does not allow for gauge invariance by means of a Wilson line.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=4852972','PMC'); return false;" href="https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=4852972"><span>Diffusion <span class="hlt">tensor</span> MR microscopy of tissues with low diffusional anisotropy</span></a></p> <p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pmc">PubMed Central</a></p> <p>Bajd, Franci; Mattea, Carlos; Stapf, Siegfried</p> <p>2016-01-01</p> <p>Abstract Background Diffusion <span class="hlt">tensor</span> imaging exploits preferential diffusional motion of water molecules residing within tissue compartments for assessment of tissue structural anisotropy. However, instrumentation and post-processing errors play an important role in determination of diffusion <span class="hlt">tensor</span> elements. In the study, several experimental factors affecting accuracy of diffusion <span class="hlt">tensor</span> determination were analyzed. Materials and methods Effects of signal-to-noise ratio and configuration of the applied diffusion-sensitizing gradients on fractional anisotropy bias were analyzed by means of numerical simulations. In addition, diffusion <span class="hlt">tensor</span> magnetic resonance microscopy experiments were performed on a tap water phantom and bovine articular cartilage-on-bone samples to verify the simulation results. Results In both, the simulations and the experiments, the multivariate linear regression of the diffusion-<span class="hlt">tensor</span> analysis yielded overestimated fractional anisotropy with low SNRs and with low numbers of applied diffusion-sensitizing gradients. Conclusions An increase of the apparent fractional anisotropy due to unfavorable experimental conditions can be overcome by applying a larger number of diffusion sensitizing gradients with small values of the condition number of the transformation matrix. This is in particular relevant in magnetic resonance microscopy, where imaging gradients are high and the signal-to-noise ratio is low. PMID:27247550</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/scitech/biblio/22137814','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/22137814"><span>Self-accelerating solutions of scalar-<span class="hlt">tensor</span> gravity</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Barenboim, Gabriela; Lykken, Joseph D E-mail: lykken@fnal.gov</p> <p>2008-03-15</p> <p>Scalar-<span class="hlt">tensor</span> gravity is the simplest and best understood modification of general relativity, consisting of a real scalar field coupled directly to the Ricci scalar curvature. Models of this type have self-accelerating solutions. In an example inspired by string dilaton couplings, scalar-<span class="hlt">tensor</span> gravity coupled to ordinary matter exhibits a de Sitter type expansion, even in the presence of a negative cosmological constant whose magnitude exceeds that of the matter density. This unusual behavior does not require phantoms, ghosts or other exotic sources. More generally, we show that any expansion history can be interpreted as arising partly or entirely from scalar-<span class="hlt">tensor</span> gravity. To distinguish any quintessence or inflation model from its scalar-<span class="hlt">tensor</span> variants, we use the fact that scalar-<span class="hlt">tensor</span> models imply deviations of the post-Newtonian parameters of general relativity and time variation of Newton's gravitational coupling G. We emphasize that next-generation probes of modified GR and the time variation of G are an essential complement to dark energy probes based on luminosity-distance measurements.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/26340788','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/26340788"><span>Decentralized Dimensionality Reduction for Distributed <span class="hlt">Tensor</span> Data Across Sensor Networks.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Liang, Junli; Yu, Guoyang; Chen, Badong; Zhao, Minghua</p> <p>2016-11-01</p> <p>This paper develops a novel decentralized dimensionality reduction algorithm for the distributed <span class="hlt">tensor</span> data across sensor networks. The main contributions of this paper are as follows. First, conventional centralized methods, which utilize entire data to simultaneously determine all the vectors of the projection matrix along each <span class="hlt">tensor</span> mode, are not suitable for the network environment. Here, we relax the simultaneous processing manner into the one-vector-by-one-vector (OVBOV) manner, i.e., determining the projection vectors (PVs) related to each <span class="hlt">tensor</span> mode one by one. Second, we prove that in the OVBOV manner each PV can be determined without modifying any <span class="hlt">tensor</span> data, which simplifies corresponding computations. Third, we cast the decentralized PV determination problem as a set of subproblems with consensus constraints, so that it can be solved in the network environment only by local computations and information communications among neighboring nodes. Fourth, we introduce the null space and transform the PV determination problem with complex orthogonality constraints into an equivalent hidden convex one without any orthogonality constraint, which can be solved by the Lagrange multiplier method. Finally, experimental results are given to show that the proposed algorithm is an effective dimensionality reduction scheme for the distributed <span class="hlt">tensor</span> data across the sensor networks.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2010SPIE.7623E..29I','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2010SPIE.7623E..29I"><span>White matter degeneration in schizophrenia: a comparative diffusion <span class="hlt">tensor</span> analysis</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Ingalhalikar, Madhura A.; Andreasen, Nancy C.; Kim, Jinsuh; Alexander, Andrew L.; Magnotta, Vincent A.</p> <p>2010-03-01</p> <p>Schizophrenia is a serious and disabling mental disorder. Diffusion <span class="hlt">tensor</span> imaging (DTI) studies performed on schizophrenia have demonstrated white matter degeneration either due to loss of myelination or deterioration of fiber tracts although the areas where the changes occur are variable across studies. Most of the population based studies analyze the changes in schizophrenia using scalar indices computed from the diffusion <span class="hlt">tensor</span> such as fractional anisotropy (FA) and relative anisotropy (RA). The scalar measures may not capture the complete information from the diffusion <span class="hlt">tensor</span>. In this paper we have applied the RADTI method on a group of 9 controls and 9 patients with schizophrenia. The RADTI method converts the <span class="hlt">tensors</span> to log-Euclidean space where a linear regression model is applied and hypothesis testing is performed between the control and patient groups. Results show that there is a significant difference in the anisotropy between patients and controls especially in the parts of forceps minor, superior corona radiata, anterior limb of internal capsule and genu of corpus callosum. To check if the <span class="hlt">tensor</span> analysis gives a better idea of the changes in anisotropy, we compared the results with voxelwise FA analysis as well as voxelwise geodesic anisotropy (GA) analysis.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016SPIE10020E..1BS','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016SPIE10020E..1BS"><span>Binocular stereo matching method based on structure <span class="hlt">tensor</span></span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Song, Xiaowei; Yang, Manyi; Fan, Yubo; Yang, Lei</p> <p>2016-10-01</p> <p>In a binocular visual system, to recover the three-dimensional information of the object, the most important step is to acquire matching points. Structure <span class="hlt">tensor</span> is the vector representation of each point in its local neighborhood. Therefore, structure <span class="hlt">tensor</span> performs well in region detection of local structure, and it is very suitable for detecting specific graphics such as pedestrians, cars and road signs in the image. In this paper, the structure <span class="hlt">tensor</span> is combined with the luminance information to form the extended structure <span class="hlt">tensor</span>. The directional derivatives of luminance in x and y directions are calculated, so that the local structure of the image is more prominent. Meanwhile, the Euclidean distance between the eigenvectors of key points is used as the similarity determination metric of key points in the two images. By matching, the coordinates of the matching points in the detected target are precisely acquired. In this paper, experiments were performed on the captured left and right images. After the binocular calibration, image matching was done to acquire the matching points, and then the target depth was calculated according to these matching points. By comparison, it is proved that the structure <span class="hlt">tensor</span> can accurately acquire the matching points in binocular stereo matching.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=3428540','PMC'); return false;" href="https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=3428540"><span>Magnetic resonance diffusion <span class="hlt">tensor</span> imaging and diffusion <span class="hlt">tensor</span> tractography of human visual pathway</span></a></p> <p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pmc">PubMed Central</a></p> <p>Zhang, Yan; Wan, Si-Hai; Wu, Gui-Jun; Zhang, Xue-Lin</p> <p>2012-01-01</p> <p>AIM To investigate the visual pathway in normal subjects and patients with lesion involved by diffusion <span class="hlt">tensor</span> imaging (DTI) and diffusion <span class="hlt">tensor</span> tractography (DTT). METHODS Thirty normal volunteers, 3 subjects with orbital tumors involved the optic nerve (ON) and 33 subjects with occipital lobe tumors involved the optic radiation (OR) (10 gliomas, 6 meningiomas and 17 cerebral metastases) undertook routine cranium magnetic resonance imaging (MRI), DTI and DTT. Visual pathway fibers were analyzed by DTI and DTT images. Test fractional anisotropy (FA) and mean diffusivity (MD) values in different part of the visual pathway. RESULTS The whole visual pathway but optic chiasm manifested as hyperintensity in FA maps and homogenous green signal in the direction encoded color maps. The optic chiasm did not display clearly. There was no significant difference between the bilateral FA values and MD values of normal visual pathway but optic chiasm, which the FA values tested were much too low (all P>0.05). The ONs of subjects with orbital tumors were compressed and displaced. Only one subject had lower FA values and higher MD values. OR of 9 gliomas subjects were infiltrated, with displacement in 2 and disruption in 7 subjects. All OR in 6 meniongiomas subjects were displaced. OR in 17 cerebral metastases subjects all developed displacement while 7 of them had disruption also. CONCLUSION MR-DTI is highly sensitive in manifesting visual pathway. Visual pathway can be analyzed quantitatively in FA and MD values. DTT supplies accurate three dimensional conformations of visual pathway. But optic chiasm's manifestation still needs to improve. PMID:22937504</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/1113388','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/1113388"><span>A General Realizability Method for the Reynolds <span class="hlt">Stress</span> for 2-Equation RANS Models</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Ulitsky, M</p> <p>2009-06-19</p> <p>This report has described a general, robust method due to Chuck Cranfill for ensuring that the Boussinesq model for the turbulent variable density Reynolds <span class="hlt">stress</span> <span class="hlt">tensor</span> is always positive semi-definite (non-negative definite). The method uses a single constant or scale factor to keep the deviatoric part of the <span class="hlt">stress</span> <span class="hlt">tensor</span> well behaved, without changing the turbulent pressure part of the <span class="hlt">tensor</span>. It should be kept in mind that this method does not address the accuracy or appropriateness of the Boussinesq approximation in the first place. That topic can be addressed by comparing components of the modeled <span class="hlt">tensor</span> to the analagous <span class="hlt">stress</span> correlations that come from high quality 3D DNS or experimental data. This report is really dealing with the fact that while the prevalent Boussinesq model for the <span class="hlt">stress</span> <span class="hlt">tensor</span> in the literature is symmetric, it does not guarantee (even for statistically 1D problems) that the 3 eigenvalues associated with the <span class="hlt">stress</span> <span class="hlt">tensor</span> will remain greater than or equal to zero as the turbulent flow evolves. When there are regions of the flow that contain strong compressions or rarefactions (or noisy velocity gradients), it is more likely for the <span class="hlt">tensor</span> to suffer from realizability problems.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/926252','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/926252"><span>Seismic monitoring of EGS tests at the Coso Geothermal area, California, using accurate MEQ locations and full moment <span class="hlt">tensors</span></span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Foulger, Gillian R.; Julian, Bruce R.; Monastero, Francis C.</p> <p>2008-03-31</p> <p>In this study, we studied high-resolution relative locations and full moment <span class="hlt">tensors</span> of microearthquakes (MEQs) occurring before, during and following Enhanced Geothermal Systems (EGS) experiments in two wells at the Coso geothermal area, California. The objective was to map new fractures, determine the mode and sense of failure, and characterize the <span class="hlt">stress</span> cycle associated with injection. New software developed for this work combines waveform cross-correlation measurement of arrival times with relative relocation methods, and assesses confidence regions for moment <span class="hlt">tensors</span> derived using linear-programming methods. For moment <span class="hlt">tensor</span> determination we also developed a convenient Graphical User Interface (GUI), to streamline the work. We used data from the U.S. Navy’s permanent network of three-component digital borehole seismometers and from 14 portable three-component digital instruments. The latter supplemented the permanent network during injection experiments in well 34A-9 in 2004 and well 34-9RD2 in 2005. In the experiment in well 34A-9, the co-injection earthquakes were more numerous, smaller, more explosive and had more horizontal motion, compared with the pre-injection earthquakes. In the experiment in well 34-9RD2 the relocated hypocenters reveal a well-defined planar structure, 700 m long and 600 m high in the depth range 0.8 to 1.4 km below sea level, striking N 20° E and dipping at 75° to the WNW. The moment <span class="hlt">tensors</span> show that it corresponds to a mode I (opening) crack. Finally, for both wells, the perturbed <span class="hlt">stress</span> state near the bottom of the well persisted for at least two months following the injection.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/1312950','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/1312950"><span><span class="hlt">Quantum</span> memristors</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Pfeiffer, P.; Sanz, M.</p> <p>2016-07-06</p> <p>Technology based on memristors, resistors with memory whose resistance depends on the history of the crossing charges, has lately enhanced the classical paradigm of computation with neuromorphic architectures. However, in contrast to the known quantized models of passive circuit elements, such as inductors, capacitors or resistors, the design and realization of a <span class="hlt">quantum</span> memristor is still missing. Here, we introduce the concept of a <span class="hlt">quantum</span> memristor as a <span class="hlt">quantum</span> dissipative device, whose decoherence mechanism is controlled by a continuous-measurement feedback scheme, which accounts for the memory. Indeed, we provide numerical simulations showing that memory effects actually persist in the <span class="hlt">quantum</span> regime. Our quantization method, specifically designed for superconducting circuits, may be extended to other <span class="hlt">quantum</span> platforms, allowing for memristor-type constructions in different <span class="hlt">quantum</span> technologies. As a result, the proposed <span class="hlt">quantum</span> memristor is then a building block for neuromorphic <span class="hlt">quantum</span> computation and <span class="hlt">quantum</span> simulations of non-Markovian systems.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=4933948','PMC'); return false;" href="https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=4933948"><span><span class="hlt">Quantum</span> memristors</span></a></p> <p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pmc">PubMed Central</a></p> <p>Pfeiffer, P.; Egusquiza, I. L.; Di Ventra, M.; Sanz, M.; Solano, E.</p> <p>2016-01-01</p> <p>Technology based on memristors, resistors with memory whose resistance depends on the history of the crossing charges, has lately enhanced the classical paradigm of computation with neuromorphic architectures. However, in contrast to the known quantized models of passive circuit elements, such as inductors, capacitors or resistors, the design and realization of a <span class="hlt">quantum</span> memristor is still missing. Here, we introduce the concept of a <span class="hlt">quantum</span> memristor as a <span class="hlt">quantum</span> dissipative device, whose decoherence mechanism is controlled by a continuous-measurement feedback scheme, which accounts for the memory. Indeed, we provide numerical simulations showing that memory effects actually persist in the <span class="hlt">quantum</span> regime. Our quantization method, specifically designed for superconducting circuits, may be extended to other <span class="hlt">quantum</span> platforms, allowing for memristor-type constructions in different <span class="hlt">quantum</span> technologies. The proposed <span class="hlt">quantum</span> memristor is then a building block for neuromorphic <span class="hlt">quantum</span> computation and <span class="hlt">quantum</span> simulations of non-Markovian systems. PMID:27381511</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2000JPhD...33.2899L','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2000JPhD...33.2899L"><span>Calculation of nonlinear magnetic susceptibility <span class="hlt">tensors</span> for a uniaxial antiferromagnet</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Lim, Siew-Choo; Osman, Junaidah; Tilley, D. R.</p> <p>2000-11-01</p> <p>In this paper, we present a derivation of the nonlinear susceptibility <span class="hlt">tensors</span> for a two-sublattice uniaxial antiferromagnet up to the third-order effects within the standard definition by which the rf magnetization m is defined as a power series expansion in the rf fields h with the susceptibility <span class="hlt">tensors</span> χ(q) as the coefficients. The starting point is the standard set of torque equations of motion for this problem. A complete set of <span class="hlt">tensor</span> elements is derived for the case of a single-frequency input wave. Within a circular polarization frame (pnz) expressions are given for the first-order susceptibility, second-harmonic generation, optical rectification, third-harmonic generation and intensity-dependent susceptibility. Some of the coefficients with representative resonance features in the far infrared are illustrated graphically and we conclude with a brief discussion of the implications of the resonance features arising from the calculations and their potential applications.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=4288545','PMC'); return false;" href="https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=4288545"><span>Extracting the diffusion <span class="hlt">tensor</span> from molecular dynamics simulation with Milestoning</span></a></p> <p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pmc">PubMed Central</a></p> <p>Mugnai, Mauro L.; Elber, Ron</p> <p>2015-01-01</p> <p>We propose an algorithm to extract the diffusion <span class="hlt">tensor</span> from Molecular Dynamics simulations with Milestoning. A Kramers-Moyal expansion of a discrete master equation, which is the Markovian limit of the Milestoning theory, determines the diffusion <span class="hlt">tensor</span>. To test the algorithm, we analyze overdamped Langevin trajectories and recover a multidimensional Fokker-Planck equation. The recovery process determines the flux through a mesh and estimates local kinetic parameters. Rate coefficients are converted to the derivatives of the potential of mean force and to coordinate dependent diffusion <span class="hlt">tensor</span>. We illustrate the computation on simple models and on an atomically detailed system—the diffusion along the backbone torsions of a solvated alanine dipeptide. PMID:25573551</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/1998AIPC..420.1509B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/1998AIPC..420.1509B"><span>A propulsion-mass <span class="hlt">tensor</span> coupling in relativistic rocket motion</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Brito, Hector Hugo</p> <p>1998-01-01</p> <p>Following earlier speculations about antigravity machines and works on the relativistic dynamics of constant and variable rest mass point particles, a mass <span class="hlt">tensor</span> is found in connection with the closed system consisting of the rocket driven spaceship and its propellant mass, provided a ``solidification'' point other than the system center of mass is considered. Therefore, the mass <span class="hlt">tensor</span> form depends on whether the system is open or closed, and upon where the ``solidification'' point is located. An alternative propulsion principle is subsequently derived from the <span class="hlt">tensor</span> mass approach. The new principle, the covariant equivalent of Newton's Third Law for the physical interpretation of the relativistic rocket motion, reads: A spaceship undergoes a propulsion effect when the whole system mass 4-ellipsoid warps.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2015PhRvD..92d6001C','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015PhRvD..92d6001C"><span>Antisymmetric <span class="hlt">tensor</span> field and spontaneous magnetization in holographic duality</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Cai, Rong-Gen; Yang, Run-Qiu</p> <p>2015-08-01</p> <p>A real antisymmetric <span class="hlt">tensor</span> field was introduced to realize a holographic magnetic ordered phase in our previous papers. However, a more careful analysis shows there is a vector ghost in the model. In this paper we present a modified Lagrangian density for the antisymmetric <span class="hlt">tensor</span>, which is ghost free and causality is well defined, and keeps all the significant results in the original model qualitatively. We show this modified Lagrangian density could come from the dimensional compactification of p -form field in string/M theory. For static curved space-time, we also prove that this modified model is ghost free and does not violate causality. This new model offers a solid foundation for the application of antisymmetric <span class="hlt">tensor</span> field in holographic duality, especially for the spontaneous magnetization.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2014PhRvL.113w1301C','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2014PhRvL.113w1301C"><span>Resilience of the Standard Predictions for Primordial <span class="hlt">Tensor</span> Modes</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Creminelli, Paolo; Gleyzes, Jérôme; Noreña, Jorge; Vernizzi, Filippo</p> <p>2014-12-01</p> <p>We show that the prediction for the primordial <span class="hlt">tensor</span> power spectrum cannot be modified at leading order in derivatives. Indeed, one can always set to unity the speed of propagation of gravitational waves during inflation by a suitable disformal transformation of the metric, while a conformal one can make the Planck mass time independent. Therefore, the <span class="hlt">tensor</span> amplitude unambiguously fixes the energy scale of inflation. Using the effective field theory of inflation, we check that predictions are independent of the choice of frame, as expected. The first corrections to the standard prediction come from two parity violating operators with three derivatives. Also the correlator ⟨γ γ γ ⟩ is standard and only receives higher derivative corrections. These results hold also in multifield models of inflation and in alternatives to inflation and make the connection between a (quasi-)scale-invariant <span class="hlt">tensor</span> spectrum and inflation completely robust.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19810045389&hterms=gradiometer&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D40%26Ntt%3Dgradiometer','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19810045389&hterms=gradiometer&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D40%26Ntt%3Dgradiometer"><span>Superconducting <span class="hlt">tensor</span> gravity gradiometer for satellite geodesy and inertial navigation</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Paik, H. J.</p> <p>1981-01-01</p> <p>A sensitive gravity gradiometer can provide much needed gravity data of the earth and improve the accuracy of inertial navigation. Superconductivity and other properties of materials at low temperatures can be used to obtain a sensitive, low-drift gravity gradiometer; by differencing the outputs of accelerometer pairs using superconducting circuits, it is possible to construct a <span class="hlt">tensor</span> gravity gradiometer which measures all the in-line and cross components of the <span class="hlt">tensor</span> simultaneously. Additional superconducting circuits can be provided to determine the linear and angular acceleration vectors. A <span class="hlt">tensor</span> gravity gradiometer with these features is being developed for satellite geodesy. The device constitutes a complete package of inertial navigation instruments with angular and linear acceleration readouts as well as gravity signals.</p> </li> </ol> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_21");'>21</a></li> <li><a href="#" onclick='return showDiv("page_22");'>22</a></li> <li><a href="#" onclick='return showDiv("page_23");'>23</a></li> <li class="active"><span>24</span></li> <li><a href="#" onclick='return showDiv("page_25");'>25</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div><!-- col-sm-12 --> </div><!-- row --> </div><!-- page_24 --> <div id="page_25" class="hiddenDiv"> <div class="row"> <div class="col-sm-12"> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_21");'>21</a></li> <li><a href="#" onclick='return showDiv("page_22");'>22</a></li> <li><a href="#" onclick='return showDiv("page_23");'>23</a></li> <li><a href="#" onclick='return showDiv("page_24");'>24</a></li> <li class="active"><span>25</span></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div> </div> <div class="row"> <div class="col-sm-12"> <ol class="result-class" start="481"> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=4004091','PMC'); return false;" href="https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=4004091"><span><span class="hlt">Tensor</span> Regression with Applications in Neuroimaging Data Analysis</span></a></p> <p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pmc">PubMed Central</a></p> <p>Zhou, Hua; Li, Lexin; Zhu, Hongtu</p> <p>2013-01-01</p> <p>Classical regression methods treat covariates as a vector and estimate a corresponding vector of regression coefficients. Modern applications in medical imaging generate covariates of more complex form such as multidimensional arrays (<span class="hlt">tensors</span>). Traditional statistical and computational methods are proving insufficient for analysis of these high-throughput data due to their ultrahigh dimensionality as well as complex structure. In this article, we propose a new family of <span class="hlt">tensor</span> regression models that efficiently exploit the special structure of <span class="hlt">tensor</span> covariates. Under this framework, ultrahigh dimensionality is reduced to a manageable level, resulting in efficient estimation and prediction. A fast and highly scalable estimation algorithm is proposed for maximum likelihood estimation and its associated asymptotic properties are studied. Effectiveness of the new methods is demonstrated on both synthetic and real MRI imaging data. PMID:24791032</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016APS..DPPG10140P','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016APS..DPPG10140P"><span>Agyrotropic pressure <span class="hlt">tensor</span> induced by the plasma velocity shear</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Pegoraro, Francesco; Del Sarto, Danele; Califano, Francesco</p> <p>2016-10-01</p> <p>We show that the spatial inhomogeneity of a shear flow in a fluid plasma is transferred to a pressure anisotropy that has both a gyrotropic and a non gyrotropic component. We investigate this process both analytically and numerically by including the full pressure <span class="hlt">tensor</span> dynamics. We determine the time evolution of the pressure agyrotropy and in general of the pressure <span class="hlt">tensor</span> anisotropization which arise from the action of both the magnetic eld and the flow strain <span class="hlt">tensor</span>. This mechanism can affect the onset and development of shear-induced fluid instabilities in plasmas and is relevant to the understanding of the origin of some of the non-Maxwellian distribution functions evidenced both in Vlasov simulations and in space plasma measurements that exhibit pressure agyrotropy.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/1155560','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/1155560"><span>Relating spectral indices to <span class="hlt">tensor</span> and scalar amplitudes in inflation</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Kolb, Edward W.; Vadas, Sharon L.</p> <p>1994-02-01</p> <p>Within an expansion in slow-roll inflation parameters, we derive the complete second-order expressions relating the ratio of <span class="hlt">tensor</span> to scalar density perturbations and the spectral index of the scalar spectrum. We find that ``corrections'' to previously derived formulae can dominate if the <span class="hlt">tensor</span> to scalar ratio is small. For instance, if VV"/(V')<sup>2</sup>≠1 or if [mPI<sup>2</sup>/(4π)]||V'"/V'|| ≳ 1, where V(Φ) is the inflaton potential and m<sub>Pl</sub>is the Planck mass, then the previously used simple relations between the indices and the <span class="hlt">tensor</span> to scalar ratio fails. This failure occurs in particular for natural inflation, Coleman--Weinberg inflation, and ``chaotic'' inflation.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/1995Ap.....38..261G','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/1995Ap.....38..261G"><span>The symmetric <span class="hlt">tensor</span> field in the relativistic theory of gravitation</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Grigoryan, A. Sh.; Gottlöber, S.</p> <p>1995-07-01</p> <p>The system of a self-gravitating scalar field is frequently used in inflationary cosmological models. In the present paper we study a more complicated system containing an extra linear <span class="hlt">tensor</span> field ψik=ψki with minimal coupling. We determine five of the six free parameters that occur in the most general expression for the actionS ψ of this field. In doing so we assume that in flat space-time the field ψik must be invariant under gauge transformations. In a special case theS ψ found becomes a known expression for the action of a massless <span class="hlt">tensor</span> field ψik. We compute the metric energy-momentum <span class="hlt">tensor</span> that determines the contribution of ψik to the Einstein equations. We also exhibit the equations of motion of ψik in curved space-time.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/28298873','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/28298873"><span>New iterative criteria for strong [Formula: see text]-<span class="hlt">tensors</span> and an application.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Cui, Jingjing; Peng, Guohua; Lu, Quan; Huang, Zhengge</p> <p>2017-01-01</p> <p>Strong [Formula: see text]-<span class="hlt">tensors</span> play an important role in identifying the positive definiteness of even-order real symmetric <span class="hlt">tensors</span>. In this paper, some new iterative criteria for identifying strong [Formula: see text]-<span class="hlt">tensors</span> are obtained. These criteria only depend on the elements of the <span class="hlt">tensors</span>, and it can be more effective to determine whether a given <span class="hlt">tensor</span> is a strong [Formula: see text]-<span class="hlt">tensor</span> or not by increasing the number of iterations. Some numerical results show the feasibility and effectiveness of the algorithm.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016JHEP...08..127D','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016JHEP...08..127D"><span>Universal corrections to entanglement entropy of local <span class="hlt">quantum</span> quenches</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>David, Justin R.; Khetrapal, Surbhi; Kumar, S. Prem</p> <p>2016-08-01</p> <p>We study the time evolution of single interval Rényi and entanglement entropies following local <span class="hlt">quantum</span> quenches in two dimensional conformal field theories at finite temperature for which the locally excited states have a finite temporal width ɛ. We show that, for local quenches produced by the action of a conformal primary field, the time dependence of Rényi and entanglement entropies at order ɛ2 is universal. It is determined by the expectation value of the <span class="hlt">stress</span> <span class="hlt">tensor</span> in the replica geometry and proportional to the conformal dimension of the primary field generating the local excitation. We also show that in CFTs with a gravity dual, the ɛ2 correction to the holographic entanglement entropy following a local quench precisely agrees with the CFT prediction. We then consider CFTs admitting a higher spin symmetry and turn on a higher spin chemical potential μ. We calculate the time dependence of the order ɛ2 correction to the entanglement entropy for small μ, and show that the contribution at order μ 2 is universal. We verify our arguments against exact results for minimal models and the free fermion theory.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/scitech/biblio/22382048','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/22382048"><span>Inflationary <span class="hlt">tensor</span> fossils in large-scale structure</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Dimastrogiovanni, Emanuela; Fasiello, Matteo; Jeong, Donghui; Kamionkowski, Marc E-mail: mrf65@case.edu E-mail: kamion@jhu.edu</p> <p>2014-12-01</p> <p>Inflation models make specific predictions for a <span class="hlt">tensor</span>-scalar-scalar three-point correlation, or bispectrum, between one gravitational-wave (<span class="hlt">tensor</span>) mode and two density-perturbation (scalar) modes. This <span class="hlt">tensor</span>-scalar-scalar correlation leads to a local power quadrupole, an apparent departure from statistical isotropy in our Universe, as well as characteristic four-point correlations in the current mass distribution in the Universe. So far, the predictions for these observables have been worked out only for single-clock models in which certain consistency conditions between the <span class="hlt">tensor</span>-scalar-scalar correlation and <span class="hlt">tensor</span> and scalar power spectra are satisfied. Here we review the requirements on inflation models for these consistency conditions to be satisfied. We then consider several examples of inflation models, such as non-attractor and solid-inflation models, in which these conditions are put to the test. In solid inflation the simplest consistency conditions are already violated whilst in the non-attractor model we find that, contrary to the standard scenario, the <span class="hlt">tensor</span>-scalar-scalar correlator probes directly relevant model-dependent information. We work out the predictions for observables in these models. For non-attractor inflation we find an apparent local quadrupolar departure from statistical isotropy in large-scale structure but that this power quadrupole decreases very rapidly at smaller scales. The consistency of the CMB quadrupole with statistical isotropy then constrains the distance scale that corresponds to the transition from the non-attractor to attractor phase of inflation to be larger than the currently observable horizon. Solid inflation predicts clustering fossils signatures in the current galaxy distribution that may be large enough to be detectable with forthcoming, and possibly even current, galaxy surveys.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016MPLA...3150151S','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016MPLA...3150151S"><span>Proposal for the proper gravitational energy-momentum <span class="hlt">tensor</span></span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Shimizu, Katsutaro</p> <p>2016-08-01</p> <p>We propose a gravitational energy-momentum (GEMT) <span class="hlt">tensor</span> of the general relativity obtained using Noether’s theorem. It transforms as a <span class="hlt">tensor</span> under general coordinate transformations. One of the two indices of the GEMT labels a local Lorentz frame that satisfies the energy-momentum conservation law. The energies for a gravitational wave, a Schwarzschild black hole and a Friedmann-Lemaitre-Robertson-Walker (FLRW) universe are calculated as examples. The gravitational energy of the Schwarzschild black hole exists only outside the horizon, its value being the negative of the black hole mass.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016JHEP...03..052B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016JHEP...03..052B"><span>Abelian <span class="hlt">tensor</span> hierarchy in 4D, N = 1 superspace</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Becker, Katrin; Becker, Melanie; Linch, William D.; Robbins, Daniel</p> <p>2016-03-01</p> <p>With the goal of constructing the supersymmetric action for all fields, massless and massive, obtained by Kaluza-Klein compactification from type II theory or M-theory in a closed form, we embed the (Abelian) <span class="hlt">tensor</span> hierarchy of p-forms in four-dimensional, N =1superspaceandconstructitsChern-Simons-likeinvariants. Whenspecializedtothe case in which the <span class="hlt">tensors</span> arise from a higher-dimensional theory, the invariants may be interpreted as higher-dimensional Chern-Simons forms reduced to four dimensions. As an application of the formalism, we construct the eleven-dimensional Chern-Simons form in terms of four-dimensional, N = 1 superfields.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2015PTEP.2015d3E01F','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015PTEP.2015d3E01F"><span>Can a spectator scalar field enhance inflationary <span class="hlt">tensor</span> mode?</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Fujita, Tomohiro; Yokoyama, Jun'ichi; Yokoyama, Shuichiro</p> <p>2015-04-01</p> <p>We consider the possibility of enhancing the inflationary <span class="hlt">tensor</span> mode by introducing a spectator scalar field with a small sound speed which induces gravitational waves as a second-order effect. We analytically obtain the power spectra of gravitational waves and curvature perturbation induced by the spectator scalar field. We find that the small sound speed amplifies the curvature perturbation much more than the <span class="hlt">tensor</span> mode and the current observational constraint forces the induced gravitational waves to be negligible compared with those from the vacuum fluctuation during inflation.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=3951172','PMC'); return false;" href="https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=3951172"><span>Feature Selection in the <span class="hlt">Tensor</span> Product Feature Space</span></a></p> <p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pmc">PubMed Central</a></p> <p>Smalter, Aaron; Huan, Jun; Lushington, Gerald</p> <p>2014-01-01</p> <p>Classifying objects that are sampled jointly from two or more domains has many applications. The <span class="hlt">tensor</span> product feature space is useful for modeling interactions between feature sets in different domains but feature selection in the <span class="hlt">tensor</span> product feature space is challenging. Conventional feature selection methods ignore the structure of the feature space and may not provide the optimal results. In this paper we propose methods for selecting features in the original feature spaces of different domains. We obtained sparsity through two approaches, one using integer quadratic programming and another using L1-norm regularization. Experimental studies on biological data sets validate our approach. PMID:24632658</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016JChPh.145l4101R','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016JChPh.145l4101R"><span>Calculating vibrational spectra of molecules using <span class="hlt">tensor</span> train decomposition</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Rakhuba, Maxim; Oseledets, Ivan</p> <p>2016-09-01</p> <p>We propose a new algorithm for calculation of vibrational spectra of molecules using <span class="hlt">tensor</span> train decomposition. Under the assumption that eigenfunctions lie on a low-parametric manifold of low-rank <span class="hlt">tensors</span> we suggest using well-known iterative methods that utilize matrix inversion (locally optimal block preconditioned conjugate gradient method, inverse iteration) and solve corresponding linear systems inexactly along this manifold. As an application, we accurately compute vibrational spectra (84 states) of acetonitrile molecule CH3CN on a laptop in one hour using only 100 MB of memory to represent all computed eigenfunctions.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19770032991&hterms=gravitation&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D30%26Ntt%3Dgravitation','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19770032991&hterms=gravitation&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D30%26Ntt%3Dgravitation"><span>Scalar-<span class="hlt">tensor</span> theory of gravitation with negative coupling constant</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Smalley, L. L.; Eby, P. B.</p> <p>1976-01-01</p> <p>The possibility of a Brans-Dicke scalar-<span class="hlt">tensor</span> gravitation theory with a negative coupling constant is considered. The admissibility of a negative-coupling theory is investigated, and a simplified cosmological solution is obtained which allows a negative derivative of the gravitation constant. It is concluded that a Brans-Dicke theory with a negative coupling constant can be a viable alternative to general relativity and that a large negative value for the coupling constant seems to bring the original scalar-<span class="hlt">tensor</span> theory into close agreement with perihelion-precession results in view of recent observations of small solar oblateness.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://pubs.er.usgs.gov/publication/70017412','USGSPUBS'); return false;" href="http://pubs.er.usgs.gov/publication/70017412"><span>Rapid determination of global moment-<span class="hlt">tensor</span> solutions</span></a></p> <p><a target="_blank" href="http://pubs.er.usgs.gov/pubs/index.jsp?view=adv">USGS Publications Warehouse</a></p> <p>Sipkin, S.A.</p> <p>1994-01-01</p> <p>In an effort to improve data services, the National Earthquake Information Center has begun a program, in cooperation with the Incorporated Research Institutions for Seismology Data Management Center (IRIS DMC), to produce rapid estimates of the seismic moment <span class="hlt">tensor</span> for most earthquakes with a bodywave magnitude of 5.8 or greater. An estimate of the moment <span class="hlt">tensor</span> can usually be produced within 20 minutes of the arrival of the broadband P-waveform data from the IRIS DMC. The solutions do not vary significantly from the final solutions determined using the entire network. -from Author</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.osti.gov/scitech/servlets/purl/1055452','DOE-PATENT-XML'); return false;" href="http://www.osti.gov/scitech/servlets/purl/1055452"><span>Analytical effective <span class="hlt">tensor</span> for flow-through composites</span></a></p> <p><a target="_blank" href="http://www.osti.gov/doepatents">DOEpatents</a></p> <p>Sviercoski, Rosangela De Fatima [Los Alamos, NM</p> <p>2012-06-19</p> <p>A machine, method and computer-usable medium for modeling an average flow of a substance through a composite material. Such a modeling includes an analytical calculation of an effective <span class="hlt">tensor</span> K.sup.a suitable for use with a variety of media. The analytical calculation corresponds to an approximation to the <span class="hlt">tensor</span> K, and follows by first computing the diagonal values, and then identifying symmetries of the heterogeneity distribution. Additional calculations include determining the center of mass of the heterogeneous cell and its angle according to a defined Cartesian system, and utilizing this angle into a rotation formula to compute the off-diagonal values and determining its sign.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017IJGMM..1450023B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017IJGMM..1450023B"><span>Parallel second-order <span class="hlt">tensors</span> on Vaisman manifolds</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Bejan, Cornelia Livia; Crasmareanu, Mircea</p> <p></p> <p>The aim of this paper is to study the class of parallel <span class="hlt">tensor</span> fields α of (0, 2)-type in a Vaisman geometry (M,J,g). A sufficient condition for the reduction of such symmetric <span class="hlt">tensors</span> α to a constant multiple of g is given by the skew-symmetry of α with respect to the complex structure J. As an application of the main result, we prove that certain vector fields on a P0K-manifold turn out to be Killing. Also, we connect our main result with the Weyl connection of conformal geometry as well as with possible Ricci solitons in P0K manifolds.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/27150599','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/27150599"><span>The internal-strain <span class="hlt">tensor</span> of crystals for nuclear-relaxed elastic and piezoelectric constants: on the full exploitation of its symmetry features.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Erba, Alessandro</p> <p>2016-05-18</p> <p>Symmetry features of the internal-strain <span class="hlt">tensor</span> of crystals (whose components are mixed second-energy derivatives with respect to atomic displacements and lattice strains) are formally presented, which originate from translational-invariance, atomic equivalences, and atomic invariances. A general computational scheme is devised, and implemented into the public Crystal program, for the <span class="hlt">quantum</span>-mechanical evaluation of the internal-strain <span class="hlt">tensor</span> of crystals belonging to any space-group, which takes full-advantage of the exploitation of these symmetry-features. The gain in computing time due to the full symmetry exploitation is documented to be rather significant not just for high-symmetry crystalline systems such as cubic, hexagonal or trigonal, but also for low-symmetry ones such as monoclinic and orthorhombic. The internal-strain <span class="hlt">tensor</span> is used for the evaluation of the nuclear relaxation term of the fourth-rank elastic and third-rank piezoelectric <span class="hlt">tensors</span> of crystals, where, apart from a reduction of the computing time, the exploitation of symmetry is documented to remarkably increase the numerical precision of computed coefficients.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2015ApPhL.106s2904C','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015ApPhL.106s2904C"><span>Multi-mode technique for the determination of the biaxial Y2SiO5 permittivity <span class="hlt">tensor</span> from 300 to 6 K</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Carvalho, N. C.; Le Floch, J.-M.; Krupka, J.; Tobar, M. E.</p> <p>2015-05-01</p> <p>The Y2SiO5 (YSO) crystal is a dielectric material with biaxial anisotropy with known values of refractive index at optical frequencies. It is a well-known rare-earth (RE) host material for optical research and more recently has shown promising performance for <span class="hlt">quantum</span>-engineered devices. In this paper, we report the first microwave characterization of the real permittivity <span class="hlt">tensor</span> of a bulk YSO sample, as well as an investigation of the temperature dependence of the <span class="hlt">tensor</span> components from 296 K down to 6 K. Estimated uncertainties were below 0.26%, limited by the precision of machining the cylindrical dielectric. Also, the electrical Q-factors of a few electromagnetic modes were recorded as a way to provide some information about the crystal losses over the temperature range. To solve the <span class="hlt">tensor</span> components necessary for a biaxial crystal, we developed the multi-mode technique, which uses simultaneous measurement of low order whispering gallery modes. Knowledge of the permittivity <span class="hlt">tensor</span> offers important data, essential for the design of technologies involving YSO, such as microwave coupling to electron and hyperfine transitions in RE doped samples at low temperatures.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016EGUGA..18.9609T','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016EGUGA..18.9609T"><span>Experimental Measurement of In Situ <span class="hlt">Stress</span></span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Tibbo, Maria; Milkereit, Bernd; Nasseri, Farzine; Schmitt, Douglas; Young, Paul</p> <p>2016-04-01</p> <p>The World <span class="hlt">Stress</span> Map data is determined by <span class="hlt">stress</span> indicators including earthquake focal mechanisms, in situ measurement in mining, oil and gas boreholes as well as the borehole cores, and geologic data. Unfortunately, these measurements are not only infrequent but sometimes infeasible, and do not provide nearly enough data points with high accuracy to correctly infer <span class="hlt">stress</span> fields in deep mines around the world. Improvements in <span class="hlt">stress</span> measurements of Earth's crust is fundamental to several industries such as oil and gas, mining, nuclear waste management, and enhanced geothermal systems. Quantifying the state of <span class="hlt">stress</span> and the geophysical properties of different rock types is a major complication in geophysical monitoring of deep mines. Most <span class="hlt">stress</span> measurement techniques involve either the boreholes or their cores, however these measurements usually only give <span class="hlt">stress</span> along one axis, not the complete <span class="hlt">stress</span> <span class="hlt">tensor</span>. The goal of this project is to investigate a new method of acquiring a complete <span class="hlt">stress</span> <span class="hlt">tensor</span> of the in situ <span class="hlt">stress</span> in the Earth's crust. This project is part of a comprehensive, exploration geophysical study in a deep, highly <span class="hlt">stressed</span> mine located in Sudbury, Ontario, Canada, and focuses on two boreholes located in this mine. These boreholes are approximately 400 m long with NQ diameters and are located at depths of about 1300 - 1600 m and 1700 - 2000 m. Two borehole logging surveys were performed on both boreholes, October 2013 and July 2015, in order to perform a time-lapse analysis of the geophysical changes in the mine. These multi-parameter surveys include caliper, full waveform sonic, televiewer, chargeability (IP), and resistivity. Laboratory experiments have been performed on borehole core samples of varying geologies from each borehole. These experiments have measured the geophysical properties including elastic modulus, bulk modulus, P- and S-wave velocities, and density. The apparatus' used for this project are geophysical imaging cells capable</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2015JHEP...08..061B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015JHEP...08..061B"><span>Smooth and sharp creation of a Dirichlet wall in 1+1 <span class="hlt">quantum</span> field theory: how singular is the sharp creation limit?</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Brown, Eric G.; Louko, Jorma</p> <p>2015-08-01</p> <p>We present and utilize a simple formalism for the smooth creation of boundary conditions within relativistic <span class="hlt">quantum</span> field theory. We consider a massless scalar field in (1 + 1)-dimensional flat spacetime and imagine smoothly transitioning from there being no boundary condition to there being a two-sided Dirichlet mirror. The act of doing this, expectantly, generates a flux of real quanta that emanates from the mirror as it is being created. We show that the local <span class="hlt">stress</span>-energy <span class="hlt">tensor</span> of the flux is finite only if an infrared cutoff is introduced, no matter how slowly the mirror is created, in agreement with the perturbative results of Obadia and Parentani. In the limit of instaneous mirror creation the total energy injected into the field becomes ultraviolet divergent, but the response of an Unruh-DeWitt particle detector passing through the infinite burst of energy nevertheless remains finite. Implications for vacuum entanglement extraction and for black hole firewalls are discussed.</p> </li> </ol> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_21");'>21</a></li> <li><a href="#" onclick='return showDiv("page_22");'>22</a></li> <li><a href="#" onclick='return showDiv("page_23");'>23</a></li> <li><a href="#" onclick='return showDiv("page_24");'>24</a></li> <li class="active"><span>25</span></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div><!-- col-sm-12 --> </div><!-- row --> </div><!-- page_25 --> <center> <div class="footer-extlink text-muted"><small>Some links on this page may take you to non-federal websites. 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