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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

    2017-04-01

    The sublithospheric stress 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 tensor of stress can be computed at any point inside this elastic layer. Here, we present mathematical foundations for recovering such a tensor from gravitational tensor 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 (SHs) or Legendre polynomials is involved in the expressions. Here, new relations between the SH coefficients of the stress and gravitational tensor elements are presented. Thereafter, integral equations are established from them to recover the elements of stress tensor from those of the gravitational tensor. 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 mission (GOCE), in 2009 November, over the South American plate and its surroundings to recover the stress tensor at a depth of 35 km. The recovered stress fields are in good agreement with the tectonic and geological features of the area.

  4. 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/2017PhRvB..95x5127W','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017PhRvB..95x5127W"><span>Fermionic topological <span class="hlt">quantum</span> states as <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>Wille, C.; Buerschaper, O.; Eisert, J.</p> <p>2017-06-01</p> <p><span class="hlt">Tensor</span> network states, and in particular projected entangled pair states, play an important role in the description of strongly correlated <span class="hlt">quantum</span> lattice systems. They do not only serve as variational states in numerical simulation methods, but also provide a framework for classifying phases of <span class="hlt">quantum</span> matter and capture notions of topological order in a stringent and rigorous language. The rapid development in this field for spin models and bosonic systems has not yet been mirrored by an analogous development for fermionic models. In this work, we introduce a <span class="hlt">tensor</span> network formalism capable of capturing notions of topological order for <span class="hlt">quantum</span> systems with fermionic components. At the heart of the formalism are axioms of fermionic matrix-product operator injectivity, stable under concatenation. Building upon that, we formulate a Grassmann number <span class="hlt">tensor</span> network ansatz for the ground state of fermionic twisted <span class="hlt">quantum</span> double models. A specific focus is put on the paradigmatic example of the fermionic toric code. This work shows that the program of describing topologically ordered systems using <span class="hlt">tensor</span> networks carries over to fermionic models.</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://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('https://eric.ed.gov/?q=electric+AND+current&pg=5&id=EJ963896','ERIC'); return false;" href="https://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://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/2017JMP....58d2302O','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017JMP....58d2302O"><span>Kinematic projective <span class="hlt">quantum</span> states for loop <span class="hlt">quantum</span> gravity coupled to <span class="hlt">tensor</span> fields</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Okołów, Andrzej</p> <p>2017-04-01</p> <p>We present a construction of kinematic <span class="hlt">quantum</span> states for theories of <span class="hlt">tensor</span> fields of an arbitrary sort. The construction is based on projective techniques by Kijowski. Applying projective <span class="hlt">quantum</span> states for Loop <span class="hlt">Quantum</span> Gravity (LQG) obtained by Lanéry and Thiemann we construct <span class="hlt">quantum</span> states for LQG coupled to <span class="hlt">tensor</span> fields.</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/2017PhDT........38D','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017PhDT........38D"><span><span class="hlt">Quantum</span> Gravity Effects in Scalar, Vector and <span class="hlt">Tensor</span> Field Propagation</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Dutta, Anindita</p> <p></p> <p><span class="hlt">Quantum</span> theory of gravity deals with the physics of the gravitational field at Planck length scale (10-35 m). Even though it is experimentally hard to reach the Planck length scale, on can look for evidence of <span class="hlt">quantum</span> gravity that is detectable in astrophysics. In this thesis, we try to find effects of loop <span class="hlt">quantum</span> gravity corrections on observable phenomena. We show that the <span class="hlt">quantum</span> fluctuation strain for LIGO data would be 10 -125 on the Earth. Th correction is, however, substantial near the black hole horizon. We discuss the effect of this for scalar field propagation followed by vector and <span class="hlt">tensor</span> fields. For the scalar field, the correction introduces a new asymmetry; for the vector field, we found a new perturbation solution and for the <span class="hlt">tensor</span> field, we found the corrected Einstein equations which are yet to solve. These will affect phenomena like Hawking radiation, black hole entropy and gravitational waves.</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://adsabs.harvard.edu/abs/2006JChPh.125c4101M','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2006JChPh.125c4101M"><span>The <span class="hlt">stress</span> <span class="hlt">tensor</span> of a molecular system: An exercise in statistical mechanics</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Morante, S.; Rossi, G. C.; Testa, M.</p> <p>2006-07-01</p> <p>We prove that conservation of the <span class="hlt">stress</span> <span class="hlt">tensor</span> is a consequence of the invariance of the partition function under canonical diffeomorphisms. From this observation a simple and general derivation of the formula which gives the local expression of the <span class="hlt">stress</span> <span class="hlt">tensor</span> of a molecular system in terms of its microscopic degrees of freedom readily follows. The derivation is valid in the canonical as well as the microcanonical ensemble. It works both in the classical and in the <span class="hlt">quantum</span> mechanical settings and for arbitrary boundary conditions. In particular, if periodic boundary conditions are assigned to the system, the usual minimal-image prescription is naturally born out for mathematical consistency. An interesting outcome of our general analysis is that only in the case of a short-range interaction potential a truly local formula for the <span class="hlt">stress</span> <span class="hlt">tensor</span> can exist.</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> </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/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('http://adsabs.harvard.edu/abs/2017PhRvD..96b4005I','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017PhRvD..96b4005I"><span>Holographic <span class="hlt">stress</span>-energy <span class="hlt">tensor</span> near the Cauchy horizon inside a rotating black hole</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Ishibashi, Akihiro; Maeda, Kengo; Mefford, Eric</p> <p>2017-07-01</p> <p>We investigate a <span class="hlt">stress</span>-energy <span class="hlt">tensor</span> for a conformal field theory (CFT) at strong coupling inside a small five-dimensional rotating Myers-Perry black hole with equal angular momenta by using the holographic method. As a gravitational dual, we perturbatively construct a black droplet solution by applying the "derivative expansion" method, generalizing the work of Haddad [Classical <span class="hlt">Quantum</span> Gravity 29, 245001 (2012), 10.1088/0264-9381/29/24/245001] and analytically compute the holographic <span class="hlt">stress</span>-energy <span class="hlt">tensor</span> for our solution. We find that the <span class="hlt">stress</span>-energy <span class="hlt">tensor</span> is finite at both the future and past outer (event) horizons and that the energy density is negative just outside the event horizons due to the Hawking effect. Furthermore, we apply the holographic method to the question of <span class="hlt">quantum</span> instability of the Cauchy horizon since, by construction, our black droplet solution also admits a Cauchy horizon inside. We analytically show that the null-null component of the holographic <span class="hlt">stress</span>-energy <span class="hlt">tensor</span> negatively diverges at the Cauchy horizon, suggesting that a singularity appears there, in favor of strong cosmic censorship.</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/2010MolPh.108..223D','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2010MolPh.108..223D"><span>Analytical <span class="hlt">stress</span> <span class="hlt">tensor</span> and pressure calculations with the CRYSTAL code</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Doll, K.</p> <p>2010-02-01</p> <p>The calculation of the <span class="hlt">stress</span> <span class="hlt">tensor</span> and related properties and its implementation in the CRYSTAL code are described. The <span class="hlt">stress</span> <span class="hlt">tensor</span> is obtained from the earlier implemented analytical gradients with respect to the cell parameters. Subsequently, the pressure and enthalpy are computed, and a test concerning the pressure-driven phase transition in KI is used as an illustration. Finally, the possibility of applying external pressure is implemented. The constant-pressure optimization offers an alternative optimization method in addition to the already implemented optimization at constant volume.</p> </li> <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/2017PhRvL.119l1601K','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017PhRvL.119l1601K"><span>2D <span class="hlt">Stress</span> <span class="hlt">Tensor</span> for 4D Gravity</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Kapec, Daniel; Mitra, Prahar; Raclariu, Ana-Maria; Strominger, Andrew</p> <p>2017-09-01</p> <p>We use the subleading soft-graviton theorem to construct an operator Tz z whose insertion in the four-dimensional tree-level <span class="hlt">quantum</span> gravity S matrix obeys the Virasoro-Ward identities of the energy momentum <span class="hlt">tensor</span> of a two-dimensional conformal field theory (CFT2 ). The celestial sphere at Minkowskian null infinity plays the role of the Euclidean sphere of the CFT2 , with the Lorentz group acting as the unbroken S L (2 ,C ) subgroup.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017PApGe.174.2677E','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017PApGe.174.2677E"><span>Lithospheric <span class="hlt">Stress</span> <span class="hlt">Tensor</span> from Gravity and Lithospheric Structure Models</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Eshagh, Mehdi; Tenzer, Robert</p> <p>2017-07-01</p> <p>In this study we investigate the lithospheric <span class="hlt">stresses</span> computed from the gravity and lithospheric structure models. The functional relation between the lithospheric <span class="hlt">stress</span> <span class="hlt">tensor</span> and the gravity field parameters is formulated based on solving the boundary-value problem of elasticity in order to determine the propagation of <span class="hlt">stresses</span> inside the lithosphere, while assuming the horizontal shear <span class="hlt">stress</span> components (computed at the base of the lithosphere) as lower boundary values for solving this problem. We further suppress the signature of global mantle flow in the <span class="hlt">stress</span> spectrum by subtracting the long-wavelength harmonics (below the degree of 13). This numerical scheme is applied to compute the normal and shear <span class="hlt">stress</span> <span class="hlt">tensor</span> components globally at the Moho interface. The results reveal that most of the lithospheric <span class="hlt">stresses</span> are accumulated along active convergent tectonic margins of oceanic subductions and along continent-to-continent tectonic plate collisions. These results indicate that, aside from a frictional drag caused by mantle convection, the largest <span class="hlt">stresses</span> within the lithosphere are induced by subduction slab pull forces on the side of subducted lithosphere, which are coupled by slightly less pronounced <span class="hlt">stresses</span> (on the side of overriding lithospheric plate) possibly attributed to trench suction. Our results also show the presence of (intra-plate) lithospheric loading <span class="hlt">stresses</span> along Hawaii islands. The signature of ridge push (along divergent tectonic margins) and basal shear traction resistive forces is not clearly manifested at the investigated <span class="hlt">stress</span> spectrum (between the degrees from 13 to 180).</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> <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/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('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/2015NatSR...5E9491S','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015NatSR...5E9491S"><span>Anisotropy of Local <span class="hlt">Stress</span> <span class="hlt">Tensor</span> Leads to Line Tension</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Shao, Mingzhe; Wang, Jianjun; Zhou, Xin</p> <p>2015-04-01</p> <p>Line tension of three-phase contact lines is an important physical quantity in understanding many physical processes such as heterogeneous nucleation, soft lithography and behaviours in biomembrane, such as budding, fission and fusion. Although the concept of line tension was proposed as the excess free energy in three-phase coexistence regions a century ago, its microscopic origin is subtle and achieves long-term concerns. In this paper, we correlate line tension with anisotropy of diagonal components of <span class="hlt">stress</span> <span class="hlt">tensor</span> and give a general formula of line tension. By performing molecular dynamic simulations, we illustrate the formula proposed in Lennard-Jones gas/liquid/liquid and gas/liquid/solid systems, and find that the spatial distribution of line tension can be well revealed when the local distribution of <span class="hlt">stress</span> <span class="hlt">tensor</span> is considered.</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('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('http://adsabs.harvard.edu/abs/2002JHEP...01..029K','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2002JHEP...01..029K"><span><span class="hlt">Stress</span> Energy <span class="hlt">tensor</span> in LCFT and the Logarithmic Sugawara construction</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Kogan, Ian I.; Nichols, Alexander</p> <p>2002-01-01</p> <p>We discuss the partners of the <span class="hlt">stress</span> energy <span class="hlt">tensor</span> and their structure in Logarithmic conformal field theories. In particular we draw attention to the fundamental differences between theories with zero and non-zero central charge. However they are both characterised by at least two independent parameters. We show how, by using a generalised Sugawara construction, one can calculate the logarithmic partner of T. We show that such a construction works in the c = -2 theory using the conformal dimension one primary currents which generate a logarithmic extension of the Kac-Moody algebra.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/scitech/biblio/21192228','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/21192228"><span><span class="hlt">Stress</span> <span class="hlt">tensor</span> and bulk viscosity in relativistic nuclear collisions</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Fries, Rainer J.; Mueller, Berndt; Schaefer, Andreas</p> <p>2008-09-15</p> <p>We discuss the influence of different initial conditions for the <span class="hlt">stress</span> <span class="hlt">tensor</span> and the effect of bulk viscosity on the expansion and cooling of the fireball created in relativistic heavy ion collisions. In particular, we explore the evolution of longitudinal and transverse components of the pressure and the extent of dissipative entropy production in the one-dimensional, boost-invariant hydrodynamic model. We find that a bulk viscosity consistent with recent estimates from lattice QCD further slows the equilibration of the system; however, it does not significantly increase the entropy produced.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/28430496','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/28430496"><span>Renormalized <span class="hlt">Stress</span>-Energy <span class="hlt">Tensor</span> of an Evaporating Spinning Black Hole.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Levi, Adam; Eilon, Ehud; Ori, Amos; van de Meent, Maarten</p> <p>2017-04-07</p> <p>We provide the first calculation of the renormalized <span class="hlt">stress</span>-energy <span class="hlt">tensor</span> (RSET) of a <span class="hlt">quantum</span> field in Kerr spacetime (describing a stationary spinning black hole). More specifically, we employ a recently developed mode-sum regularization method to compute the RSET of a minimally coupled massless scalar field in the Unruh vacuum state, the <span class="hlt">quantum</span> state corresponding to an evaporating black hole. The computation is done here for the case a=0.7M, using two different variants of the method: t splitting and φ splitting, yielding good agreement between the two (in the domain where both are applicable). We briefly discuss possible implications of the results for computing semiclassical corrections to certain quantities, and also for simulating dynamical evaporation of a spinning black hole.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016PhDT........87W','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016PhDT........87W"><span>Applications of <span class="hlt">Tensor</span> Network Algorithms in <span class="hlt">Quantum</span> Many-Body Physics</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>West, Colin G.</p> <p></p> <p>The classical simulation of many-body <span class="hlt">quantum</span> systems is an essential tool in understanding many fundamental aspects of condensed matter physics. But a major obstacle arises from the number of degrees of freedom involved in describing such systems, which is exponential in the system size. Recently, however, a class of numerical techniques based on structures called "<span class="hlt">tensor</span> networks" has emerged, which allows many "typical" <span class="hlt">quantum</span> states (such as the ground states of gapped, local Hamiltonians) to be represented much more efficiently. In this work we extend and apply these techniques to consider several central topics in <span class="hlt">quantum</span> many-body physics. After reviewing the relevant background material from the field of <span class="hlt">tensor</span> networks and <span class="hlt">tensor</span> network states, we demonstrate a method for computing high order moments and cumulants of operators with respect to such states, including the so-called "Binder cumulant," a powerful tool for detecting phase transitions. Next, we employ <span class="hlt">tensor</span> network algorithms to characterize the ground state phase diagram of a <span class="hlt">quantum</span> spin model, including both symmetry-breaking phases and symmetry protected topological order, and find a signicant variety of phases and phase transitions. Finally, we consider the entanglement properties of <span class="hlt">quantum</span> states exhibiting many-body localization, using a combination of exact diagonalization and <span class="hlt">tensor</span> network techniques.</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.ncbi.nlm.nih.gov/pubmed/27934045','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/27934045"><span>Accurate Long-Time Mixed <span class="hlt">Quantum</span>-Classical Liouville Dynamics via the Transfer <span class="hlt">Tensor</span> Method.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Kananenka, Alexei A; Hsieh, Chang-Yu; Cao, Jianshu; Geva, Eitan</p> <p>2016-12-01</p> <p>In this Letter, we combine the recently introduced transfer <span class="hlt">tensor</span> method with the mixed <span class="hlt">quantum</span>-classical Liouville method. The resulting protocol provides an accurate, general, flexible and robust new route for simulating the reduced dynamics of the <span class="hlt">quantum</span> subsystem for arbitrarily long times, starting with computationally feasible short-time mixed <span class="hlt">quantum</span>-classical Liouville dynamical maps. The accuracy and feasibility of the methodology are demonstrated on a spin-boson benchmark model.</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/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/2003IJMPA..18.4771K','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2003IJMPA..18.4771K"><span><span class="hlt">Stress</span> Energy <span class="hlt">Tensor</span> in LCFT and LOGARITHMIC Sugawara Construction</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Kogan, Ian I.; Nichols, Alexander</p> <p></p> <p>We discuss the partners of the <span class="hlt">stress</span> energy <span class="hlt">tensor</span> and their structure in Logarithmic conformal field theories. In particular we draw attention to the fundamental differences between theories with zero and non-zero central charge. However they are both characterised by at least two independent parameters. We show how, by using a generalised Sugawara construction, one can calculate the logarithmic partner of T. We show that such a construction works in the c=-2 theory using the conformal dimension one primary currents which generate a logarithmic extension of the Kac-Moody algebra. This is an expanded version of a talk presented by A. Nichols at the conference on Logarithmic Conformal Field Theory and its Applications in Tehran Iran, 2001.</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/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('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.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('http://adsabs.harvard.edu/abs/2009JPCA..11312715H','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2009JPCA..11312715H"><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://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</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>2009-09-01</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.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('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.ncbi.nlm.nih.gov/pubmed/28763215','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/28763215"><span><span class="hlt">Tensor</span>-Train Split-Operator Fourier Transform (TT-SOFT) Method: Multidimensional Nonadiabatic <span class="hlt">Quantum</span> Dynamics.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Greene, Samuel M; Batista, Victor S</p> <p>2017-09-12</p> <p>We introduce the "<span class="hlt">tensor</span>-train split-operator Fourier transform" (TT-SOFT) method for simulations of multidimensional nonadiabatic <span class="hlt">quantum</span> dynamics. TT-SOFT is essentially the grid-based SOFT method implemented in dynamically adaptive <span class="hlt">tensor</span>-train representations. In the same spirit of all matrix product states, the <span class="hlt">tensor</span>-train format enables the representation, propagation, and computation of observables of multidimensional wave functions in terms of the grid-based wavepacket <span class="hlt">tensor</span> components, bypassing the need of actually computing the wave function in its full-rank <span class="hlt">tensor</span> product grid space. We demonstrate the accuracy and efficiency of the TT-SOFT method as applied to propagation of 24-dimensional wave packets, describing the S1/S2 interconversion dynamics of pyrazine after UV photoexcitation to the S2 state. Our results show that the TT-SOFT method is a powerful computational approach for simulations of <span class="hlt">quantum</span> dynamics of polyatomic systems since it avoids the exponential scaling problem of full-rank grid-based representations.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017PhRvB..96i4303S','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017PhRvB..96i4303S"><span>Density of states of many-body <span class="hlt">quantum</span> systems from <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>Schrodi, Fabian; Silvi, Pietro; Tschirsich, Ferdinand; Fazio, Rosario; Montangero, Simone</p> <p>2017-09-01</p> <p>We present a technique to compute the microcanonical thermodynamical properties of a many-body <span class="hlt">quantum</span> system using <span class="hlt">tensor</span> networks. The density of States, and more general spectral properties, are evaluated by means of a Hubbard-Stratonovich transformation performed on top of a real-time evolution, which is carried out via numerical methods based on <span class="hlt">tensor</span> networks. As a consequence, the free energy and thermal averages can be also calculated. We test this approach on the one-dimensional Ising and Fermi-Hubbard models. Using matrix product states, we show that the thermodynamical quantities as a function of temperature are in very good agreement with the exact results.</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> <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/2016PhLB..760..713B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016PhLB..760..713B"><span>Flat-space holography and <span class="hlt">stress</span> <span class="hlt">tensor</span> of Kerr black hole</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Baghchesaraei, Omid; Fareghbal, Reza; Izadi, Yousef</p> <p>2016-09-01</p> <p>We propose a <span class="hlt">stress</span> <span class="hlt">tensor</span> for the Kerr black hole written in the Boyer-Lindquist coordinate. To achieve this, we use the dictionary of the Flat/CCFT correspondence and take the flat-space limit from the quasi-local <span class="hlt">stress</span> <span class="hlt">tensor</span> of the four-dimensional Kerr-AdS black hole. The proposed <span class="hlt">stress</span> <span class="hlt">tensor</span> yields the correct values for the mass and angular momentum of the Kerr black hole at spatial infinity. We also calculate some components of the energy momentum <span class="hlt">tensor</span> of the three dimensional CCFT and show that they are consistent with the holographic calculation of the Kerr black hole. The calculation we present in this paper is another confirmation for the Flat/CCFT proposal.</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('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/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('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('https://www.osti.gov/scitech/biblio/20711315','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/20711315"><span>Short distance and initial state effects in inflation: <span class="hlt">Stress</span> <span class="hlt">tensor</span> and decoherence</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Anderson, Paul R.; Molina-Paris, Carmen; Mottola, Emil</p> <p>2005-08-15</p> <p>We present a consistent low energy effective field theory framework for parametrizing the effects of novel short distance physics in inflation, and their possible observational signatures in the cosmic microwave background. We consider the class of general homogeneous, isotropic initial states for <span class="hlt">quantum</span> scalar fields in Robertson-Walker (RW) spacetimes, subject to the requirement that their ultraviolet behavior be consistent with renormalizability of the covariantly conserved <span class="hlt">stress</span> <span class="hlt">tensor</span> which couples to gravity. In the functional Schroedinger picture such states are coherent, squeezed, mixed states characterized by a Gaussian density matrix. This Gaussian has parameters which approach those of the adiabatic vacuum at large wave number, and evolve in time according to an effective classical Hamiltonian. The one complex parameter family of {alpha} squeezed states in de Sitter spacetime does not fall into this UV allowed class, except for the special value of the parameter corresponding to the Bunch-Davies state. We determine the finite contributions to the inflationary power spectrum and <span class="hlt">stress</span> <span class="hlt">tensor</span> expectation value of general UV allowed adiabatic states, and obtain quantitative limits on the observability and backreaction effects of some recently proposed models of short distance modifications of the initial state of inflation. For all UV allowed states, the second order adiabatic basis provides a good description of particles created in the expanding RW universe. Because of the absence of particle creation for the massless, minimally coupled scalar field in de Sitter space, there is no phase decoherence in the simplest free field inflationary models. We apply adiabatic regularization to the renormalization of the decoherence functional in cosmology to corroborate this result.</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/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/2017PhRvB..96f4427L','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017PhRvB..96f4427L"><span>Griffiths singularities in the random <span class="hlt">quantum</span> Ising antiferromagnet: A tree <span class="hlt">tensor</span> network renormalization group study</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Lin, Yu-Ping; Kao, Ying-Jer; Chen, Pochung; Lin, Yu-Cheng</p> <p>2017-08-01</p> <p>The antiferromagnetic Ising chain in both transverse and longitudinal magnetic fields is one of the paradigmatic models of a <span class="hlt">quantum</span> phase transition. The antiferromagnetic system exhibits a zero-temperature critical line separating an antiferromagnetic phase and a paramagnetic phase; the critical line connects an integrable <span class="hlt">quantum</span> critical point at zero longitudinal field and a classical first-order transition point at zero transverse field. Using a strong-disorder renormalization group method formulated as a tree <span class="hlt">tensor</span> network, we study the zero-temperature phase of the <span class="hlt">quantum</span> Ising chain with bond randomness. We introduce a new matrix product operator representation of high-order moments, which provides an efficient and accurate tool for determining <span class="hlt">quantum</span> phase transitions via the Binder cumulant of the order parameter. Our results demonstrate an infinite-randomness <span class="hlt">quantum</span> critical point in zero longitudinal field accompanied by pronounced <span class="hlt">quantum</span> Griffiths singularities, arising from rare ordered regions with anomalously slow fluctuations inside the paramagnetic phase. The strong Griffiths effects are signaled by a large dynamical exponent z >1 , which characterizes a power-law density of low-energy states of the localized rare regions and becomes infinite at the <span class="hlt">quantum</span> critical point. Upon application of a longitudinal field, the <span class="hlt">quantum</span> phase transition between the paramagnetic phase and the antiferromagnetic phase is completely destroyed. Furthermore, <span class="hlt">quantum</span> Griffiths effects are suppressed, showing z <1 , when the dynamics of the rare regions is hampered by the longitudinal field.</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.osti.gov/scitech/biblio/21409609','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/21409609"><span>Vacuum <span class="hlt">stress</span>-energy <span class="hlt">tensor</span> of a massive scalar field in a wormhole spacetime</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Bezerra, V. B.; Bezerra de Mello, E. R.; Khusnutdinov, N. R.; Sushkov, S. V.</p> <p>2010-04-15</p> <p>The vacuum average value of the <span class="hlt">stress</span>-energy <span class="hlt">tensor</span> of a massive scalar field with nonminimal coupling {xi} to the curvature on the short-throat flat-space wormhole background is calculated. The final analysis is made numerically. It was shown that the energy-momentum <span class="hlt">tensor</span> does not violate the null energy condition near the throat. Therefore, the vacuum polarization cannot self-consistently support the wormhole.</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/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('https://eric.ed.gov/?q=Capacitors&pg=6&id=EJ155856','ERIC'); return false;" href="https://eric.ed.gov/?q=Capacitors&pg=6&id=EJ155856"><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://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/1999JMMM..195..174L','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/1999JMMM..195..174L"><span>Effects of compressive <span class="hlt">stress</span> on a steel cube using <span class="hlt">tensor</span> magnetization and magnetostriction analysis</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Liorzou, F.; Atherton, D. L.</p> <p>1999-04-01</p> <p>Measurements of the effects of a compressive <span class="hlt">stress</span> on magnetization and magnetostriction loops of a cubic sample from a steel pipe are presented. The compressive <span class="hlt">stress</span> was applied perpendicularly to the magnetic field and, in order to take account of the anisotropy of the sample, measurements were performed in all three orthogonal directions with field applied successively parallel to each direction of the cube edges. This gives rise to 3×3 matrices defining the magnetization and magnetostriction <span class="hlt">tensors</span>. Analysis of each element of the <span class="hlt">tensors</span> enabled, firstly, the initial preferential orientation of the magnetic domains due to the texture to be identified and, secondly, permitted us to follow the changes in the bulk easy axis induced when the compressive <span class="hlt">stress</span> was applied. Valuable information about these changes in the domain arrangements was obtained from analysis of the off-diagonal elements of the magnetization <span class="hlt">tensor</span>.</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://adsabs.harvard.edu/abs/2017PhRvB..95p1104C','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017PhRvB..95p1104C"><span>Series-expansion thermal <span class="hlt">tensor</span> network approach for <span class="hlt">quantum</span> lattice models</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Chen, Bin-Bin; Liu, Yun-Jing; Chen, Ziyu; Li, Wei</p> <p>2017-04-01</p> <p>We propose a series-expansion thermal <span class="hlt">tensor</span> network (SETTN) approach for efficient simulations of <span class="hlt">quantum</span> lattice models. This continuous-time SETTN method is based on the numerically exact Taylor series expansion of the equilibrium density operator e-β H (with H the total Hamiltonian and β the imaginary time), and is thus Trotter-error free. We discover, through simulating XXZ spin chain and square-lattice <span class="hlt">quantum</span> Ising models, that not only the Hamiltonian H , but also its powers Hn, can be efficiently expressed as matrix product operators, which enables us to calculate with high precision the equilibrium and dynamical properties of <span class="hlt">quantum</span> lattice models at finite temperatures. Our SETTN method provides an alternative to conventional Trotter-Suzuki renormalization-group (RG) approaches, and achieves a very high standard of thermal RG simulations in terms of accuracy and flexibility.</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> </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/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('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> <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/2016EGUGA..1811369Y','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016EGUGA..1811369Y"><span>Separation of deviatoric <span class="hlt">stress</span> <span class="hlt">tensors</span> from heterogeneous calcite twin data using a statistical mixture model</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Yamaji, Atsushi</p> <p>2016-04-01</p> <p>It is essential for the techniques of paleostress analysis to separate <span class="hlt">stresses</span> from heterogeneous data (e.g., Tikoff et al., 2013). A statistical mixture model is shown in this paper to be effective for calcite twinning paleopiezometry: Given the orientations of twinned e-planes and their gliding directions, the present inverse method based on the mixture model determines not only deviatoric <span class="hlt">stress</span> <span class="hlt">tensors</span>, but also estimates the number of <span class="hlt">tensors</span> that should be read from a data set using Bayesian information criterion. The present method is based on the fact that mechanical twinning occurs on an e-plane if the resolved shear <span class="hlt">stress</span> along its gliding direction, τ, is greater than a critical value, τc (e.g., Lacombe, 2010). The orientation data from e-planes corresponds to points on a 5-dimensional unit sphere, a spherical cap on which indicates a deviatoric <span class="hlt">stress</span> <span class="hlt">tensor</span>. The twinning condition, τ > τc, is identical with the condition that the points corresponding to the orientation data are distributed upon the spherical cap (Yamaji, 2015a). It means that the paleostress analysis of calcite twins comes down to the problem of fitting a spherical cap to data points on the sphere (Yamaji, 2015b). Given a heterogeneous data set, two or more spherical caps should be fitted to the data point on the sphere. A statistical mixture model is employed for this fitting in the present work. Such a statistical model enables us to evaluate the number of <span class="hlt">stresses</span> recorded in the data set. The present method was tested with artificial data sets and a natural data set obtained from a Miocene graben in central Japan. From the former type of data sets, the method determined the deviatoric <span class="hlt">stress</span> <span class="hlt">tensors</span> that were assumed to generate the data sets. The natural data were inverted to give two <span class="hlt">stresses</span> that appeared appropriate for the tectonic setting of the area where the data were obtained.</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('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="http://www.dtic.mil/">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://adsabs.harvard.edu/abs/1986LMaPh..11..133O','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/1986LMaPh..11..133O"><span><span class="hlt">Stress</span> <span class="hlt">tensor</span> for GYM in 4 p dimensions and viability of GYM-Higgs in four dimensions</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>O'Brien, G. M.; Tchrakian, D. H.</p> <p>1986-02-01</p> <p>We present the <span class="hlt">stress</span> <span class="hlt">tensor</span> for GYM systems in 4 p dimensions and give a method to compute this <span class="hlt">tensor</span> density for a GYM-Higgs system in four dimensions. This computation is made explicitly for the first such system and its viability in four Euclidean dimensions is checked. The possibility of extracting phenomenological models from this system is analysed briefly.</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://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('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://adsabs.harvard.edu/abs/2017PhRvB..96a4420C','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017PhRvB..96a4420C"><span>Overcoming the sign problem at finite temperature: <span class="hlt">Quantum</span> <span class="hlt">tensor</span> network for the orbital eg model on an infinite 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>Czarnik, Piotr; Dziarmaga, Jacek; Oleś, Andrzej M.</p> <p>2017-07-01</p> <p>The variational <span class="hlt">tensor</span> network renormalization approach to two-dimensional (2D) <span class="hlt">quantum</span> systems at finite temperature is applied to a model suffering the notorious <span class="hlt">quantum</span> Monte Carlo sign problem—the orbital eg model with spatially highly anisotropic orbital interactions. Coarse graining of the <span class="hlt">tensor</span> network along the inverse temperature β yields a numerically tractable 2D <span class="hlt">tensor</span> network representing the Gibbs state. Its bond dimension D —limiting the amount of entanglement—is a natural refinement parameter. Increasing D we obtain a converged order parameter and its linear susceptibility close to the critical point. They confirm the existence of finite order parameter below the critical temperature Tc, provide a numerically exact estimate of Tc, and give the critical exponents within 1 % of the 2D Ising universality class.</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('http://adsabs.harvard.edu/abs/2004JCoAM.168..235H','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2004JCoAM.168..235H"><span>Computation of electromagnetic force densities: Maxwell <span class="hlt">stress</span> <span class="hlt">tensor</span> vs. virtual work principle</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Henrotte, Francois; Hameyer, Kay</p> <p>2004-07-01</p> <p>A couple of fundamental formulae are demonstrated in this paper, which allow a systematic algebraic derivation of local electromagnetic forces in any material, starting from the expression of the energy density of that material. The derivation can be achieved in terms of vector and <span class="hlt">tensor</span> analysis notions exclusively, provided the distinction is properly made between fields that are `flux densities' (like b) or `circulation densities' (like h). Applying the procedure to the particular case of a nonmagnetic material, the Maxwell <span class="hlt">stress</span> <span class="hlt">tensor</span> of empty space and the virtual work principle based formula for nodal forces are both readily found back. This makes the link obvious between those methods. The formulae are further applied to a permanent magnet material.</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('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.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> </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('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('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('http://adsabs.harvard.edu/abs/2017CPL...677..156H','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017CPL...677..156H"><span>The normal modes of vibration of benzene from the trajectories of <span class="hlt">stress</span> <span class="hlt">tensor</span> eigenvector projection space</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Hu, Ming Xing; Xu, Tianlv; Momen, Roya; Azizi, Alireza; Kirk, Steven R.; Jenkins, Samantha</p> <p>2017-06-01</p> <p>A QTAIM and <span class="hlt">Stress</span> <span class="hlt">tensor</span> eigenvector projection Uσ space formalism has been used to provide a detailed description of the participation of each of the bonds of the four infrared active normal modes of benzene. Analysis of the maximum Uσ space trajectory projections revealed a mixture of Csbnd C and Csbnd H bonding characteristics. The four infrared active Uσ space trajectories were found to be unique. The normal mode with the highest infrared intensity was the only mode with non-zero maximum Uσ space trajectory projections in the most preferred and least preferred directions for the Csbnd C and Csbnd H bond critical points respectively.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=223552','PMC'); return false;" href="https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=223552"><span>ON THE DECOMPOSITION OF <span class="hlt">STRESS</span> AND STRAIN <span class="hlt">TENSORS</span> INTO SPHERICAL AND DEVIATORIC PARTS</span></a></p> <p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pmc">PubMed Central</a></p> <p>Augusti, G.; Martin, J. B.; Prager, W.</p> <p>1969-01-01</p> <p>It is well known that Hooke's law for a linearly elastic, isotropic solid may be written in the form of two relations that involve only the spherical or only the deviatoric parts of the <span class="hlt">tensors</span> of <span class="hlt">stress</span> and strain. The example of the linearly elastic, transversely isotropic solid is used to show that this decomposition is not, in general, feasible for linearly elastic, anisotropic solids. The discussion is extended to a large class of work-hardening rigid, plastic solids, and it is shown that the considered decomposition can only be achieved for the incompressible solids of this class. PMID:16591754</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/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/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('https://www.ncbi.nlm.nih.gov/pubmed/26518060','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/26518060"><span>Brain glioma growth model using reaction-diffusion equation with viscous <span class="hlt">stress</span> <span class="hlt">tensor</span> on brain MR images.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Yuan, Jianjun; Liu, Lipei</p> <p>2016-02-01</p> <p>In this paper, a new reaction-diffusion model with viscous <span class="hlt">stress</span> <span class="hlt">tensor</span> is proposed for modeling the diffusion and invasion of brain glioma cells, which is based on the model in Yuan J.J., Liu L., Hu Q.M. Mathematical modeling of brain glioma growth using modified reaction-diffusion equation on brain MR images. Comput Biol Med 2013;43:2007-2013. The corresponding parameters are computed. The viscous <span class="hlt">stress</span> <span class="hlt">tensor</span> is introduced into reaction-diffusion equation, and can describe more accurately the adhesion of gliomas and normal cells. The experimental results demonstrate the effectiveness and accuracy of the proposed reaction-diffusion equation with viscous <span class="hlt">stress</span> <span class="hlt">tensor</span> for real brain glioma MR images. Copyright © 2015 Elsevier Inc. All rights reserved.</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('http://adsabs.harvard.edu/abs/2014PhRvA..89d3845J','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2014PhRvA..89d3845J"><span>Critical study and discrimination of different formulations of electromagnetic force density and consequent <span class="hlt">stress</span> <span class="hlt">tensors</span> inside matter</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Jazayeri, Amir M.; Mehrany, Khashayar</p> <p>2014-04-01</p> <p>By examination of the exerted electromagnetic (EM) force on boundary of an object in a few examples, we look into the compatibility of the <span class="hlt">stress</span> <span class="hlt">tensors</span> corresponding to different formulas of the EM force density with special relativity. Ampere-Lorentz's formula of the EM force density is physically justifiable in that the electric field and the magnetic flux density act on the densities of the total charges and the total currents, unlike Minkowski's formula which completely excludes the densities of the bounded charges and the bounded currents inside homogeneous media. Abraham's formula is fanciful and devoid of physical meaning. Einstein-Laub's formula seems to include the densities of the total charges and the total currents at first sight, but grouping the bounded charges and the bounded currents into pointlike dipoles erroneously results in the hidden momentum being omitted, hence the error in [Phys. Rev. Lett. 108, 193901 (2012), 10.1103/PhysRevLett.108.193901]. Naturally, the Ampere-Lorentz <span class="hlt">stress</span> <span class="hlt">tensor</span> accords with special relativity. The Minkowski sress <span class="hlt">tensor</span> is also consistent with special relativity. It is worth noting that the mathematical expression of the Minkowski <span class="hlt">stress</span> <span class="hlt">tensor</span> can be quite different from the well-known form of this <span class="hlt">stress</span> <span class="hlt">tensor</span> in the literature. We show that the Einstein-Laub <span class="hlt">stress</span> <span class="hlt">tensor</span> is incompatible with special relativity, and therefore we rebut the Einstein-Laub force density. Since the Abraham momentum density of the EM fields is inherently corresponding to the Einstein-Laub force density [Phys. Rev. Lett. 111, 043602 (2013), 10.1103/PhysRevLett.111.043602], our rebuttal may also shed light on the controversy over the momentum of light.</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/2015JHEP...06..198C','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015JHEP...06..198C"><span>Correlation functions of the chiral <span class="hlt">stress-tensor</span> multiplet in SYM</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; Doobary, Reza; Eden, Burkhard; Heslop, Paul; Korchemsky, Gregory P.; Mason, Lionel; Sokatchev, Emery</p> <p>2015-06-01</p> <p>We give a new method for computing the correlation functions of the chiral part of the <span class="hlt">stress-tensor</span> supermultiplet that relies on the reformulation of SYM in twistor space. It yields the correlation functions in the Born approximation as a sum of Feynman diagrams on twistor space that involve only propagators and no integration vertices. We use this unusual feature of the twistor Feynman rules to compute the correlation functions in terms of simple building blocks which we identify as a new class of off-shell superconformal invariants. Making use of the duality between correlation functions and planar scattering amplitudes, we demonstrate that these invariants represent an off-shell generalisation of the on-shell invariants defining tree-level scattering amplitudes in SYM.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2005PhLB..609..392B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2005PhLB..609..392B"><span>On universality of <span class="hlt">stress</span>-energy <span class="hlt">tensor</span> correlation functions in supergravity [rapid communication</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Buchel, Alex</p> <p>2005-03-01</p> <p>Using the Minkowski space AdS/CFT prescription we explicitly compute in the low-energy limit the two-point correlation function of the boundary <span class="hlt">stress</span>-energy <span class="hlt">tensor</span> in a large class of type IIB supergravity backgrounds with a regular translationally invariant horizon. The relevant set of supergravity backgrounds includes all geometries which can be interpreted via gauge theory/string theory correspondence as being holographically dual to finite temperature gauge theories in Minkowski space-times. The fluctuation-dissipation theorem relates this correlation function computation to the previously established universality of the shear viscosity from supergravity duals, and to the universality of the low energy absorption cross section for minimally coupled massless scalars into a general spherically symmetric black hole. It further generalizes the latter results for the supergravity black brane geometries with non-spherical horizons.</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> <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('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('http://adsabs.harvard.edu/abs/2011CQGra..28a5007O','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2011CQGra..28a5007O"><span>Renormalized vacuum polarization and <span class="hlt">stress</span> <span class="hlt">tensor</span> on the horizon of a Schwarzschild black hole threaded by a cosmic string</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Ottewill, Adrian C.; Taylor, Peter</p> <p>2011-01-01</p> <p>We calculate the renormalized vacuum polarization and <span class="hlt">stress</span> <span class="hlt">tensor</span> for a massless, arbitrarily coupled scalar field in the Hartle-Hawking vacuum state on the horizon of a Schwarzschild black hole threaded by an infinite straight cosmic string. This calculation relies on a generalized Heine identity for non-integer Legendre functions which we derive without using specific properties of the Legendre functions themselves.</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> </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('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/2017NJPh...19f3029L','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017NJPh...19f3029L"><span>Invariant perfect <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>Li, Youning; Han, Muxin; Grassl, Markus; Zeng, Bei</p> <p>2017-06-01</p> <p>Invariant <span class="hlt">tensors</span> are states in the SU(2) <span class="hlt">tensor</span> product representation that are invariant under SU(2) action. They play an important role in the study of loop <span class="hlt">quantum</span> gravity. On the other hand, perfect <span class="hlt">tensors</span> are highly entangled many-body <span class="hlt">quantum</span> states with local density matrices maximally mixed. Recently, the notion of perfect <span class="hlt">tensors</span> has attracted a lot of attention in the fields of <span class="hlt">quantum</span> information theory, condensed matter theory, and <span class="hlt">quantum</span> gravity. In this work, we introduce the concept of an invariant perfect <span class="hlt">tensor</span> (IPT), which is an n-valent <span class="hlt">tensor</span> that is both invariant and perfect. We discuss the existence and construction of IPTs. For bivalent <span class="hlt">tensors</span>, the IPT is the unique singlet state for each local dimension. The trivalent IPT also exists and is uniquely given by Wigner’s 3j symbol. However, we show that, surprisingly, 4-valent IPTs do not exist for any identical local dimension d. On the contrary, when the dimension is large, almost all invariant <span class="hlt">tensors</span> are asymptotically perfect, which is a consequence of the phenomenon of the concentration of measure for multipartite <span class="hlt">quantum</span> states.</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('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('http://adsabs.harvard.edu/abs/2015PhRvD..91h4035B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015PhRvD..91h4035B"><span>Comparison of primordial <span class="hlt">tensor</span> power spectra from the deformed algebra and dressed metric approaches in loop <span class="hlt">quantum</span> cosmology</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Bolliet, Boris; Grain, Julien; Stahl, Clément; Linsefors, Linda; Barrau, Aurélien</p> <p>2015-04-01</p> <p>Loop <span class="hlt">quantum</span> cosmology tries to capture the main ideas of loop <span class="hlt">quantum</span> gravity and to apply them to the Universe as a whole. Two main approaches within this framework have been considered to date for the study of cosmological perturbations: the dressed metric approach and the deformed algebra approach. They both have advantages and drawbacks. In this article, we accurately compare their predictions. In particular, we compute the associated primordial <span class="hlt">tensor</span> power spectra. We show—numerically and analytically—that the large scale behavior is similar for both approaches and compatible with the usual prediction of general relativity. The small scale behavior is, the other way round, drastically different. Most importantly, we show that in a range of wave numbers explicitly calculated, both approaches do agree on predictions that, in addition, differ from standard general relativity and do not depend on unknown parameters. These features of the power spectrum at intermediate scales might constitute a universal loop <span class="hlt">quantum</span> cosmology prediction that can hopefully lead to observational tests and constraints. We also present a complete analytical study of the background evolution for the bouncing universe that can be used for other purposes.</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('http://adsabs.harvard.edu/abs/2016JChPh.144i4502L','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016JChPh.144i4502L"><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="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Levashov, V. A.</p> <p>2016-03-01</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('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/2015AGUFMMR41B2630T','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015AGUFMMR41B2630T"><span>Assessment of rock mechanical behavior considering <span class="hlt">stress</span> dependent stiffness of the cracked domain within crack <span class="hlt">tensor</span>-based approach</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Takemura, T.; Panaghi, K.; Golshani, A.; Takahashi, M.; Sato, M.</p> <p>2015-12-01</p> <p>The analyses dedicated to media with prevalent discontinuities such as rocks has mostly been limited to inevitable simplifications to make engineering judgments on the material behavior feasible. Such assumptions, though favorable in numerical simulations, usually lead to overestimations in aseismic design of earthen structures. One of the forbidding tasks in modeling rock behavior is taking the <span class="hlt">stress</span> dependency of stiffness into consideration which implies more complicated formulations. Although the theoretical relationship for such computations has already been proposed by scholars, there still remains some gaps in the real-world application of the aforementioned. The crack <span class="hlt">tensor</span>-based formulation in describing <span class="hlt">stress</span>-strain behavior of cracked rock is a case in point in which the fourth-rank crack <span class="hlt">tensor</span> effect is usually ignored due to adopting equal normal and shear stiffnesses for the medium. Once the stiffnesses were distinguished in different values, the accompanying condition imposed by the formulation requires computation of fourth rank <span class="hlt">tensor</span> which has not been obtained in a practical manner so far. In the present study, we aim to acquire the values via experimental measurements and implement the results to further improve the accuracy of the formulation used in characterizing mechanical behavior of rock samples.</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('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://www.osti.gov/scitech/biblio/20014963','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/20014963"><span>Effect of non-glide components of the <span class="hlt">stress</span> <span class="hlt">tensor</span> on deformation behavior of bcc transition metals</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Ito, K.; Vitek, V.</p> <p>1999-07-01</p> <p>In this paper the authors demonstrate by atomic computer simulation that the non-Schmid slip behavior in bcc metals is a direct consequence of the non-planar core structure of 1/2<111> screw dislocations and their response to the applied <span class="hlt">stress</span> <span class="hlt">tensor</span>. The analysis has been carried out in detail for tantalum using the Finnis-Sinclair type central force many-body potentials. Two distinct non-Schmid effects have been discerned. The first is twinning-antitwinning slip asymmetry on {l{underscore}brace}112{r{underscore}brace} planes. This is an intrinsic property of the bcc structure and depends on the sense of the applied glide <span class="hlt">stress</span>. The second non-Schmid effect is extrinsic and is controlled by the non-glide shear <span class="hlt">stresses</span> perpendicular to the total Burgers vector on {l{underscore}brace}110{r{underscore}brace} planes into which the <span class="hlt">stress</span>-free core of screw dislocations spread.</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.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/1999JGR...10414947L','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/1999JGR...10414947L"><span><span class="hlt">Stress</span> <span class="hlt">tensor</span> inversion using detailed microearthquake information and stability constraints: Application to Ölfus in southwest Iceland</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Lund, BjöRn; Slunga, Ragnar</p> <p>1999-07-01</p> <p>Using detailed microearthquake data, we present a <span class="hlt">stress</span> <span class="hlt">tensor</span> inversion scheme with new methods for selecting the fault planes and allowing for errors in the focal mechanisms. The nonuniqueness of earthquake focal mechanisms is accounted for in our inversion scheme through the introduction into the inversion of a range of well-fitting focal mechanisms for each event. The range of focal mechanisms significantly improves the quality of the estimated <span class="hlt">stress</span> <span class="hlt">tensor</span>. Relative localization of clusters of microearthquakes is used to obtain information about which nodal plane could be correct fault plane. The clusters frequently fall on a common fault plane, and if there are acceptable focal mechanisms where one nodal plane has orientation similar to the common plane, we assume this is the correct fault plane for the event. If there is no predefined fault plane, we utilize a simple Mohr-Coloumb failure criterion to obtain a physical choice of fault plane between the two nodal planes in the focal mechanism. The nodal plane with highest relative instability is chosen as the fault plane. Differences between the instability and the standard slip angle criterion are investigated. The new inversion scheme has been applied to microearthquake data from the Ölfus area in the vicinity of the southwest Iceland triple junction. We estimate an oblique strike-slip state of <span class="hlt">stress</span>, maximum horizontal <span class="hlt">stress</span> at N30°E, and minimum horizontal <span class="hlt">stress</span> at N60°W, with significant normal faulting influence. The instability fault selection criterion predicts very well the orientation of faults mapped by relative localization.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017PhRvB..96h5309W','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017PhRvB..96h5309W"><span>Electrically sign-reversible transverse g -factors of holes in droplet epitaxial GaAs/AlGaAs <span class="hlt">quantum</span> dots under 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>Wu, Yu-Nien; Wu, Ming-Fan; Ou, Ya-Wen; Chou, Ying-Lin; Cheng, Shun-Jen</p> <p>2017-08-01</p> <p>We present a theoretical investigation of anisotropic g -factor <span class="hlt">tensors</span> of single holes confined in droplet epitaxial GaAs/AlGaAs <span class="hlt">quantum</span> dots under electrical and mechanical controls using the gauge-invariant discretization method within the framework of four-band Luttinger-Kohn k ⃗.p ⃗ theory. We reveal an intrinsic obstacle to realize the electrical sign reversal of the hole g -factors, being a key condition required for a full spin control in the scheme of g -<span class="hlt">tensor</span> modulation, for the <span class="hlt">quantum</span> dots solely with electrical bias control. Constructively, our studies show that, besides electrical gating, slightly <span class="hlt">stressing</span> an inherently unstrained droplet epitaxial GaAs/AlGaAs <span class="hlt">quantum</span> dot can offset the transverse hole g -factor to be nearly zero and make the electrical sign reversal of the hole g -factors feasible.</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('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/2016PhFl...28b5114V','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016PhFl...28b5114V"><span>A dynamic regularized gradient model of the subgrid-scale <span class="hlt">stress</span> <span class="hlt">tensor</span> for large-eddy simulation</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Vollant, A.; Balarac, G.; Corre, C.</p> <p>2016-02-01</p> <p>Large-eddy simulation (LES) solves only the large scales part of turbulent flows by using a scales separation based on a filtering operation. The solution of the filtered Navier-Stokes equations requires then to model the subgrid-scale (SGS) <span class="hlt">stress</span> <span class="hlt">tensor</span> to take into account the effect of scales smaller than the filter size. In this work, a new model is proposed for the SGS <span class="hlt">stress</span> model. The model formulation is based on a regularization procedure of the gradient model to correct its unstable behavior. The model is developed based on a priori tests to improve the accuracy of the modeling for both structural and functional performances, i.e., the model ability to locally approximate the SGS unknown term and to reproduce enough global SGS dissipation, respectively. LES is then performed for a posteriori validation. This work is an extension to the SGS <span class="hlt">stress</span> <span class="hlt">tensor</span> of the regularization procedure proposed by Balarac et al. ["A dynamic regularized gradient model of the subgrid-scale scalar flux for large eddy simulations," Phys. Fluids 25(7), 075107 (2013)] to model the SGS scalar flux. A set of dynamic regularized gradient (DRG) models is thus made available for both the momentum and the scalar equations. The second objective of this work is to compare this new set of DRG models with direct numerical simulations (DNS), filtered DNS in the case of classic flows simulated with a pseudo-spectral solver and with the standard set of models based on the dynamic Smagorinsky model. Various flow configurations are considered: decaying homogeneous isotropic turbulence, turbulent plane jet, and turbulent channel flows. These tests demonstrate the stable behavior provided by the regularization procedure, along with substantial improvement for velocity and scalar statistics predictions.</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/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/2008AGUFM.T23C2068A','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2008AGUFM.T23C2068A"><span>4D Quantification of <span class="hlt">Stress</span> and Strain <span class="hlt">Tensors</span> at Sheep Mountain Anticline (Wyoming, USA) Using Calcite Twin Analysis</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Amrouch, K.; Lacombe, O.; Daniel, J.</p> <p>2008-12-01</p> <p>We use the calcite twin analysis to investigate the relationship between fold development, <span class="hlt">stress</span> and strain distribution. We chose for this study the Sheep Mountain Anticline (Wyoming, USA) as a natural laboratory. Because it's asymmetric and basement-cored fold, this anticline was formed during the Laramide orogeny in the Early Tertiary.The calcite twin have been measured in folded Lower Carboniferous to Permian age carbonates and sandstones. Calcite twin recorded both in the matrix and in the veins, highlight three different tectonic stages: the first phase is a pre-folding compression parallel to fold axis, a second one is also pre- folding compression but it's perpendicular to the future fold axis and the third stage is also perpendicular to the fold axis but it's a post-folding compression. Furthermore, calcite twin data provide information about the evolution of <span class="hlt">stress</span> (Etchecopar's method) and strain (Groshong's method) through time and space. Both pre- folding and post-folding NE-directed compressional <span class="hlt">stress</span> and/or shortening were recorded within pre-folding veins (set I) as well as in fold-related veins (sets II and III). Set III veins also recorded outer rim extension along the fold hinge line.Besides, calcite twin analysis allow us to quantify <span class="hlt">stress</span> and strain. Our results point out both temporal and spatial evolution of <span class="hlt">stress</span> and strain <span class="hlt">tensors</span>. Spatially, we notice that both strain and particularly differential-<span class="hlt">stress</span> in the backlimb are higher than in the forelimb. We are also able to show that differential-<span class="hlt">stress</span> drops both in the backlimb and in the forelimb between pre-folding and post-folding stages. Our new dataset should putting better constrains on numerical models in order to increase our knowledge on fold mechanics.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/1989Tecto...8..265H','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/1989Tecto...8..265H"><span>Possible paleo-<span class="hlt">stress</span> <span class="hlt">tensor</span> configurations derived from fault-slip data in eastern Vermont and western New Hampshire</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Hardcastle, Kenneth C.</p> <p>1989-04-01</p> <p>3 plunges gently east. Field relations indicate set T faults document the transition from normal (sets N1 and N2) to strike-slip faulting regimes (set RL). A compatible sequence of Mesozoic <span class="hlt">stress</span> fields is suggested de Boer et al. [1988]. North-northeast trending, right-lateral faults of set RL (n=7) are mineralized with quartz-limonite-calcite-chlorite. Calcite twins are bent and fractured, and quartz grains show minor internal strain, suggesting that these faults developed while host rocks were at relatively shallow crustal levels. The plunge of σ1 is gently northeast and, σ3 plunges gently east-southeast. Seven distinctly mineralized (feldspar-siderite-quartzoalcite-1imonite-chlorite) gently northwest dipping, thrust faults of set F define the sixth <span class="hlt">tensor</span>. These faults are cut by essentially vertical, east-side-up faults and are assumed to be Mesozoic in age by analogy with similar faults in western Massachusetts.</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/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('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> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/26565444','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/26565444"><span><span class="hlt">Tensor</span> Network Renormalization.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Evenbly, G; Vidal, G</p> <p>2015-10-30</p> <p>We introduce a coarse-graining transformation for <span class="hlt">tensor</span> networks that can be applied to study both the partition function of a classical statistical system and the Euclidean path integral of a <span class="hlt">quantum</span> many-body system. The scheme is based upon the insertion of optimized unitary and isometric <span class="hlt">tensors</span> (disentanglers and isometries) into the <span class="hlt">tensor</span> network and has, as its key feature, the ability to remove short-range entanglement or correlations at each coarse-graining step. Removal of short-range entanglement results in scale invariance being explicitly recovered at criticality. In this way we obtain a proper renormalization group flow (in the space of <span class="hlt">tensors</span>), one that in particular (i) is computationally sustainable, even for critical systems, and (ii) has the correct structure of fixed points, both at criticality and away from it. We demonstrate the proposed approach in the context of the 2D classical Ising model.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/24954425','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/24954425"><span>Midurethral autologous fascial sling surgery with reconstruction of the lower abdominal wall using the <span class="hlt">tensor</span> fascia lata muscle flap for post-hemipelvectomy <span class="hlt">stress</span> urinary incontinence.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Niimi, Aya; Igawa, Yasuhiko; Fujimura, Tetsuya; Suzuki, Motofumi; Mihara, Makoto; Koshima, Isao; Homma, Yukio</p> <p>2014-09-01</p> <p>Hemipelvectomy is surgery for pelvic bone neoplasms. In the case of pubic bone osteosarcoma, the distal end of the rectus abdominis muscle is severed from the pubic and ischium bones, and the pelvic floor muscles are resected en bloc with the bone, which leads to <span class="hlt">stress</span> urinary incontinence. Cancer control is prioritized over complications, and <span class="hlt">stress</span> urinary incontinence is generally disregarded. A 25-year-old woman presented with <span class="hlt">stress</span> urinary incontinence. She had undergone a hemipelvectomy for left pubic bone osteosarcoma, and <span class="hlt">stress</span> urinary incontinence appeared and persisted since the surgery. We carried out a reconstruction of the tissue deficit of the rectus abdominis using the <span class="hlt">tensor</span> fascia lata muscle flap simultaneously with a midurethral autologous fascial sling anchoring to the <span class="hlt">tensor</span> fascia lata flap. <span class="hlt">Stress</span> incontinence was successfully improved without morbidity. This is the first reported case of midurethral suspension with reconstruction of the lower abdominal wall with the <span class="hlt">tensor</span> fascia lata flap for post-hemipelvectomy <span class="hlt">stress</span> urinary incontinence. © 2014 The Japanese Urological Association.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016EGUGA..18.3297V','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016EGUGA..18.3297V"><span>Lunisolar tidal and tidal load elastic <span class="hlt">stress</span> <span class="hlt">tensor</span> components within the Earth's mantle and their influence on earthquake occurrences</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Varga, Peter; Grafarend, Erik</p> <p>2016-04-01</p> <p>The relationship of earthquakes with the tidal phenomenon since long is a subject of scientific debates and it cannot be regarded as clarified even today. For the purpose of theoretical investigation of this problem a set of second order spheroidal Love-Shida numbers (h(r), k(r), l(r)) and their radial derivatives were determined for the case of a symmetric, non-rotating, elastic, isotropic (SNREI) Earth with a liquid core. By these means, the <span class="hlt">stress</span> <span class="hlt">tensor</span> components from the surface to the core-mantle boundary (CMB) were calculated for the case of zonal, tesseral and sectorial tides. Since the tidal potential and its derivatives are coordinate dependent and the zonal, tesseral and sectorial tides have different distributions on and within the Earth, the lunisolar <span class="hlt">stress</span> cannot influence the break-out of every seismological event in the same degree. A correlation between earthquake energy release and the lunisolar effect can exist in some cases where the seismic area is well determined and has either one seismic source or severe similar ones. Particularly in volcanic areas, where the seismic activity is connected to the volcano's activity, or in the case of some aftershock swarms, significant correlation was found by different authors.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=5593075','PMC'); return false;" href="https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=5593075"><span>Towards the Irving-Kirkwood limit of the mechanical <span class="hlt">stress</span> <span class="hlt">tensor</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>Heyes, D. M.; Dini, D.</p> <p>2017-01-01</p> <p>The probability density functions (PDFs) of the local measure of pressure as a function of the sampling volume are computed for a model Lennard-Jones (LJ) fluid using the Method of Planes (MOP) and Volume Averaging (VA) techniques. This builds on the study of Heyes, Dini, and Smith [J. Chem. Phys. 145, 104504 (2016)] which only considered the VA method for larger subvolumes. The focus here is typically on much smaller subvolumes than considered previously, which tend to the Irving-Kirkwood limit where the pressure <span class="hlt">tensor</span> is defined at a point. The PDFs from the MOP and VA routes are compared for cubic subvolumes, V=ℓ3. Using very high grid-resolution and box-counting analysis, we also show that any measurement of pressure in a molecular system will fail to exactly capture the molecular configuration. This suggests that it is impossible to obtain the pressure in the Irving-Kirkwood limit using the commonly employed grid based averaging techniques. More importantly, below ℓ≈3 in LJ reduced units, the PDFs depart from Gaussian statistics, and for ℓ=1.0, a double peaked PDF is observed in the MOP but not VA pressure distributions. This departure from a Gaussian shape means that the average pressure is not the most representative or common value to arise. In addition to contributing to our understanding of local pressure formulas, this work shows a clear lower limit on the validity of simply taking the average value when coarse graining pressure from molecular (and colloidal) systems.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017JChPh.146v4109S','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017JChPh.146v4109S"><span>Towards the Irving-Kirkwood limit of the mechanical <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>Smith, E. R.; Heyes, D. M.; Dini, D.</p> <p>2017-06-01</p> <p>The probability density functions (PDFs) of the local measure of pressure as a function of the sampling volume are computed for a model Lennard-Jones (LJ) fluid using the Method of Planes (MOP) and Volume Averaging (VA) techniques. This builds on the study of Heyes, Dini, and Smith [J. Chem. Phys. 145, 104504 (2016)] which only considered the VA method for larger subvolumes. The focus here is typically on much smaller subvolumes than considered previously, which tend to the Irving-Kirkwood limit where the pressure <span class="hlt">tensor</span> is defined at a point. The PDFs from the MOP and VA routes are compared for cubic subvolumes, V =ℓ3. Using very high grid-resolution and box-counting analysis, we also show that any measurement of pressure in a molecular system will fail to exactly capture the molecular configuration. This suggests that it is impossible to obtain the pressure in the Irving-Kirkwood limit using the commonly employed grid based averaging techniques. More importantly, below ℓ ≈3 in LJ reduced units, the PDFs depart from Gaussian statistics, and for ℓ =1.0 , a double peaked PDF is observed in the MOP but not VA pressure distributions. This departure from a Gaussian shape means that the average pressure is not the most representative or common value to arise. In addition to contributing to our understanding of local pressure formulas, this work shows a clear lower limit on the validity of simply taking the average value when coarse graining pressure from molecular (and colloidal) systems.</p> </li> <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="http://www.dtic.mil/">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('http://adsabs.harvard.edu/abs/2017CQGra..34n5009N','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017CQGra..34n5009N"><span>Mother canonical <span class="hlt">tensor</span> model</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Narain, Gaurav; Sasakura, Naoki</p> <p>2017-07-01</p> <p>The canonical <span class="hlt">tensor</span> model (CTM) is a <span class="hlt">tensor</span> model formulated in the Hamilton formalism as a totally constrained system with first class constraints, the algebraic structure of which is very similar to that of the ADM formalism of general relativity. It has recently been shown that a formal continuum limit of the classical equation of motion of CTM in a derivative expansion of the <span class="hlt">tensor</span> up to the fourth derivatives agrees with that of a coupled system of general relativity and a scalar field in the Hamilton-Jacobi formalism. This suggests the existence of a ‘mother’ <span class="hlt">tensor</span> model which derives CTM through the Hamilton-Jacobi procedure, and we have successfully found such a ‘mother’ CTM (mCTM) in this paper. The quantization of the mCTM is as straightforward as the CTM. However, we have not been able to identify all the secondary constraints, and therefore the full structure of the model has been left for future study. Nonetheless, we have found some exact physical wave functions and classical phase spaces, which can be shown to solve the primary and all the (possibly infinite) secondary constraints in the <span class="hlt">quantum</span> and classical cases, respectively, and have thereby proven the non-triviality of the model. It has also been shown that the mCTM has more interesting dynamics than the CTM from the perspective of randomly connected <span class="hlt">tensor</span> networks.</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/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('https://www.ncbi.nlm.nih.gov/pubmed/28368642','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/28368642"><span>Loop Optimization for <span class="hlt">Tensor</span> Network Renormalization.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Yang, Shuo; Gu, Zheng-Cheng; Wen, Xiao-Gang</p> <p>2017-03-17</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> </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/2000JMoSt.556..131G','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2000JMoSt.556..131G"><span>A higher level ab initio <span class="hlt">quantum</span>-mechanical study of the quadrupole moment <span class="hlt">tensor</span> components of carbon dioxide</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Glaser, R.; Wu, Z.; Lewis, M.</p> <p>2000-12-01</p> <p>The quadrupolarity of carbon dioxide has been studied with higher level ab initio methods. Carbon dioxide exhibits {- + -} quadrupolarity in all directions and an explanation is provided of the origin of the sign of the diagonal elements Qii. The quadrupole moment <span class="hlt">tensor</span> has been computed using restricted Hartree-Fock theory, second-order Møller-Plesset perturbation theory and quadratic configuration interaction theory. A variety of basis sets have been employed up to basis sets of the type [5s, 4p, 2d, 1f] (23s, 8p, 2d, 1f). The quadrupole moment <span class="hlt">tensor</span> component Q∥ of carbon dioxide falls in the range between -18.5 and -20.5 Debye Å. The quadrupole moment <span class="hlt">tensor</span> components Q⊥ of carbon dioxide are smaller, ranging from -14.5 to -15 Debye Å, and they are less sensitive to the choice of the theoretical model. The correlated methods consistently predict an increase of Q∥ while they predict a more modest reduction of Q⊥. It is for the opposing electron correlation effects on Q∥ and Q⊥ that the average values of the diagonal elements, <Qii>, are essentially independent of the method and exhibit only a small variation depending on the basis set. On the other hand, the anisotropy of the quadrupolarity, the quadrupole moment Θ, is affected most by the opposing electron correlation effects on Q∥ and Q⊥. The accurate reproduction of the measured quadrupolarity Θ=-4.3 Debye Å requires a theoretical model that employs both a good method and a good basis set. The results suggest that the use of second-order Møller-Plesset perturbation theory in conjunction with well-polarized triple-ζ basis sets provides a cost-effective and quite accurate method for the estimation of correlation effects on quadrupole moments.</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/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/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/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/2017CPL...685..127W','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017CPL...685..127W"><span>Insights into the all-metal [Sb3Au3Sb3]3- sandwich complex from a QTAIM and <span class="hlt">stress</span> <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>Wang, Lingling; Ping, Yang; Momen, Roya; Azizi, Alireza; Xu, Tianlv; Rodríguez, Juan I.; Anderson, James S. M.; Kirk, Steven R.; Jenkins, Samantha</p> <p>2017-10-01</p> <p>A QTAIM investigation of the [Sb3Au3Sb3]3- sandwich complex is consistent with a previous investigation and reveals all of the bond critical points (BCPs) to be closed-shell BCPs with a degree of covalent character. All of the Sb-Au BCPs and Sb-Sb BCPs are found to possess metallicity. From the <span class="hlt">stress</span> <span class="hlt">tensor</span> analysis a topological instability in the Sb-Au BCPs and Sb-Sb BCPs is revealed highlighting the need for an improved charge density. The topological instability is removed by using the SR-ZORA method to describe relativistic effects.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016JPhD...49U5302D','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016JPhD...49U5302D"><span>The role of <span class="hlt">stress</span> in CdTe <span class="hlt">quantum</span> dot doped glasses</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>de Thomaz, A. A.; Almeida, D. B.; Pelegati, V. B.; Carvalho, H. F.; Moreira, S. G. C.; Barbosa, L. C.; Cesar, C. L.</p> <p>2016-11-01</p> <p>In this work, we unequivocally demonstrate the influence of matrix-related <span class="hlt">stresses</span> on <span class="hlt">quantum</span> dots by measuring, side by side, a CdTe <span class="hlt">quantum</span> dot doped glass and a colloidal sample with similar sizes. We measured the fluorescence spectra and fluorescence lifetime for both samples as a function of the temperature. We show that the expansion coefficient mismatch between CdTe <span class="hlt">quantum</span> dots and the glass host causes <span class="hlt">stresses</span> and drastically changes its behavior compared to its colloidal counterpart, even leading to phase transitions. This finding indicates that most experimental data on glass-doped <span class="hlt">quantum</span> dots used to validate confinement models should be revised, taking <span class="hlt">stress</span> into account.</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://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://adsabs.harvard.edu/abs/2017PhRvB..96d5128X','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017PhRvB..96d5128X"><span>Optimized contraction scheme for <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>Xie, Z. Y.; Liao, H. J.; Huang, R. Z.; Xie, H. D.; Chen, J.; Liu, Z. Y.; Xiang, T.</p> <p>2017-07-01</p> <p>In the <span class="hlt">tensor</span>-network framework, the expectation values of two-dimensional <span class="hlt">quantum</span> states are evaluated by contracting a double-layer <span class="hlt">tensor</span> network constructed from initial and final <span class="hlt">tensor</span>-network states. The computational cost of carrying out this contraction is generally very high, which limits the largest bond dimension of <span class="hlt">tensor</span>-network states that can be accurately studied to a relatively small value. We propose an optimized contraction scheme to solve this problem by mapping the double-layer <span class="hlt">tensor</span> network onto an intersected single-layer <span class="hlt">tensor</span> network. This reduces greatly the bond dimensions of local <span class="hlt">tensors</span> to be contracted and improves dramatically the efficiency and accuracy of the evaluation of expectation values of <span class="hlt">tensor</span>-network states. It almost doubles the largest bond dimension of <span class="hlt">tensor</span>-network states whose physical properties can be efficiently and reliably calculated, and it extends significantly the application scope of <span class="hlt">tensor</span>-network methods.</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> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017PhRvL.119g0401V','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017PhRvL.119g0401V"><span>Bridging Perturbative Expansions 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>Vanderstraeten, Laurens; Mariën, Michaël; Haegeman, Jutho; Schuch, Norbert; Vidal, Julien; Verstraete, Frank</p> <p>2017-08-01</p> <p>We demonstrate that perturbative expansions for <span class="hlt">quantum</span> many-body systems can be rephrased in terms of <span class="hlt">tensor</span> networks, thereby providing a natural framework for interpolating perturbative expansions across a <span class="hlt">quantum</span> phase transition. This approach leads to classes of <span class="hlt">tensor</span>-network states parametrized by few parameters with a clear physical meaning, while still providing excellent variational energies. We also demonstrate how to construct perturbative expansions of the entanglement Hamiltonian, whose eigenvalues form the entanglement spectrum, and how the <span class="hlt">tensor</span>-network approach gives rise to order parameters for topological phase transitions.</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://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/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/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('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://www.osti.gov/scitech/servlets/purl/1253357','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/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('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> </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('http://adsabs.harvard.edu/abs/2017JGP...120..262P','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017JGP...120..262P"><span>Surgery in colored <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>Pérez-Sánchez, Carlos I.</p> <p>2017-10-01</p> <p>Rooted in group field theory and matrix models, random <span class="hlt">tensor</span> models are a recent background-invariant approach to <span class="hlt">quantum</span> gravity in arbitrary dimensions. Colored <span class="hlt">tensor</span> models (CTM) generate random triangulated orientable (pseudo)-manifolds. We analyze, in low dimensions, which known spaces are triangulated by specific CTM interactions. As a tool, we develop the graph-encoded surgery that is compatible with the <span class="hlt">quantum</span>-field-theory-structure and use it to prove that a single model, the complex φ4-interaction in rank- 2, generates all orientable 2-bordisms, thus, in particular, also all orientable, closed surfaces. We show that certain quartic rank- 3 CTM, the φ34 -theory, has as boundary sector all closed, possibly disconnected, orientable surfaces. Hence all closed orientable surfaces are cobordant via manifolds generated by the φ34 -theory.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017PhRvB..95n4428D','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017PhRvB..95n4428D"><span>Bilayer linearized <span class="hlt">tensor</span> renormalization group approach for thermal <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>Dong, Yong-Liang; Chen, Lei; Liu, Yun-Jing; Li, Wei</p> <p>2017-04-01</p> <p>Thermal <span class="hlt">tensor</span> networks constitute an efficient and versatile representation for <span class="hlt">quantum</span> lattice models at finite temperatures. By Trotter-Suzuki decomposition, one obtains a D +1 dimensional TTN for the D -dimensional <span class="hlt">quantum</span> system and then employs efficient renormalizaton group (RG) contractions to obtain the thermodynamic properties with high precision. The linearized <span class="hlt">tensor</span> renormalization group (LTRG) method, which can be used to contract TTN efficiently and calculate the thermodynamics, is briefly reviewed and then generalized to a bilayer form. We dub this bilayer algorithm as LTRG++ and explore its performance in both finite- and infinite-size systems, finding the numerical accuracy significantly improved compared to single-layer algorithm. Moreover, we show that the LTRG++ algorithm in an infinite-size system is in essence equivalent to transfer-matrix renormalization group method, while reformulated in a <span class="hlt">tensor</span> network language. As an application of LTRG++, we simulate an extended fermionic Hubbard model numerically, where the phase separation phenomenon, ground-state phase diagram, as well as <span class="hlt">quantum</span> criticality-enhanced magnetocaloric effects, are investigated.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2011JMP....52j3510S','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2011JMP....52j3510S"><span><span class="hlt">Tensor</span> models and 3-ary algebras</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Sasakura, Naoki</p> <p>2011-10-01</p> <p><span class="hlt">Tensor</span> models are the generalization of matrix models, and are studied as models of <span class="hlt">quantum</span> gravity in general dimensions. In this paper, I discuss the algebraic structure in the fuzzy space interpretation of the <span class="hlt">tensor</span> models which have a <span class="hlt">tensor</span> with three indices as its only dynamical variable. The algebraic structure is studied mainly from the perspective of 3-ary algebras. It is shown that the <span class="hlt">tensor</span> models have algebraic expressions, and that their symmetries are represented by 3-ary algebras. It is also shown that the 3-ary algebras of coordinates, which appear in the nonassociative fuzzy flat spacetimes corresponding to a certain class of configurations with Gaussian functions in the <span class="hlt">tensor</span> models, form Lie triple systems, and the associated Lie algebras are shown to agree with those of the Snyder's noncommutative spacetimes. The Poincare transformations of the coordinates on the fuzzy flat spacetimes are shown to be generated by 3-ary algebras.</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('https://www.ncbi.nlm.nih.gov/pubmed/23006185','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/23006185"><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="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Hu, Hao; Liu, Miao; Wang, Z F; Zhu, Junyi; Wu, Dangxin; Ding, Hepeng; Liu, Zheng; Liu, Feng</p> <p>2012-08-03</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 (σ(QE)) is derived in relation to deformation potential of electronic states (Ξ) and variation of electron density (Δn), σ(QE) = 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/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://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://www.ncbi.nlm.nih.gov/pubmed/21796514','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/21796514"><span>Electronic <span class="hlt">stress</span> as a guiding force for chemical bonding.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Guevara-García, Alfredo; Ayers, Paul W; Jenkins, Samantha; Kirk, Steven R; Echegaray, Eleonora; Toro-Labbe, Alejandro</p> <p>2014-01-01</p> <p>In the electron-preceding picture of chemical change, the paramount problem is identifying favorable changes in electronic structure. The electronic <span class="hlt">stress</span> <span class="hlt">tensor</span> provides this information; its eigenvectors represent electronic normal modes, pointing the way towards energetically favorable (or unfavorable) chemical rearrangements. The resulting method is well founded in both density functional theory and the <span class="hlt">quantum</span> theory of atoms in molecules (QTAIM). <span class="hlt">Stress</span> <span class="hlt">tensor</span> analysis is a natural way to extend the QTAIM to address chemical reactivity. The definition and basic properties of the electronic <span class="hlt">stress</span> <span class="hlt">tensor</span> are reviewed and the inherent ambiguity of the <span class="hlt">stress</span> <span class="hlt">tensor</span> is discussed. Extending previous work in which the <span class="hlt">stress</span> <span class="hlt">tensor</span> was used to analyze hydrogen-bonding patterns, this work focuses on chemical bonding patterns in organic reactions. Other related material (charge-shift bonding, links to the second-density-derivative <span class="hlt">tensor</span>) is summarized and reviewed. The <span class="hlt">stress</span> <span class="hlt">tensor</span> provides a multifaceted characterization of bonding and can be used to predict and describe bond formation and migration.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017EJPh...38d5202Y','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017EJPh...38d5202Y"><span>On deriving the Maxwell <span class="hlt">stress</span> <span class="hlt">tensor</span> method for calculating the optical force and torque on an object in harmonic electromagnetic fields</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Ye, Qian; Lin, Haoze</p> <p>2017-07-01</p> <p>Though extensively used in calculating optical force and torque acting on a material object illuminated by laser, the Maxwell <span class="hlt">stress</span> <span class="hlt">tensor</span> (MST) method follows the electromagnetic linear and angular momentum balance that is usually derived in most textbooks for a continuous volume charge distribution in free space, if not resorting to the application of Noether’s theorem in electrodynamics. To cast the conservation laws into a physically appealing form involving the current densities of linear and angular momentum, on which the MST method is based, the divergence theorem is employed to transform a volume integral into a surface integral. When a material object of finite volume is put into the field, it brings about a discontinuity of field across its surface, due to the presence of induced surface charge and surface current. Ambiguity arises among students in whether the divergence theorem can still be directly used without any justification. By taking into account the effect of the induced surface charge and current, we present a simple pedagogical derivation for the MST method for calculating the optical force and torque on an object immersed in monochromatic optical field, without resorting to Noether’s theorem. Although the results turn out to be identical to those given in the standard textbooks, our derivation avoids the direct use of the divergence theorem on a discontinuous function.</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('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('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/2014NuPhB.886..436K','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2014NuPhB.886..436K"><span>Anyon condensation and <span class="hlt">tensor</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>Kong, Liang</p> <p>2014-09-01</p> <p>Instead of studying anyon condensation in various concrete models, we take a bootstrap approach by considering an abstract situation, in which an anyon condensation happens in a 2-d topological phase with anyonic excitations given by a modular <span class="hlt">tensor</span> category C; and the anyons in the condensed phase are given by another modular <span class="hlt">tensor</span> category D. By a bootstrap analysis, we derive a relation between anyons in D-phase and anyons in C-phase from natural physical requirements. It turns out that the vacuum (or the <span class="hlt">tensor</span> unit) A in D-phase is necessary to be a connected commutative separable algebra in C, and the category D is equivalent to the category of local A-modules as modular <span class="hlt">tensor</span> categories. This condensation also produces a gapped domain wall with wall excitations given by the category of A-modules in C. A more general situation is also studied in this paper. We will also show how to determine such algebra A from the initial and final data. Multi-condensations and 1-d condensations will also be briefly discussed. Examples will be given in the toric code model, Kitaev <span class="hlt">quantum</span> double models, Levin-Wen types of lattice models and some chiral topological phases.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/pages/biblio/1258327-electrode-stress-induced-nanoscale-disorder-si-quantum-electronic-devices','SCIGOV-DOEP'); return false;" href="https://www.osti.gov/pages/biblio/1258327-electrode-stress-induced-nanoscale-disorder-si-quantum-electronic-devices"><span>Electrode-<span class="hlt">stress</span>-induced nanoscale disorder in Si <span class="hlt">quantum</span> electronic devices</span></a></p> <p><a target="_blank" href="http://www.osti.gov/pages">DOE PAGES</a></p> <p>Park, J.; Ahn, Y.; Tilka, J. A.; ...</p> <p>2016-06-20</p> <p>Disorder in the potential-energy landscape presents a major obstacle to the more rapid development of semiconductor <span class="hlt">quantum</span> device technologies. We report a large-magnitude source of disorder, beyond commonly considered unintentional background doping or fixed charge in oxide layers: nanoscale strain fields induced by residual <span class="hlt">stresses</span> in nanopatterned metal gates. Quantitative analysis of synchrotron coherent hard x-ray nanobeam diffraction patterns reveals gate-induced curvature and strains up to 0.03% in a buried Si <span class="hlt">quantum</span> well within a Si/SiGe heterostructure. Furthermore, electrode <span class="hlt">stress</span> presents both challenges to the design of devices and opportunities associated with the lateral manipulation of electronic energy levels.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016APLM....4f6102P','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016APLM....4f6102P"><span>Electrode-<span class="hlt">stress</span>-induced nanoscale disorder in Si <span class="hlt">quantum</span> electronic devices</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Park, J.; Ahn, Y.; Tilka, J. A.; Sampson, K. C.; Savage, D. E.; Prance, J. R.; Simmons, C. B.; Lagally, M. G.; Coppersmith, S. N.; Eriksson, M. A.; Holt, M. V.; Evans, P. G.</p> <p>2016-06-01</p> <p>Disorder in the potential-energy landscape presents a major obstacle to the more rapid development of semiconductor <span class="hlt">quantum</span> device technologies. We report a large-magnitude source of disorder, beyond commonly considered unintentional background doping or fixed charge in oxide layers: nanoscale strain fields induced by residual <span class="hlt">stresses</span> in nanopatterned metal gates. Quantitative analysis of synchrotron coherent hard x-ray nanobeam diffraction patterns reveals gate-induced curvature and strains up to 0.03% in a buried Si <span class="hlt">quantum</span> well within a Si/SiGe heterostructure. Electrode <span class="hlt">stress</span> presents both challenges to the design of devices and opportunities associated with the lateral manipulation of electronic energy levels.</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. © 2015 SETAC.</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> </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://ntrs.nasa.gov/search.jsp?R=19930000179&hterms=Monograph&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D30%26Ntt%3DMonograph','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19930000179&hterms=Monograph&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D30%26Ntt%3DMonograph"><span>Monograph On <span class="hlt">Tensor</span> Notations</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Sirlin, Samuel W.</p> <p>1993-01-01</p> <p>Eight-page report describes systems of notation used most commonly to represent <span class="hlt">tensors</span> of various ranks, with emphasis on <span class="hlt">tensors</span> in Cartesian coordinate systems. Serves as introductory or refresher text for scientists, engineers, and others familiar with basic concepts of coordinate systems, vectors, and partial derivatives. Indicial <span class="hlt">tensor</span>, vector, dyadic, and matrix notations, and relationships among them described.</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/2013JPhCS.474a2018F','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2013JPhCS.474a2018F"><span>Generating functions for <span class="hlt">tensor</span> product decomposition</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Fuksa, Jan; Pošta, Severin</p> <p>2013-11-01</p> <p>The paper deals with the <span class="hlt">tensor</span> product decomposition problem. <span class="hlt">Tensor</span> product decompositions are of great importance in the <span class="hlt">quantum</span> physics. A short outline of the state of the art for the of semisimple Lie groups is mentioned. The generality of generating functions is used to solve <span class="hlt">tensor</span> products. The corresponding generating function is rational. The feature of this technique lies in the fact that the decompositions of all <span class="hlt">tensor</span> products of all irreducible representations are solved simultaneously. Obtaining the generating function is a difficult task in general. We propose some changes to an algorithm using Patera-Sharp character generators to find this generating function, which simplifies the whole problem to simple operations over rational functions.</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('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('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('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://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('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> <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('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/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/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.ncbi.nlm.nih.gov/pubmed/22611107','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/22611107"><span>Simultaneous determination of mean pressure and deviatoric <span class="hlt">stress</span> based on numerical <span class="hlt">tensor</span> analysis: a case study for polycrystalline x-ray diffraction of gold enclosed in a methanol-ethanol mixture.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Yoneda, A; Kubo, A</p> <p>2006-06-28</p> <p>It is known that the {100} and {111} planes of cubic crystals subjected to uniaxial deviatoric <span class="hlt">stress</span> conditions have strain responses that are free from the effect of lattice preferred orientation. By utilizing this special character, one can unambiguously and simultaneously determine the mean pressure and deviatoric <span class="hlt">stress</span> from polycrystalline diffraction data of the cubic sample. Here we introduce a numerical <span class="hlt">tensor</span> calculation method based on the generalized Hooke's law to simultaneously determine the hydrostatic component of the <span class="hlt">stress</span> (mean pressure) and deviatoric <span class="hlt">stress</span> in the sample. The feasibility of this method has been tested by examining the experimental data of the Au pressure marker enclosed in a diamond anvil cell using a pressure medium of methanol-ethanol mixture. The results demonstrated that the magnitude of the deviatoric <span class="hlt">stress</span> is ∼0.07 GPa at the mean pressure of 10.5 GPa, which is consistent with previous results of Au strength under high pressure. Our results also showed that even a small deviatoric <span class="hlt">stress</span> (∼0.07 GPa) could yield a ∼0.3 GPa mean pressure error at ∼10 GPa.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017JHEP...08..060Q','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017JHEP...08..060Q"><span>Holographic coherent states 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>Qi, Xiao-Liang; Yang, Zhao; You, Yi-Zhuang</p> <p>2017-08-01</p> <p>Random <span class="hlt">tensor</span> networks provide useful models that incorporate various important features of holographic duality. A <span class="hlt">tensor</span> network is usually defined for a fixed graph geometry specified by the connection of <span class="hlt">tensors</span>. In this paper, we generalize the random <span class="hlt">tensor</span> network approach to allow <span class="hlt">quantum</span> superposition of different spatial geometries. We setup a framework in which all possible bulk spatial geometries, characterized by weighted adjacient matrices of all possible graphs, are mapped to the boundary Hilbert space and form an overcomplete basis of the boundary. We name such an overcomplete basis as holographic coherent states. A generic boundary state can be expanded in this basis, which describes the state as a superposition of different spatial geometries in the bulk. We discuss how to define distinct classical geometries and small fluctuations around them. We show that small fluctuations around classical geometries define "code subspaces" which are mapped to the boundary Hilbert space isometrically with <span class="hlt">quantum</span> error correction properties. In addition, we also show that the overlap between different geometries is suppressed exponentially as a function of the geometrical difference between the two geometries. The geometrical difference is measured in an area law fashion, which is a manifestation of the holographic nature of the states considered.</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/2016JMP....57a5202M','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016JMP....57a5202M"><span>Positivity of linear maps under <span class="hlt">tensor</span> powers</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; Reeb, David; Wolf, Michael M.</p> <p>2016-01-01</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/2014GReGr..46.1823M','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2014GReGr..46.1823M"><span>Entanglement, <span class="hlt">tensor</span> networks and black hole horizons</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Molina-Vilaplana, J.; Prior, J.</p> <p>2014-11-01</p> <p>We elaborate on a previous proposal by Hartman and Maldacena on a <span class="hlt">tensor</span> network which accounts for the scaling of the entanglement entropy in a system at a finite temperature. In this construction, the ordinary entanglement renormalization flow given by the class of <span class="hlt">tensor</span> networks known as the Multi Scale Entanglement Renormalization Ansatz (MERA), is supplemented by an additional entanglement structure at the length scale fixed by the temperature. The network comprises two copies of a MERA circuit with a fixed number of layers and a pure matrix product state which joins both copies by entangling the infrared degrees of freedom of both MERA networks. The entanglement distribution within this bridge state defines reduced density operators on both sides which cause analogous effects to the presence of a black hole horizon when computing the entanglement entropy at finite temperature in the AdS/CFT correspondence. The entanglement and correlations during the thermalization process of a system after a <span class="hlt">quantum</span> quench are also analyzed. To this end, a full <span class="hlt">tensor</span> network representation of the action of local unitary operations on the bridge state is proposed. This amounts to a <span class="hlt">tensor</span> network which grows in size by adding succesive layers of bridge states. Finally, we discuss on the holographic interpretation of the <span class="hlt">tensor</span> network through a notion of distance within the network which emerges from its entanglement distribution.</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> </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.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=4357235','PMC'); return false;" href="https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=4357235"><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="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pmc">PubMed Central</a></p> <p></p> <p>2015-01-01</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. PMID:25844072</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016CQGra..33a5008C','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016CQGra..33a5008C"><span>Coordinate independent expression for transverse trace-free <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>Conboye, Rory</p> <p>2016-01-01</p> <p>The transverse and trace-free (TT) part of the extrinsic curvature represents half of the dynamical degrees of freedom of the gravitational field in the 3 + 1 formalism. As such, it is part of the freely specifiable initial data for numerical relativity. Though TT <span class="hlt">tensors</span> in three-space possess only two component degrees of freedom, they cannot ordinarily be given solely by two scalar potentials. Such expressions have been derived, however, in coordinate form, for all TT <span class="hlt">tensors</span> in flat space which are also translationally or axially symmetric (Conboye and Murchadha 2014 Class. <span class="hlt">Quantum</span> Grav. 31 085019). Since TT <span class="hlt">tensors</span> are conformally covariant, these also give TT <span class="hlt">tensors</span> in conformally flat space. In this article, the work above has been extended by giving a coordinate-independent expression for these TT <span class="hlt">tensors</span>. The translational and axial symmetry conditions have also been generalized to invariance along any hypersurface orthogonal Killing vector.</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/2017PhDT........19J','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017PhDT........19J"><span>Symmetric Topological Phases and <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>Jiang, Shenghan</p> <p></p> <p>Classification and simulation of <span class="hlt">quantum</span> phases are one of main themes in condensed matter physics. <span class="hlt">Quantum</span> phases can be distinguished by their symmetrical and topological properties. The interplay between symmetry and topology in condensed matter physics often leads to exotic <span class="hlt">quantum</span> phases and rich phase diagrams. Famous examples include <span class="hlt">quantum</span> Hall phases, spin liquids and topological insulators. In this thesis, I present our works toward a more systematically understanding of symmetric topological <span class="hlt">quantum</span> phases in bosonic systems. In the absence of global symmetries, gapped <span class="hlt">quantum</span> phases are characterized by topological orders. Topological orders in 2+1D are well studied, while a systematically understanding of topological orders in 3+1D is still lacking. By studying a family of exact solvable models, we find at least some topological orders in 3+1D can be distinguished by braiding phases of loop excitations. In the presence of both global symmetries and topological orders, the interplay between them leads to new phases termed as symmetry enriched topological (SET) phases. We develop a framework to classify a large class of SET phases using <span class="hlt">tensor</span> networks. For each <span class="hlt">tensor</span> class, we can write down generic variational wavefunctions. We apply our method to study gapped spin liquids on the kagome lattice, which can be viewed as SET phases of on-site symmetries as well as lattice symmetries. In the absence of topological order, symmetry could protect different topological phases, which are often referred to as symmetry protected topological (SPT) phases. We present systematic constructions of <span class="hlt">tensor</span> network wavefunctions for bosonic symmetry protected topological (SPT) phases respecting both onsite and spatial symmetries.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017EGUGA..19.5838M','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017EGUGA..19.5838M"><span>Pre-state of <span class="hlt">stress</span> on the fault of the 2016 Kumamoto earthquake (Mj7.3) inferred from moment <span class="hlt">tensor</span> data of micro-earthquakes before the mainshock</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Matsumoto, Satoshi; Yamashita, Yusuke; Nakamoto, Manami; Miyazaki, Masahiro; Sakai, Shin-ichi; Iio, Yoshihisa; Goto, Kazuhiko; Okada, Tomomi; Ohzono, Mako; Terakawa, Toshiko; Kosuga, Masahiro; Yoshimi, Masayuki; Asano, Youichi</p> <p>2017-04-01</p> <p>The 2016 Kumamoto earthquake (Mj7.3, Mj: magnitude scale by Japan Metrological Agency) occurred on 16 April 2016 in Kumamoto prefecture, middle part of Kyushu Island, Japan. Several earthquakes over Mj 6 also occurred before and after the mainshock. The earthquake killed resident people and heavily damaged the cities around the hypocentral area. The seismic activity in and around the area was highest in the Kyushu Island before the earthquake occurrence. Surface breaks appeared along the active faults called Hinagu and Futagawa faults during the sequence of the Kumamoto earthquake. Dense seismic observation carried out in the area enable us to estimate high precision focal mechanism solutions. Here we analyzed the focal mechanisms before and after the occurrence of the sequence as seismic moment <span class="hlt">tensors</span> and estimated <span class="hlt">stress</span> field in the hypocentral area. As general tendency, dominated minimum principal <span class="hlt">stress</span> (sigma 3) in the N-S direction obtained and the maximum principal <span class="hlt">stress</span> takes value close to the moderate one. The <span class="hlt">stress</span> field reveals spatial heterogeneous feature, which varies from southern to northern part of the area. We calculate maximum shear <span class="hlt">stress</span> direction on the fault of the mainshock from the heterogeneous <span class="hlt">stress</span> field. Comparing the direction with co-seismic rupture direction estimated from the strong motion records around the hypocentral area, we found that co-seismic fault slip mainly controlled by pre-state of <span class="hlt">stress</span> on the fault. This result from the seismic observation provides an evidence to confirm the hypothesis based on laboratory experiments for fault behavior. This suggests a possibility that the fault behavior can be estimated from the <span class="hlt">stress</span> field inferred from fault plane solutions.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/1998quan.book.....E','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/1998quan.book.....E"><span><span class="hlt">Quantum</span></span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Elbaz, Edgard</p> <p></p> <p>This book gives a new insight into the interpretation of <span class="hlt">quantum</span> mechanics (stochastic, integral paths, decoherence), a completely new treatment of angular momentum (graphical spin algebra) and an introduction to Fermion fields (Dirac equation) and Boson fields (e.m. and Higgs) as well as an introduction to QED (<span class="hlt">quantum</span> electrodynamics), supersymmetry and <span class="hlt">quantum</span> cosmology.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2012JChPh.137v4106P','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2012JChPh.137v4106P"><span><span class="hlt">Tensor</span> hypercontraction. II. Least-squares renormalization</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Parrish, Robert M.; Hohenstein, Edward G.; Martínez, Todd J.; Sherrill, C. David</p> <p>2012-12-01</p> <p>The least-squares <span class="hlt">tensor</span> hypercontraction (LS-THC) representation for the electron repulsion integral (ERI) <span class="hlt">tensor</span> is presented. Recently, we developed the generic <span class="hlt">tensor</span> hypercontraction (THC) ansatz, which represents the fourth-order ERI <span class="hlt">tensor</span> as a product of five second-order <span class="hlt">tensors</span> [E. G. Hohenstein, R. M. Parrish, and T. J. Martínez, J. Chem. Phys. 137, 044103 (2012)], 10.1063/1.4732310. Our initial algorithm for the generation of the THC factors involved a two-sided invocation of overlap-metric density fitting, followed by a PARAFAC decomposition, and is denoted PARAFAC <span class="hlt">tensor</span> hypercontraction (PF-THC). LS-THC supersedes PF-THC by producing the THC factors through a least-squares renormalization of a spatial quadrature over the otherwise singular 1/r12 operator. Remarkably, an analytical and simple formula for the LS-THC factors exists. Using this formula, the factors may be generated with O(N^5) effort if exact integrals are decomposed, or O(N^4) effort if the decomposition is applied to density-fitted integrals, using any choice of density fitting metric. The accuracy of LS-THC is explored for a range of systems using both conventional and density-fitted integrals in the context of MP2. The grid fitting error is found to be negligible even for extremely sparse spatial quadrature grids. For the case of density-fitted integrals, the additional error incurred by the grid fitting step is generally markedly smaller than the underlying Coulomb-metric density fitting error. The present results, coupled with our previously published factorizations of MP2 and MP3, provide an efficient, robust O(N^4) approach to both methods. Moreover, LS-THC is generally applicable to many other methods in <span class="hlt">quantum</span> chemistry.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017JHEP...03..070C','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017JHEP...03..070C"><span><span class="hlt">Tensor</span> Galileons and gravity</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Chatzistavrakidis, Athanasios; Khoo, Fech Scen; Roest, Diederik; Schupp, Peter</p> <p>2017-03-01</p> <p>The particular structure of Galileon interactions allows for higher-derivative terms while retaining second order field equations for scalar fields and Abelian p-forms. In this work we introduce an index-free formulation of these interactions in terms of two sets of Grassmannian variables. We employ this to construct Galileon interactions for mixed-symmetry <span class="hlt">tensor</span> fields and coupled systems thereof. We argue that these <span class="hlt">tensors</span> are the natural generalization of scalars with Galileon symmetry, similar to p-forms and scalars with a shift-symmetry. The simplest case corresponds to linearised gravity with Lovelock invariants, relating the Galileon symmetry to diffeomorphisms. Finally, we examine the coupling of a mixed-symmetry <span class="hlt">tensor</span> to gravity, and demonstrate in an explicit example that the inclusion of appropriate counterterms retains second order field equations.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/scitech/biblio/22251717','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/22251717"><span>The <span class="hlt">tensor</span> hierarchy algebra</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Palmkvist, Jakob</p> <p>2014-01-15</p> <p>We introduce an infinite-dimensional Lie superalgebra which is an extension of the U-duality Lie algebra of maximal supergravity in D dimensions, for 3 ⩽ D ⩽ 7. The level decomposition with respect to the U-duality Lie algebra gives exactly the <span class="hlt">tensor</span> hierarchy of representations that arises in gauge deformations of the theory described by an embedding <span class="hlt">tensor</span>, for all positive levels p. We prove that these representations are always contained in those coming from the associated Borcherds-Kac-Moody superalgebra, and we explain why some of the latter representations are not included in the <span class="hlt">tensor</span> hierarchy. The most remarkable feature of our Lie superalgebra is that it does not admit a triangular decomposition like a (Borcherds-)Kac-Moody (super)algebra. Instead the Hodge duality relations between level p and D − 2 − p extend to negative p, relating the representations at the first two negative levels to the supersymmetry and closure constraints of the embedding <span class="hlt">tensor</span>.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017JGP...117....1H','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017JGP...117....1H"><span>Killing <span class="hlt">tensors</span> on tori</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Heil, Konstantin; Moroianu, Andrei; Semmelmann, Uwe</p> <p>2017-07-01</p> <p>We show that Killing <span class="hlt">tensors</span> on conformally flat n-dimensional tori whose conformal factor only depends on one variable, are polynomials in the metric and in the Killing vector fields. In other words, every first integral of the geodesic flow polynomial in the momenta on the sphere bundle of such a torus is linear in the momenta.</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('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/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('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.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/2008mgm..conf.1552M','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2008mgm..conf.1552M"><span>x<span class="hlt">TENSOR</span>:. a Free Fast Abstract <span class="hlt">Tensor</span> Manipulator</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Martín-García, José M.</p> <p>2008-09-01</p> <p>The package x<span class="hlt">Tensor</span> is introduced, a very fast and general manipulator of <span class="hlt">tensor</span> expressions for Mathematica. Manifolds and vector bundles can be defined containing <span class="hlt">tensor</span> fields with arbitrary symmetry, connections of any type, metrics and other objects. Based on the Penrose abstract-index notation, x<span class="hlt">Tensor</span> has a single canonicalizer which fully simplifies all expressions, using highly efficient techniques of computational group theory. A number of companion packages have been developed to address particular problems in General Relativity, like metric perturbation theory or the manipulation of the Riemann <span class="hlt">tensor</span>.</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.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> </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('https://www.ncbi.nlm.nih.gov/pubmed/19478381','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/19478381"><span>Evaluation of bayesian <span class="hlt">tensor</span> estimation using <span class="hlt">tensor</span> coherence.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Kim, Dae-Jin; Kim, In-Young; Jeong, Seok-Oh; Park, Hae-Jeong</p> <p>2009-06-21</p> <p>Fiber tractography, a unique and non-invasive method to estimate axonal fibers within white matter, constructs the putative streamlines from diffusion <span class="hlt">tensor</span> MRI by interconnecting voxels according to the propagation direction defined by the diffusion <span class="hlt">tensor</span>. This direction has uncertainties due to the properties of underlying fiber bundles, neighboring structures and image noise. Therefore, robust estimation of the diffusion direction is essential to reconstruct reliable fiber pathways. For this purpose, we propose a <span class="hlt">tensor</span> estimation method using a Bayesian framework, which includes an a priori probability distribution based on <span class="hlt">tensor</span> coherence indices, to utilize both the neighborhood direction information and the inertia moment as regularization terms. The reliability of the proposed <span class="hlt">tensor</span> estimation was evaluated using Monte Carlo simulations in terms of accuracy and precision with four synthetic <span class="hlt">tensor</span> fields at various SNRs and in vivo human data of brain and calf muscle. Proposed Bayesian estimation demonstrated the relative robustness to noise and the higher reliability compared to the simple <span class="hlt">tensor</span> regression.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2007ApPhL..91b1101M','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2007ApPhL..91b1101M"><span>Temperature induced <span class="hlt">stress</span> phase transition in CdTe <span class="hlt">quantum</span> dots observed by dielectric constant and thermal diffusivity measurements</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Moreira, S. G. C.; da Silva, E. C.; Mansanares, A. M.; Barbosa, L. C.; Cesar, C. L.</p> <p>2007-07-01</p> <p>The authors measured the dielectric constant by capacitance method and the thermal diffusivity by thermal lens technique in the temperature range from 20to300K for CdTe <span class="hlt">quantum</span> dot doped borosilicate glass samples. Results show a huge difference between the thermal behavior of the pure glass matrix, without <span class="hlt">quantum</span> dots, and of the doped glass, especially around 90 and 250K. The authors attributed this difference to the phase transition experienced by the CdTe nanocrystals due to the high pressure exerted by the glass matrix over the CdTe <span class="hlt">quantum</span> dots. The temperature induced <span class="hlt">stress</span> is caused by the thermal expansion coefficient mismatch between the <span class="hlt">quantum</span> dot and the glass matrix.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/scitech/biblio/22525772','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/22525772"><span><span class="hlt">Tensor</span> perturbations in a general class of Palatini theories</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Jiménez, Jose Beltrán; Heisenberg, Lavinia; Olmo, Gonzalo J. E-mail: laviniah@kth.se</p> <p>2015-06-01</p> <p>We study a general class of gravitational theories formulated in the Palatini approach and derive the equations governing the evolution of <span class="hlt">tensor</span> perturbations. In the absence of torsion, the connection can be solved as the Christoffel symbols of an auxiliary metric which is non-trivially related to the space-time metric. We then consider background solutions corresponding to a perfect fluid and show that the <span class="hlt">tensor</span> perturbations equations (including anisotropic <span class="hlt">stresses</span>) for the auxiliary metric around such a background take an Einstein-like form. This facilitates the study in a homogeneous and isotropic cosmological scenario where we explicitly establish the relation between the auxiliary metric and the space-time metric <span class="hlt">tensor</span> perturbations. As a general result, we show that both <span class="hlt">tensor</span> perturbations coincide in the absence of anisotropic <span class="hlt">stresses</span>.</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('https://www.ncbi.nlm.nih.gov/pubmed/18618148','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/18618148"><span>Feeding sustains photosynthetic <span class="hlt">quantum</span> yield of a scleractinian coral during thermal <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>Borell, Esther M; Bischof, Kai</p> <p>2008-10-01</p> <p>Thermal resistance of the coral-zooxanthellae symbiosis has been associated with chronic photoinhibition, increased antioxidant activity and protein repair involving high demands of nitrogen and energy. While the relative importance of heterotrophy as a source of nutrients and energy for cnidarian hosts, and as a means of nitrogen acquisition for their zooxanthellae, is well documented, the effect of feeding on the thermal sensitivity of the symbiotic association has been so far overlooked. Here we examine the effect of zooplankton feeding versus starvation on the bleaching susceptibility and photosynthetic activity of photosystem II (PSII) of zooxanthellae in the scleractinian coral Stylophora pistillata in response to thermal <span class="hlt">stress</span> (daily temperature rises of 2-3 degrees C) over 10 days, employing pulse-amplitude-modulated chlorophyll fluorometry. Fed and starved corals displayed a decrease in daily maximum potential <span class="hlt">quantum</span> yield (F (v)/F (m)) of PSII, effective <span class="hlt">quantum</span> yield (F/F (m)') and relative electron transport rates over the course of 10 days. However after 10 days of exposure to elevated temperature, F (v)/F (m) of fed corals was still 50-70% higher than F (v)/F (m) of starved corals. Starved corals showed strong signs of chronic photoinhibition, which was reflected in a significant decline in nocturnal recovery rates of PSII relative to fed corals. This was paralleled by the progressive inability to dissipate excess excitation energy via non-photochemical quenching (NPQ). After 10 days, NPQ of starved corals had decreased by about 80% relative to fed corals. Feeding treatment had no significant effect on chlorophyll a and c (2) concentrations and zooxanthellae densities, but the mitotic indices were significantly lower in starved than in fed corals. Collectively the results indicate that exogenous food may reduce the photophysiological damage of zooxanthellae that typically leads to bleaching and could therefore play an important role in mediating the</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://pubs.er.usgs.gov/publication/70188620','USGSPUBS'); return false;" href="http://pubs.er.usgs.gov/publication/70188620"><span>Using regional moment <span class="hlt">tensors</span> to constrain the kinematics and <span class="hlt">stress</span> evolution of the 2010–2013 Canterbury earthquake sequence, South Island, New Zealand</span></a></p> <p><a target="_blank" href="http://pubs.er.usgs.gov/pubs/index.jsp?view=adv">USGS Publications Warehouse</a></p> <p>Herman, Matthew W.; Herrmann, Robert B.; Benz, Harley M.; Furlong, Kevin P.</p> <p>2014-01-01</p> <p>On September 3, 2010, a MW 7.0 (U.S. Geological Survey moment magnitude) earthquake ruptured across the Canterbury Plains in South Island, New Zealand. Since then, New Zealand GNS Science has recorded over 10,000 aftershocks ML 2.0 and larger, including three destructive ~ MW 6.0 earthquakes near Christchurch. We treat the Canterbury earthquake sequence as an intraplate earthquake sequence, and compare its kinematics to an Andersonian model for fault slip in a uniform <span class="hlt">stress</span> field. We determined moment magnitudes and double couple solutions for 150 earthquakes having MW 3.7 and larger through the use of a waveform inversion technique using data from broadband seismic stations on South Island, New Zealand. The majority (126) of these double couple solutions have strike-slip focal mechanisms, with right-lateral slip on ENE fault planes or equivalently left-lateral slip on SSE fault planes. The remaining focal mechanisms indicate reverse faulting, except for two normal faulting events. The strike-slip segments have compatible orientations for slip in a <span class="hlt">stress</span> field with a horizontal σ1 oriented ~ N115°E, and horizontal σ3. The preference for right lateral strike-slip earthquakes suggests that these structures are inherited from previous stages of deformation. Reverse slip is interpreted to have occurred on previously existing structures in regions with an absence of existing structures optimally oriented for strike-slip deformation. Despite the variations in slip direction and faulting style, most aftershocks had nearly the same P-axis orientation, consistent with the regional σ1. There is no evidence for significant changes in these <span class="hlt">stress</span> orientations throughout the Canterbury earthquake sequence.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2008JBIS...61..358M','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2008JBIS...61..358M"><span>Computer <span class="hlt">Tensor</span> Codes to Design the War Drive</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Maccone, C.</p> <p></p> <p>To address problems in Breakthrough Propulsion Physics (BPP) and design the Warp Drive one needs sheer computing capabilities. This is because General Relativity (GR) and <span class="hlt">Quantum</span> Field Theory (QFT) are so mathematically sophisticated that the amount of analytical calculations is prohibitive and one can hardly do all of them by hand. In this paper we make a comparative review of the main <span class="hlt">tensor</span> calculus capabilities of the three most advanced and commercially available “symbolic manipulator” codes. We also point out that currently one faces such a variety of different conventions in <span class="hlt">tensor</span> calculus that it is difficult or impossible to compare results obtained by different scholars in GR and QFT. Mathematical physicists, experimental physicists and engineers have each their own way of customizing <span class="hlt">tensors</span>, especially by using different metric signatures, different metric determinant signs, different definitions of the basic Riemann and Ricci <span class="hlt">tensors</span>, and by adopting different systems of physical units. This chaos greatly hampers progress toward the design of the Warp Drive. It is thus suggested that NASA would be a suitable organization to establish standards in symbolic <span class="hlt">tensor</span> calculus and anyone working in BPP should adopt these standards. Alternatively other institutions, like CERN in Europe, might consider the challenge of starting the preliminary implementation of a Universal <span class="hlt">Tensor</span> Code to design the Warp Drive.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017JPhA...50v3001B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017JPhA...50v3001B"><span>Hand-waving and interpretive dance: an introductory course on <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>Bridgeman, Jacob C.; Chubb, Christopher T.</p> <p>2017-06-01</p> <p>The curse of dimensionality associated with the Hilbert space of spin systems provides a significant obstruction to the study of condensed matter systems. <span class="hlt">Tensor</span> networks have proven an important tool in attempting to overcome this difficulty in both the numerical and analytic regimes. These notes form the basis for a seven lecture course, introducing the basics of a range of common <span class="hlt">tensor</span> networks and algorithms. In particular, we cover: introductory <span class="hlt">tensor</span> network notation, applications to <span class="hlt">quantum</span> information, basic properties of matrix product states, a classification of <span class="hlt">quantum</span> phases using <span class="hlt">tensor</span> networks, algorithms for finding matrix product states, basic properties of projected entangled pair states, and multiscale entanglement renormalisation ansatz states. The lectures are intended to be generally accessible, although the relevance of many of the examples may be lost on students without a background in many-body physics/<span class="hlt">quantum</span> information. For each lecture, several problems are given, with worked solutions in an ancillary file.</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('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> <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/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('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.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/2004ApPhL..85.3008D','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2004ApPhL..85.3008D"><span>Improvement in spatial resolution of plasma-enhanced <span class="hlt">quantum</span>-well intermixing by <span class="hlt">stress</span>-inducing dielectric mask</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Djie, H. S.; Mei, T.; Arokiaraj, J.</p> <p>2004-10-01</p> <p>We report the use of a <span class="hlt">stress</span>-inducing dielectric mask to improve the spatial resolution of the proximity <span class="hlt">quantum</span>-well intermixing process. Photoluminescence and Raman spectroscopy were used to study the band gap modification and the spatial resolution using Ar plasma in the InGaAs /InGaAsP laser structure. A spatial resolution of 2.4μm has been achieved with the presence of an SixNy annealing cap as a <span class="hlt">stress</span>-inducing mask. The simple technique provides a promising approach of lateral band gap tuning with a high spatial resolution for high-density photonic integrated circuits.</p> </li> <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('https://www.osti.gov/scitech/biblio/7300951','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/7300951"><span>The <span class="hlt">quantum</span> hydrodynamic model for semiconductor devices</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Gardner, C.L. )</p> <p>1994-04-01</p> <p>The classical hydrodynamic equations can be extended to include <span class="hlt">quantum</span> effects by incorporating the first <span class="hlt">quantum</span> corrections. The full three-dimensional <span class="hlt">quantum</span> hydrodynamic (QHD) model is derived for the first time by a moment expansion of the Wigner-Boltzmann equations. The QHD conservation laws have the same form as the classical hydrodynamic equations, but the energy density and <span class="hlt">stress</span> <span class="hlt">tensor</span> have additional <span class="hlt">quantum</span> terms. These <span class="hlt">quantum</span> terms allow particles to tunnel through potential barriers and to build up in potential wells. The three-dimensional QHD transport equations are mathematically classified as having two Schroedinger modes, two hyperbolic modes, and one parabolic mode. The one-dimensional steady-state QHD equations are discretized in conservation form using the second upwind method. Simulations of a resonant tunneling diode are presented that show charge buildup in the <span class="hlt">quantum</span> well and negative differential resistance (NDR) in the current-voltage curve. These are the first simulations of the full QHD equations to show NDR in the resonant tunneling diode. The computed current-voltage curve agrees quantitatively with experimental measurements. NDR interpreted in terms of the time spent by electrons in the <span class="hlt">quantum</span> well.</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> </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('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.ncbi.nlm.nih.gov/pubmed/21279600','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/21279600"><span>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>Jones, Derek K; Leemans, Alexander</p> <p>2011-01-01</p> <p>Diffusion <span class="hlt">tensor</span> MRI (DT-MRI) is the only non-invasive method for characterising the microstructural organization of tissue in vivo. Generating parametric maps that help to visualise different aspects of the tissue microstructure (mean diffusivity, tissue anisotropy and dominant fibre orientation) involves a number of steps from deciding on the optimal acquisition parameters on the scanner, collecting the data, pre-processing the data and fitting the model to generating final parametric maps for entry into statistical data analysis. Here, we describe an entire protocol that we have used on over 400 subjects with great success in our laboratory. In the 'Notes' section, we justify our choice of the various parameters/choices along the way so that the reader may adapt/modify the protocol to their own time/hardware constraints.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2008SPIE.6914E..2HL','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2008SPIE.6914E..2HL"><span><span class="hlt">Tensor</span> distribution function</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Leow, Alex D.; Zhu, Siwei</p> <p>2008-03-01</p> <p>Diffusion weighted MR imaging is a powerful tool that can be employed to study white matter microstructure by examining the 3D displacement profile of water molecules in brain tissue. By applying diffusion-sensitizing gradients along a minimum of 6 directions, second-order <span class="hlt">tensors</span> (represetnted by 3-by-3 positive definiite matrices) can be computed to model dominant diffusion processes. However, it has been shown that conventional DTI is not sufficient to resolve more complicated white matter configurations, e.g. crossing fiber tracts. More recently, High Angular Resolution Diffusion Imaging (HARDI) seeks to address this issue by employing more than 6 gradient directions. To account for fiber crossing when analyzing HARDI data, several methodologies have been introduced. For example, q-ball imaging was proposed to approximate Orientation Diffusion Function (ODF). Similarly, the PAS method seeks to reslove the angular structure of displacement probability functions using the maximum entropy principle. Alternatively, deconvolution methods extract multiple fiber tracts by computing fiber orientations using a pre-specified single fiber response function. In this study, we introduce <span class="hlt">Tensor</span> Distribution Function (TDF), a probability function defined on the space of symmetric and positive definite matrices. Using calculus of variations, we solve for the TDF that optimally describes the observed data. Here, fiber crossing is modeled as an ensemble of Gaussian diffusion processes with weights specified by the TDF. Once this optimal TDF is determined, ODF can easily be computed by analytical integration of the resulting displacement probability function. Moreover, principle fiber directions can also be directly derived from the TDF.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/15690523','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/15690523"><span>A rigorous framework for diffusion <span class="hlt">tensor</span> calculus.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Batchelor, P G; Moakher, M; Atkinson, D; Calamante, F; Connelly, A</p> <p>2005-01-01</p> <p>In biological tissue, all eigenvalues of the diffusion <span class="hlt">tensor</span> are assumed to be positive. Calculations in diffusion <span class="hlt">tensor</span> MRI generally do not take into account this positive definiteness property of the <span class="hlt">tensor</span>. Here, the space of positive definite <span class="hlt">tensors</span> is used to construct a framework for diffusion <span class="hlt">tensor</span> analysis. The method defines a distance function between a pair of <span class="hlt">tensors</span> and the associated shortest path (geodesic) joining them. From this distance a method for computing <span class="hlt">tensor</span> means, a new measure of anisotropy, and a method for <span class="hlt">tensor</span> interpolation are derived. The method is illustrated using simulated and in vivo data. Copyright 2004 Wiley-Liss, Inc.</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('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> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2013LNP...871..469D','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2013LNP...871..469D"><span><span class="hlt">Quantum</span> Criticality via Magnetic Branes</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>D'Hoker, Eric; Kraus, Per</p> <p></p> <p>Holographic methods are used to investigate the low temperature limit, including <span class="hlt">quantum</span> critical behavior, of strongly coupled 4-dimensional gauge theories in the presence of an external magnetic field, and finite charge density. In addition to the metric, the dual gravity theory contains a Maxwell field with Chern-Simons coupling. In the absence of charge, the magnetic field induces an RG flow to an infrared {AdS}3 × {R}2 geometry, which is dual to a 2-dimensional CFT representing strongly interacting fermions in the lowest Landau level. Two asymptotic Virasoro algebras and one chiral Kac-Moody algebra arise as emergent symmetries in the IR. Including a nonzero charge density reveals a <span class="hlt">quantum</span> critical point when the magnetic field reaches a critical value whose scale is set by the charge density. The critical theory is probed by the study of long-distance correlation functions of the boundary <span class="hlt">stress</span> <span class="hlt">tensor</span> and current. All quantities of major physical interest in this system, such as critical exponents and scaling functions, can be computed analytically. We also study an asymptotically AdS 6 system whose magnetic field induced <span class="hlt">quantum</span> critical point is governed by an IR Lifshitz geometry, holographically dual to a D=2+1 field theory. The behavior of these holographic theories shares important similarities with that of real world <span class="hlt">quantum</span> critical systems obtained by tuning a magnetic field, and may be relevant to materials such as Strontium Ruthenates.</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/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/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://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('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/2060/19950012873','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('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://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.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> </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://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('https://www.osti.gov/scitech/biblio/22611667','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/22611667"><span>Tuning exciton energy and fine-structure splitting in single InAs <span class="hlt">quantum</span> dots by applying uniaxial <span class="hlt">stress</span></span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Su, Dan; Dou, Xiuming; Wu, Xuefei; Liao, Yongping; Zhou, Pengyu; Ding, Kun; Ni, Haiqiao; Niu, Zhichuan; Zhu, Haijun; Jiang, Desheng; Sun, Baoquan</p> <p>2016-04-15</p> <p>Exciton and biexciton emission energies as well as excitonic fine-structure splitting (FSS) in single InAs/GaAs <span class="hlt">quantum</span> dots (QDs) have been continuously tuned in situ in an optical cryostat using a developed uniaxial <span class="hlt">stress</span> device. With increasing tensile <span class="hlt">stress</span>, the red shift of excitonic emission is up to 5 nm; FSS decreases firstly and then increases monotonically, reaching a minimum value of approximately 10 μeV; biexciton binding energy decreases from 460 to 106 μeV. This technique provides a simple and convenient means to tune QD structural symmetry, exciton energy and biexciton binding energy and can be used for generating entangled and indistinguishable photons.</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('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/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/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/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/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('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/2017JHEP...08..141L','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017JHEP...08..141L"><span><span class="hlt">Tensor</span> network models of unitary black hole evaporation</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Leutheusser, Samuel; Van Raamsdonk, Mark</p> <p>2017-08-01</p> <p>We introduce a general class of toy models to study the <span class="hlt">quantum</span> information-theoretic properties of black hole radiation. The models are governed by a set of isometries that specify how microstates of the black hole at a given energy evolve to entangled states of a <span class="hlt">tensor</span> product black-hole/radiation Hilbert space. The final state of the black hole radiation is conveniently summarized by a <span class="hlt">tensor</span> network built from these isometries. We introduce a set of quantities generalizing the Renyi entropies that provide a complete set of bipartite/multipartite entanglement measures, and give a general formula for the average of these over initial black hole states in terms of the isometries defining the model. For models where the dimension of the final <span class="hlt">tensor</span> product radiation Hilbert space is the same as that of the space of initial black hole microstates, the entanglement structure is universal, independent of the choice of isometries. In the more general case, we find that models which best capture the "information-free" property of black hole horizons are those whose isometries are <span class="hlt">tensors</span> corresponding to states of tripartite systems with maximally mixed subsystems.</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://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('http://adsabs.harvard.edu/abs/2014PhRvD..90d3532M','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2014PhRvD..90d3532M"><span><span class="hlt">Tensor</span> mode backreaction during slow-roll inflation</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Marozzi, G.; Vacca, G. P.</p> <p>2014-08-01</p> <p>We consider the backreaction of the long wavelength <span class="hlt">tensor</span> modes produced during a slow-roll inflationary regime driven by a single scalar field in a spatially flat Friedmann-Lemaître-Robertson-Walker background geometry. We investigate the effects on nonlocal observables such as the effective (averaged) expansion rate and equation of state at second order in cosmological perturbation theory. The coupling between scalar and <span class="hlt">tensor</span> perturbations induces at second-order new <span class="hlt">tensor</span> backreaction terms beyond the one already present in a de Sitter background. We analyze in detail the effects seen by the class of observers comoving with the inflaton field (taken as a clock) and the class of free-falling observers. In both cases the <span class="hlt">quantum</span> backreaction is at least 1/ɛ (with ɛ the slow-roll parameter) larger than the one which can be naively inferred from a de Sitter background. In particular, we compute the effect for a free massive inflaton model and obtain in both cases a <span class="hlt">quantum</span> correction on the background expansion rate of the order of H4/(m2MPl2). A short discussion on the issue of the breakdown of perturbation theory is given.</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('https://www.osti.gov/scitech/biblio/22596848','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/22596848"><span><span class="hlt">Quantum</span> Max-flow/Min-cut</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Cui, Shawn X.; Freedman, Michael H.; Sattath, Or; Stong, Richard Minton, Greg</p> <p>2016-06-15</p> <p>The classical max-flow min-cut theorem describes transport through certain idealized classical networks. We consider the <span class="hlt">quantum</span> analog for <span class="hlt">tensor</span> networks. By associating an integral capacity to each edge and a <span class="hlt">tensor</span> to each vertex in a flow network, we can also interpret it as a <span class="hlt">tensor</span> network and, more specifically, as a linear map from the input space to the output space. The <span class="hlt">quantum</span> max-flow is defined to be the maximal rank of this linear map over all choices of <span class="hlt">tensors</span>. The <span class="hlt">quantum</span> min-cut is defined to be the minimum product of the capacities of edges over all cuts of the <span class="hlt">tensor</span> network. We show that unlike the classical case, the <span class="hlt">quantum</span> max-flow=min-cut conjecture is not true in general. Under certain conditions, e.g., when the capacity on each edge is some power of a fixed integer, the <span class="hlt">quantum</span> max-flow is proved to equal the <span class="hlt">quantum</span> min-cut. However, concrete examples are also provided where the equality does not hold. We also found connections of <span class="hlt">quantum</span> max-flow/min-cut with entropy of entanglement and the <span class="hlt">quantum</span> satisfiability problem. We speculate that the phenomena revealed may be of interest both in spin systems in condensed matter and in <span class="hlt">quantum</span> gravity.</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('https://www.ncbi.nlm.nih.gov/pubmed/28436897','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/28436897"><span><span class="hlt">Tensor</span>-Factorized 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>Chien, Jen-Tzung; Bao, Yi-Ting</p> <p>2017-04-17</p> <p>The growing interests in multiway data analysis and deep learning have drawn <span class="hlt">tensor</span> factorization (TF) and neural network (NN) as the crucial topics. Conventionally, the NN model is estimated from a set of one-way observations. Such a vectorized NN is not generalized for learning the representation from multiway observations. The classification performance using vectorized NN is constrained, because the temporal or spatial information in neighboring ways is disregarded. More parameters are required to learn the complicated data structure. This paper presents a new <span class="hlt">tensor</span>-factorized NN (TFNN), which tightly integrates TF and NN for multiway feature extraction and classification under a unified discriminative objective. This TFNN is seen as a generalized NN, where the affine transformation in an NN is replaced by the multilinear and multiway factorization for <span class="hlt">tensor</span>-based NN. The multiway information is preserved through layerwise factorization. Tucker decomposition and nonlinear activation are performed in each hidden layer. The <span class="hlt">tensor</span>-factorized error backpropagation is developed to train TFNN with the limited parameter size and computation time. This TFNN can be further extended to realize the convolutional TFNN (CTFNN) by looking at small subtensors through the factorized convolution. Experiments on real-world classification tasks demonstrate that TFNN and CTFNN attain substantial improvement when compared with an NN and a convolutional NN, respectively.</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="http://www.dtic.mil/">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> </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/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> <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://adsabs.harvard.edu/abs/2014PhDT........35O','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2014PhDT........35O"><span>CdSe/CdS Tetrapod <span class="hlt">Quantum</span> Dots as <span class="hlt">Stress</span> Probes: Characterization, Development, and Applications to Polymer Science and Biophysics</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Olson, Andrew Carl</p> <p></p> <p>The bulk properties of materials and biological systems depend on their microscale behavior. This is intuitive to chemists who are used to thinking of molecular constituents dictating chemical properties at the macroscale. This bottom-up understanding of materials can be extended to mechanical properties, such as Young's modulus, catastrophic failure modes, which can begin as nanoscale void formation, and polymer chain deformations that occur during mechanical loading. Such fundamental mechanical properties are also crucial in biology, where the viability of an organism is dependent on cell function and behavior. For example, tumorigenesis and metastasis of cancer depends on the ability of a cancerous cell to generate traction forces and move through the body. This dissertation details recent developments on the tetrapod <span class="hlt">quantum</span> dot (tQD) as a fluorescence <span class="hlt">stress</span> probe. The nanometer size and optical properties of the tQD make it uniquely suitable for studying forces and mechanisms of mechanical deformation at the smallest length scales. First, background is provided on colloidal semiconductor <span class="hlt">quantum</span> dots in general and the tetrapod in particular. Second, development and application of the tQD in synthetic polymer materials is discussed. Third, applications of the tQD as a sensor for cellular biophysics are demonstrated. Finally, further characterization of single tQD properties and future studies are discussed and proposed.</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('http://adsabs.harvard.edu/abs/2015CoPhC.189...84L','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015CoPhC.189...84L"><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://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Lyakh, Dmitry I.</p> <p>2015-04-01</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 naïve scattering algorithm (no memory access optimization). 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('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://www.osti.gov/scitech/biblio/22308513','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/22308513"><span>Residual <span class="hlt">stress</span> induced crystalline to amorphous phase transformation in Nb{sub 2}O{sub 5} <span class="hlt">quantum</span> dots</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Dhawan, Sahil; Vedeshwar, Agnikumar G.; Dhawan, Tanuj</p> <p>2014-07-28</p> <p>Nb{sub 2}O{sub 5} <span class="hlt">quantum</span> dots (QDs) were grown using a simple technique of vacuum thermal evaporation. QDs were found to be crystalline in nature by selected area electron diffraction (SAED) in TEM. Samples with thickness up to 20 nm did not show any significant residual strain. Residual <span class="hlt">stress</span> effect on band gap of crystalline Nb{sub 2}O{sub 5} was studied for films thicker than 20 nm. Residual strain was determined using SAED of the films with reference to powder X-ray diffraction (XRD). Films thicker than 45 nm become amorphous as analyzed by both SAED and XRD. The optical absorption of films in the range 25–60 nm indicates significantly varying optical band gap of films. The varying band gap with film thickness scales linearly very well with the variation of residual <span class="hlt">stress</span> with film thickness. The residual <span class="hlt">stress</span> dependence of band gap of crystalline films yields <span class="hlt">stress</span> free band gap as 3.37 eV with pressure coefficient of band gap (∂E{sub g}/∂P){sub T} = −29.3 meV/GPa. From this study, the crystalline to amorphous transformation in tetragonal form of M-Nb{sub 2}O{sub 5} has been determined to be at about 14 GPa. Both pressure coefficient of band gap and crystalline to amorphous transition for tetragonal M-Nb{sub 2}O{sub 5} have been determined for the first time in the literature.</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('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/2016JHEP...07..018C','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016JHEP...07..018C"><span>Projectors and seed conformal blocks for traceless mixed-symmetry <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>Costa, Miguel S.; Hansen, Tobias; Penedones, João; Trevisani, Emilio</p> <p>2016-07-01</p> <p>In this paper we derive the projectors to all irreducible SO( d) representations (traceless mixed-symmetry <span class="hlt">tensors</span>) that appear in the partial wave decomposition of a conformal correlator of four <span class="hlt">stress-tensors</span> in d dimensions. These projectors are given in a closed form for arbitrary length l 1 of the first row of the Young diagram. The appearance of Gegenbauer polynomials leads directly to recursion relations in l 1 for seed conformal blocks. Further results include a differential operator that generates the projectors to traceless mixed-symmetry <span class="hlt">tensors</span> and the general normalization constant of the shadow operator.</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> <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/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('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.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('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> </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('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('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('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...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.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.osti.gov/scitech/biblio/22596619','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/22596619"><span>Fundamental limitations in the purifications of <span class="hlt">tensor</span> networks</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>De las Cuevas, G.; Cirac, J. I.; Cubitt, T. S.; Wolf, M. M.; Pérez-García, D.</p> <p>2016-07-15</p> <p>We show a fundamental limitation in the description of <span class="hlt">quantum</span> many-body mixed states with <span class="hlt">tensor</span> networks in purification form. Namely, we show that there exist mixed states which can be represented as a translationally invariant (TI) matrix product density operator valid for all system sizes, but for which there does not exist a TI purification valid for all system sizes. The proof is based on an undecidable problem and on the uniqueness of canonical forms of matrix product states. The result also holds for classical states.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017CRPhy..18..207W','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017CRPhy..18..207W"><span>Testing loop <span class="hlt">quantum</span> cosmology</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Wilson-Ewing, Edward</p> <p>2017-03-01</p> <p>Loop <span class="hlt">quantum</span> cosmology predicts that <span class="hlt">quantum</span> gravity effects resolve the big-bang singularity and replace it by a cosmic bounce. Furthermore, loop <span class="hlt">quantum</span> cosmology can also modify the form of primordial cosmological perturbations, for example by reducing power at large scales in inflationary models or by suppressing the <span class="hlt">tensor</span>-to-scalar ratio in the matter bounce scenario; these two effects are potential observational tests for loop <span class="hlt">quantum</span> cosmology. In this article, I review these predictions and others, and also briefly discuss three open problems in loop <span class="hlt">quantum</span> cosmology: its relation to loop <span class="hlt">quantum</span> gravity, the trans-Planckian problem, and a possible transition from a Lorentzian to a Euclidean space-time around the bounce point.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2003cqt..book.....G','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2003cqt..book.....G"><span>Consistent <span class="hlt">Quantum</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>Griffiths, Robert B.</p> <p>2003-11-01</p> <p>1. Introduction; 2. Wave functions; 3. Linear algebra in Dirac notation; 4. Physical properties; 5. Probabilities and physical variables; 6. Composite systems and <span class="hlt">tensor</span> products; 7. Unitary dynamics; 8. Stochastic histories; 9. The Born rule; 10. Consistent histories; 11. Checking consistency; 12. Examples of consistent families; 13. <span class="hlt">Quantum</span> interference; 14. Dependent (contextual) events; 15. Density matrices; 16. <span class="hlt">Quantum</span> reasoning; 17. Measurements I; 18. Measurements II; 19. Coins and counterfactuals; 20. Delayed choice paradox; 21. Indirect measurement paradox; 22. Incompatibility paradoxes; 23. Singlet state correlations; 24. EPR paradox and Bell inequalities; 25. Hardy's paradox; 26. Decoherence and the classical limit; 27. <span class="hlt">Quantum</span> theory and reality; Bibliography.</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.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/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.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=2700196','PMC'); return false;" href="https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=2700196"><span>TIMER: <span class="hlt">Tensor</span> Image Morphing for Elastic Registration</span></a></p> <p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pmc">PubMed Central</a></p> <p>Yap, Pew-Thian; Wu, Guorong; Zhu, Hongtu; Lin, Weili; Shen, Dinggang</p> <p>2009-01-01</p> <p>We propose a novel diffusion <span class="hlt">tensor</span> imaging (DTI) registration algorithm, called <span class="hlt">Tensor</span> Image Morphing for Elastic Registration (TIMER), which leverages the hierarchical guidance of regional distributions and local boundaries, both extracted directly from the <span class="hlt">tensors</span>. Currently available DTI registration methods generally extract <span class="hlt">tensor</span> scalar features from each <span class="hlt">tensor</span> to construct scalar maps. Subsequently, regional integration and other operations such as edge detection are performed to extract more features to guide the registration. However, there are two major limitations with these approaches. First, the computed regional features might not reflect the actual regional <span class="hlt">tensor</span> distributions. Second, by the same token, gradient maps calculated from the <span class="hlt">tensor</span>-derived scalar feature maps might not represent the actual tissue <span class="hlt">tensor</span> boundaries. To overcome these limitations, we propose a new approach which extracts regional and edge information directly from a <span class="hlt">tensor</span> neighborhood. Regional <span class="hlt">tensor</span> distribution information, such as mean and variance, is computed in a multiscale fashion directly from the <span class="hlt">tensors</span> by taking into account the voxel neighborhood of different sizes, and hence capturing <span class="hlt">tensor</span> information at different scales, which in turn can be employed to hierarchically guide the registration. Such multiscale scheme can help alleviate the problem of local minimum and is also more robust to noise since one can better determine the statistical properties of each voxel by taking into account the properties of its surrounding. Also incorporated in our method is edge information extracted directly from the <span class="hlt">tensors</span>, which is crucial to facilitate registration of tissue boundaries. Experiments involving real subjects, simulated subjects, fiber tracking, and atrophy detection indicate that TIMER performs better than the other methods in comparison (Yang et al., 2008a; Zhang et al., 2006). PMID:19398022</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/19398022','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/19398022"><span>TIMER: <span class="hlt">tensor</span> image morphing for elastic registration.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Yap, Pew-Thian; Wu, Guorong; Zhu, Hongtu; Lin, Weili; Shen, Dinggang</p> <p>2009-08-15</p> <p>We propose a novel diffusion <span class="hlt">tensor</span> imaging (DTI) registration algorithm, called <span class="hlt">Tensor</span> Image Morphing for Elastic Registration (TIMER), which leverages the hierarchical guidance of regional distributions and local boundaries, both extracted directly from the <span class="hlt">tensors</span>. Currently available DTI registration methods generally extract <span class="hlt">tensor</span> scalar features from each <span class="hlt">tensor</span> to construct scalar maps. Subsequently, regional integration and other operations such as edge detection are performed to extract more features to guide the registration. However, there are two major limitations with these approaches. First, the computed regional features might not reflect the actual regional <span class="hlt">tensor</span> distributions. Second, by the same token, gradient maps calculated from the <span class="hlt">tensor</span>-derived scalar feature maps might not represent the actual tissue <span class="hlt">tensor</span> boundaries. To overcome these limitations, we propose a new approach which extracts regional and edge information directly from a <span class="hlt">tensor</span> neighborhood. Regional <span class="hlt">tensor</span> distribution information, such as mean and variance, is computed in a multiscale fashion directly from the <span class="hlt">tensors</span> by taking into account the voxel neighborhood of different sizes, and hence capturing <span class="hlt">tensor</span> information at different scales, which in turn can be employed to hierarchically guide the registration. Such multiscale scheme can help alleviate the problem of local minimum and is also more robust to noise since one can better determine the statistical properties of each voxel by taking into account the properties of its surrounding. Also incorporated in our method is edge information extracted directly from the <span class="hlt">tensors</span>, which is crucial to facilitate registration of tissue boundaries. Experiments involving real subjects, simulated subjects, fiber tracking, and atrophy detection indicate that TIMER performs better than the other methods (Yang et al., 2008; Zhang et al., 2006).</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/scitech/biblio/1076684','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/1076684"><span>Optimizing <span class="hlt">Tensor</span> Contraction Expressions for Hybrid CPU-GPU Execution</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Ma, Wenjing; Krishnamoorthy, Sriram; Villa, Oreste; Kowalski, Karol; Agrawal, Gagan</p> <p>2013-03-01</p> <p><span class="hlt">Tensor</span> contractions are generalized multidimensional matrix multiplication operations that widely occur in <span class="hlt">quantum</span> chemistry. Efficient execution of <span class="hlt">tensor</span> contractions on Graphics Processing Units (GPUs) requires several challenges to be addressed, including index permutation and small dimension-sizes reducing thread block utilization. Moreover, to apply the same optimizations to various expressions, we need a code generation tool. In this paper, we present our approach to automatically generate CUDA code to execute <span class="hlt">tensor</span> contractions on GPUs, including management of data movement between CPU and GPU. To evaluate our tool, GPU-enabled code is generated for the most expensive contractions in CCSD(T), a key coupled cluster method, and incorporated into NWChem, a popular computational chemistry suite. For this method, we demonstrate speedup over a factor of 8.4 using one GPU (instead of one core per node) and over 2.6 when utilizing the entire system using hybrid CPU+GPU solution with 2 GPUs and 5 cores (instead of 7 cores per node). Finally, we analyze the implementation behavior on future GPU systems.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2011PhRvD..83h4027H','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2011PhRvD..83h4027H"><span><span class="hlt">Quantum</span> modifications to gravity waves in de Sitter spacetime</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Hsiang, Jen-Tsung; Ford, L. H.; Lee, Da-Shin; Yu, Hoi-Lai</p> <p>2011-04-01</p> <p>We treat a model in which <span class="hlt">tensor</span> perturbations of de Sitter spacetime, represented as a spatially flat model, are modified by the effects of the vacuum fluctuations of a massless conformally invariant field, such as the electromagnetic field. We use the semiclassical theory of gravity with the expectation value of the conformal field <span class="hlt">stress</span> <span class="hlt">tensor</span> as a source. We first study the stability of de Sitter spacetime by searching for growing, spatially homogeneous modes, and conclude that it is stable within the limits of validity of the semiclassical theory. We next examine the modification of linearized plane gravity waves by the effects of the <span class="hlt">quantum</span> <span class="hlt">stress</span> <span class="hlt">tensor</span>. We find a correction term which is of the same form as the original wave, but displaced in phase by π/2, and with an amplitude which depends upon an initial time. The magnitude of this effect is proportional to the change in scale factor after this time. We discuss alternative interpretations of this time, but pay particular attention to the view that this is the beginning of inflation. So long as the energy scale of inflation and the proper frequency of the mode at the beginning of inflation are well below the Planck scale, the fractional correction is small. However, modes which are trans-Planckian at the onset of inflation can undergo a significant correction. The increase in amplitude can potentially have observable consequences through a modification of the power spectrum of <span class="hlt">tensor</span> perturbations in inflationary cosmology. This enhancement of the power spectrum depends upon the initial time, and is greater for shorter wavelengths.</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('https://www.ncbi.nlm.nih.gov/pubmed/28228005','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/28228005"><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="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Liu, Yan; Niu, Jiebin; Wang, Hongjuan; Han, Genquan; Zhang, Chunfu; Feng, Qian; Zhang, Jincheng; Hao, Yue</p> <p>2017-12-01</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 × 10(12) 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/2009AGUFM.S21B1722C','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2009AGUFM.S21B1722C"><span>Rupture Plane Determination of Small to Moderate Earthquakes by Finite Moment <span class="hlt">Tensor</span> Inversion</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Chao, W.; Zhao, L.; Wu, Y.</p> <p>2009-12-01</p> <p>The Chia-Yi area in southwestern Taiwan is a region of relatively high seismicity with frequent earthquakes of variable magnitudes in the shallow crust. These events provide valuable information for the understanding of seismotectonics of this region. In this study, we investigate the source properties of small to moderate earthquakes (3.0 < ML < 5.5) in the Chia-Yi region by inverting for their point as well as finite moment <span class="hlt">tensors</span>. Finite moment <span class="hlt">tensor</span> is a simplified representation of a finite source, and it can be used to resolve the fault-plane ambiguity of a point source model and determine the actual rupture plane of an earthquake. Based on a three-dimensional (3D) structural model for the Chia-Yi region, we compute the strain Green <span class="hlt">tensors</span> by the finite-difference method. These strain Green <span class="hlt">tensors</span> can be used to compute the synthetic seismograms as well as the partial derivatives for the inversion of point and finite moment <span class="hlt">tensor</span> parameters. Frequency-dependent P-wave amplitude perturbations are measured from broadband and strong-motion seismograms and inverted for the point and finite moment <span class="hlt">tensors</span>, which are then used to identify the actual rupture planes of earthquakes. With this approach, more details of small and moderate earthquakes, in particular their actual rupture fault planes, can be determined in realistic 3D structure, which helps us to understand the regional seismotectonics and the <span class="hlt">stress</span> field. Keywords: Taiwan, Green function, finite moment <span class="hlt">tensors</span> (FMTs).</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> </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('https://www.osti.gov/pages/biblio/1361210-emergent-gravity-from-vanishing-energy-momentum-tensor','SCIGOV-DOEP'); return false;" href="https://www.osti.gov/pages/biblio/1361210-emergent-gravity-from-vanishing-energy-momentum-tensor"><span>Emergent gravity from vanishing energy-momentum <span class="hlt">tensor</span></span></a></p> <p><a target="_blank" href="http://www.osti.gov/pages">DOE PAGES</a></p> <p>Carone, Christopher D.; Erlich, Joshua; Vaman, Diana</p> <p>2017-03-27</p> <p>A constraint of vanishing energy-momentum <span class="hlt">tensor</span> is motivated by a variety of perspectives on <span class="hlt">quantum</span> gravity. We demonstrate in a concrete example how this constraint leads to a metric-independent theory in which <span class="hlt">quantum</span> gravity emerges as a nonperturbative artifact of regularization-scale physics. We analyze a scalar theory similar to the Dirac-Born-Infeld (DBI) theory with vanishing gauge fields, with the DBI Lagrangian modulated by a scalar potential. In the limit of a large number of scalars, we explicitly demonstrate the existence of a composite massless spin-2 graviton in the spectrum that couples to matter as in Einstein gravity. As a result,more » we comment on the cosmological constant problem and the generalization to theories with fermions and gauge fields.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2012GReGr..44.2077G','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2012GReGr..44.2077G"><span>Some remarks on the genesis of scalar-<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>Goenner, Hubert</p> <p>2012-08-01</p> <p>Between 1941 and 1962, scalar-<span class="hlt">tensor</span> theories of gravitation were suggested four times by different scientists in four different countries. The earliest originator, the Swiss mathematician W. Scherrer, was virtually unknown until now whereas the chronologically latest pair gave their names to a multitude of publications on Brans-Dicke theory. P. Jordan, one of the pioneers of <span class="hlt">quantum</span> mechanics and <span class="hlt">quantum</span> field theory, and Y. Thiry, known by his book on celestial mechanics, a student of the mathematician Lichnerowicz, complete the quartet. Diverse motivations for and conceptual interpretations of their theories will be discussed as well as relations among them. Also, external factors like language, citation habits, or closeness to the mainstream are considered. It will become clear why Brans-Dicke theory, although structurally a déjà-vu, superseded all the other approaches.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/1988IJTP...27.1083C','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/1988IJTP...27.1083C"><span>Curvature <span class="hlt">tensors</span> unified field equations on SEXn</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Chung, Kyung Tae; Lee, Il Young</p> <p>1988-09-01</p> <p>We study the curvature <span class="hlt">tensors</span> and field equations in the n-dimensional SE manifold SEXn. We obtain several basic properties of the vectors S λ and U λ and then of the SE curvature <span class="hlt">tensor</span> and its contractions, such as a generalized Ricci identity, a generalized Bianchi identity, and two variations of the Bianchi identity satisfied by the SE Einstein <span class="hlt">tensor</span>. Finally, a system of field equations is discussed in SEXn and one of its particular solutions is constructed and displayed.</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('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/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('http://adsabs.harvard.edu/abs/2017JSMTE..09.3102A','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017JSMTE..09.3102A"><span>The <span class="hlt">tensor</span> network theory library</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Al-Assam, S.; Clark, S. R.; Jaksch, D.</p> <p>2017-09-01</p> <p>In this technical paper we introduce the <span class="hlt">tensor</span> network theory (TNT) library—an open-source software project aimed at providing a platform for rapidly developing robust, easy to use and highly optimised code for TNT calculations. The objectives of this paper are (i) to give an overview of the structure of TNT library, and (ii) to help scientists decide whether to use the TNT library in their research. We show how to employ the TNT routines by giving examples of ground-state and dynamical calculations of one-dimensional bosonic lattice system. We also discuss different options for gaining access to the software available at www.tensornetworktheory.org.</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.osti.gov/scitech/biblio/20777199','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/20777199"><span>Measurements of TiO{sub x} <span class="hlt">stress</span> induced on InP/InGaAs/InGaAsP <span class="hlt">quantum</span> well heterostructures</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Francois, A.; Aimez, V.; Beauvais, J.; Barba, D.</p> <p>2006-05-15</p> <p>Measurements of <span class="hlt">stress</span> induced by TiO{sub x} layers on single <span class="hlt">quantum</span> well InP based heterostructure are presented. Strain characterization has been performed by photoluminescence (PL) and micro-Raman spectroscopy. We present a comparison of the <span class="hlt">stress</span> induced by TiO{sub x} and SiO{sub 2} layers which are commonly used as masking material for the <span class="hlt">quantum</span> well intermixing process. Micro-Raman spectroscopy and PL revealed that TiO{sub 2} is creating a <span class="hlt">stress</span> field in the top layers of the heterostructure, with a dependence on temperature and stressor thickness. A hysteresis phenomenon of the Raman shift has also been observed after measurements at low temperature (below 300 K) which shows that the <span class="hlt">stress</span> created by TiO{sub x} exceeds the elastic limit of InP. On the other hand, there is no evidence that SiO{sub 2} is inducing <span class="hlt">stress</span>. Rapid thermal annealing of samples covered with titanium oxide results in improvement of the thermal stability.</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('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://adsabs.harvard.edu/abs/2016JCAP...12..011B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016JCAP...12..011B"><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://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Bolis, Nadia; Albrecht, Andreas; Holman, R.</p> <p>2016-12-01</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 (Cl'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://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://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>... sudden negative change, such as losing a job, divorce, or illness Traumatic <span class="hlt">stress</span>, which happens when you ... <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('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('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/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('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> </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://hdl.handle.net/2060/20030000683','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20030000683"><span>Elliptic Relaxation of a <span class="hlt">Tensor</span> Representation of the Pressure-Strain and Dissipation Rate</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Carlson, John R.; Gatski, Thomas B.</p> <p>2002-01-01</p> <p>A formulation to include the effects of wall-proximity in a second moment closure model is presented that utilizes a <span class="hlt">tensor</span> representation for the redistribution term in the Reynolds <span class="hlt">stress</span> equations. 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. DNS data and Reynolds <span class="hlt">stress</span> solutions using a full differential approach at channel Reynolds number of 590 are compared to the new model.</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('http://adsabs.harvard.edu/abs/2017AnPhy.382...64L','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017AnPhy.382...64L"><span>Efficient <span class="hlt">quantum</span> circuits for Szegedy <span class="hlt">quantum</span> walks</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Loke, T.; Wang, J. B.</p> <p>2017-07-01</p> <p>A major advantage in using Szegedy's formalism over discrete-time and continuous-time <span class="hlt">quantum</span> walks lies in its ability to define a unitary <span class="hlt">quantum</span> walk by quantizing a Markov chain on a directed or weighted graph. In this paper, we present a general scheme to construct efficient <span class="hlt">quantum</span> circuits for Szegedy <span class="hlt">quantum</span> walks that correspond to classical Markov chains possessing transformational symmetry in the columns of the transition matrix. In particular, the transformational symmetry criteria do not necessarily depend on the sparsity of the transition matrix, so this scheme can be applied to non-sparse Markov chains. Two classes of Markov chains that are amenable to this construction are cyclic permutations and complete bipartite graphs, for which we provide explicit efficient <span class="hlt">quantum</span> circuit implementations. We also prove that our scheme can be applied to Markov chains formed by a <span class="hlt">tensor</span> product. We also briefly discuss the implementation of Markov chains based on weighted interdependent networks. In addition, we apply this scheme to construct efficient <span class="hlt">quantum</span> circuits simulating the Szegedy walks used in the <span class="hlt">quantum</span> Pagerank algorithm for some classes of non-trivial graphs, providing a necessary tool for experimental demonstration of the <span class="hlt">quantum</span> Pagerank algorithm.</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> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=3444512','PMC'); return false;" href="https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=3444512"><span>The Diffusion <span class="hlt">Tensor</span> Imaging Toolbox</span></a></p> <p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pmc">PubMed Central</a></p> <p>Alger, Jeffry R.</p> <p>2012-01-01</p> <p>During the past few years, the Journal of Neuroscience has published over 30 articles that describe investigations that used Diffusion <span class="hlt">Tensor</span> Imaging (DTI) and related techniques as a primary observation method. This illustrates a growing interest in DTI within the basic and clinical neuroscience communities. This article summarizes DTI methodology in terms that can be immediately understood by the neuroscientist who has little previous exposure to DTI. It describes the fundamentals of water molecular diffusion coefficient measurement in brain tissue and illustrates how these fundamentals can be used to form vivid and useful depictions of white matter macroscopic and microscopic anatomy. It also describes current research applications and the technique’s attributes and limitations. It is hoped that this article will help the readers of this Journal to more effectively evaluate neuroscience studies that use DTI. PMID:22649222</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/24323102','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/24323102"><span>Depth inpainting by <span class="hlt">tensor</span> voting.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Kulkarni, Mandar; Rajagopalan, Ambasamudram N</p> <p>2013-06-01</p> <p>Depth maps captured by range scanning devices or by using optical cameras often suffer from missing regions due to occlusions, reflectivity, limited scanning area, sensor imperfections, etc. In this paper, we propose a fast and reliable algorithm for depth map inpainting using the <span class="hlt">tensor</span> voting (TV) framework. For less complex missing regions, local edge and depth information is utilized for synthesizing missing values. The depth variations are modeled by local planes using 3D TV, and missing values are estimated using plane equations. For large and complex missing regions, we collect and evaluate depth estimates from self-similar (training) datasets. We align the depth maps of the training set with the target (defective) depth map and evaluate the goodness of depth estimates among candidate values using 3D TV. We demonstrate the effectiveness of the proposed approaches on real as well as synthetic data.</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/1997JMMM..166..290Y','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/1997JMMM..166..290Y"><span><span class="hlt">Tensor</span> magnetic hysteresis loop measurements of a steel cube</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Yu, Y.; Krause, T. W.; Weyman, P.; Atherton, D. L.</p> <p>1997-02-01</p> <p>The change in magnetic moment of a 25.4 mm steel cube sample was measured in three orthogonal directions with fields up to magnetic saturation applied in each of the three cube directions. An analysis of the diagonal components of the resulting 3 × 3 <span class="hlt">tensor</span> indicated the relative magnetic easy axis amongst three three directions measured. Additional information on the magnetization processes was obtained from an analysis of the off-diagonal changes in the magnetic moment <span class="hlt">tensor</span>. Hysteresis was also observed in these off-diagonal loops. A net magnetization vector of magnitude M was considered. Deviations of magnetization components from linearity along the diagonal directions, Δ Mil were related to the off-diagonal components, MiJ and MiK, by the simple relation Δ MiI ≈ ± ( MiJ2 + MiK2)/2 M, where i is the field direction x, y, or z and I, J, and K cyclic coordinates X, Y, and Z indicating the magnetization components measured by coils X, Y, and Z, respectively. Changes in the off-diagonal components were associated with various field dependent magnetization processes such as domain wall motion and domain vector rotation. The asymmetry of the magnetic hysteresis loop <span class="hlt">tensor</span> is associated with either a texture of the material or the existence of internal <span class="hlt">stresses</span>.</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('http://adsabs.harvard.edu/abs/2017PhRvB..96c5101L','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017PhRvB..96c5101L"><span>The structure of fixed-point <span class="hlt">tensor</span> network states characterizes the patterns of long-range entanglement</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Luo, Zhu-Xi; Lake, Ethan; Wu, Yong-Shi</p> <p>2017-07-01</p> <p>The algebraic structure of representation theory naturally arises from 2D fixed-point <span class="hlt">tensor</span> network states, and conceptually formulates the pattern of long-range entanglement realized in such states. In 3D, the same underlying structure is also shared by Turaev-Viro state-sum topological <span class="hlt">quantum</span> field theory (TQFT). We show that a 2D fixed-point <span class="hlt">tensor</span> network state arises naturally on the boundary of the 3D manifold on which the TQFT is defined, and the fact that exactly the same information is needed to construct either the <span class="hlt">tensor</span> network or the TQFT is made explicit in a form of holography. Furthermore, the entanglement of the fixed-point states leads to an emergence of pregeometry in the 3D TQFT bulk. We further extend these ideas to the case where an additional global on-site unitary symmetry is imposed on the <span class="hlt">tensor</span> network states.</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('http://adsabs.harvard.edu/abs/2015NJPh...17f3039J','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015NJPh...17f3039J"><span>Continuum <span class="hlt">tensor</span> network field states, path integral representations and spatial symmetries</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Jennings, David; Brockt, Christoph; Haegeman, Jutho; Osborne, Tobias J.; Verstraete, Frank</p> <p>2015-06-01</p> <p>A natural way to generalize <span class="hlt">tensor</span> network variational classes to <span class="hlt">quantum</span> field systems is via a continuous <span class="hlt">tensor</span> contraction. This approach is first illustrated for the class of <span class="hlt">quantum</span> field states known as continuous matrix-product states (cMPS). As a simple example of the path-integral representation we show that the state of a dynamically evolving <span class="hlt">quantum</span> field admits a natural representation as a cMPS. A completeness argument is also provided that shows that all states in Fock space admit a cMPS representation when the number of variational parameters tends to infinity. Beyond this, we obtain a well-behaved field limit of projected entangled-pair states (PEPS) in two dimensions that provide an abstract class of <span class="hlt">quantum</span> field states with natural symmetries. We demonstrate how symmetries of the physical field state are encoded within the dynamics of an auxiliary field system of one dimension less. In particular, the imposition of Euclidean symmetries on the physical system requires that the auxiliary system involved in the class’ definition must be Lorentz-invariant. The physical field states automatically inherit entropy area laws from the PEPS class, and are fully described by the dissipative dynamics of a lower dimensional virtual field system. Our results lie at the intersection many-body physics, <span class="hlt">quantum</span> field theory and <span class="hlt">quantum</span> information theory, and facilitate future exchanges of ideas and insights between these disciplines.</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/2015AGUFM.S53B2801C','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015AGUFM.S53B2801C"><span>Moment <span class="hlt">Tensor</span> Analysis of Shallow Sources</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Chiang, A.; Dreger, D. S.; Ford, S. R.; Walter, W. R.; Yoo, S. H.</p> <p>2015-12-01</p> <p>A potential issue for moment <span class="hlt">tensor</span> inversion of shallow seismic sources is that some moment <span class="hlt">tensor</span> components have vanishing amplitudes at the free surface, which can result in bias in the moment <span class="hlt">tensor</span> solution. The effects of the free-surface on the stability of the moment <span class="hlt">tensor</span> method becomes important as we continue to investigate and improve the capabilities of regional full moment <span class="hlt">tensor</span> inversion for source-type identification and discrimination. It is important to understand these free surface effects on discriminating shallow explosive sources for nuclear monitoring purposes. It may also be important in natural systems that have shallow seismicity such as volcanoes and geothermal systems. In this study, we apply the moment <span class="hlt">tensor</span> based discrimination method to the HUMMING ALBATROSS quarry blasts. These shallow chemical explosions at approximately 10 m depth and recorded up to several kilometers distance represent rather severe source-station geometry in terms of vanishing traction issues. 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. Recovering the correct yield using seismic moment estimates from moment <span class="hlt">tensor</span> inversion remains challenging but we can begin to put error bounds on our moment estimates using the NSS technique.</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/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('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://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> </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/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('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://www.diabetes.org/living-with-diabetes/complications/mental-health/stress.html','NIH-MEDLINEPLUS'); return false;" href="http://www.diabetes.org/living-with-diabetes/complications/mental-health/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>... Planning Meals Diabetes Meal Plans Create Your Plate Gluten Free Diets Meal Planning for Vegetarian Diets Cook ... <span class="hlt">stress</span> hormones. Relaxing can help by blunting this sensitivity. There are many ways to help yourself relax: ...</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/17930489','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/17930489"><span><span class="hlt">Tensor</span> renormalization group approach to two-dimensional classical lattice models.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Levin, Michael; Nave, Cody P</p> <p>2007-09-21</p> <p>We describe a simple real space renormalization group technique for two-dimensional classical lattice models. The approach is similar in spirit to block spin methods, but at the same time it is fundamentally based on the theory of <span class="hlt">quantum</span> entanglement. In this sense, the technique can be thought of as a classical analogue of the density matrix renormalization group method. We demonstrate the method - which we call the <span class="hlt">tensor</span> renormalization group method - by computing the magnetization of the triangular lattice Ising model.</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('https://www.ncbi.nlm.nih.gov/pubmed/26494360','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/26494360"><span>Diffusion <span class="hlt">Tensor</span> Imaging of Pedophilia.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Cantor, James M; Lafaille, Sophie; Soh, Debra W; Moayedi, Massieh; Mikulis, David J; Girard, Todd A</p> <p>2015-11-01</p> <p>Pedophilia is a principal motivator of child molestation, incurring great emotional and financial burdens on victims and society. Even among pedophiles who never commit any offense,the condition requires lifelong suppression and control. Previous comparison using voxel-based morphometry (VBM)of MR images from a large sample of pedophiles and controls revealed group differences in white matter. The present study therefore sought to verify and characterize white matter involvement using diffusion <span class="hlt">tensor</span> imaging (DTI), which better captures the microstructure of white matter than does VBM. Pedophilics ex offenders (n=24) were compared with healthy, age-matched controls with no criminal record and no indication of pedophilia (n=32). White matter microstructure was analyzed with Tract-Based Spatial Statistics, and the trajectories of implicated fiber bundles were identified by probabilistic tractography. Groups showed significant, highly focused differences in DTI parameters which related to participants’ genital responses to sexual depictions of children, but not to measures of psychopathy or to childhood histories of physical abuse, sexual abuse, or neglect. Some previously reported gray matter differences were suggested under highly liberal statistical conditions (p(uncorrected)<.005), but did not survive ordinary statistical correction (whole brain per voxel false discovery rate of 5%). These results confirm that pedophilia is characterized by neuroanatomical differences in white matter microstructure, over and above any neural characteristics attributable to psychopathy and childhood adversity, which show neuroanatomic footprints of their own. Although some gray matter structures were implicated previously, only few have emerged reliably.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/28847441','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/28847441"><span>[Face rejuvenation with <span class="hlt">tensor</span> threads].</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Cornette de Saint Cyr, B; Benouaiche, L</p> <p>2017-08-25</p> <p>The last decades has seen new priorities in treatment of a flabby, ageing face towards minimally invasive aesthetic surgery, to be accompanied and followed by the requirements to perform such interventions with the maximally reduced health hazards, with inconsiderable injury, without cuts and, respectively, to be followed by no resulting scars, as well as a short postoperative period. We propose a new reviewing presentation of the <span class="hlt">tensor</span> threads. After having explained the technology of the threads, we will discuss the good patient indication, the criteria which determine the choice of the threads and methods for each type of patient. There are many techniques, which we will present. Then, we will discuss the results, unsatisfactory outcomes obtained and complications encountered, as well as how to improve the cosmetic outcomes to be obtained. To conclude, we will propose a strategy for the long-term treatment of the neck and the face, preventing surgical management of the aging process. Copyright © 2017. Published by Elsevier Masson SAS.</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> <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.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('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('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.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('http://www.osti.gov/scitech/servlets/purl/1324568','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/1324568"><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/scitech">SciTech Connect</a></p> <p>Blaschke, Daniel N.; Gieres, François; Schweda, Manfred</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('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://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://www.osti.gov/scitech/servlets/purl/1149584','SCIGOV-STC'); return false;" href="http://www.osti.gov/scitech/servlets/purl/1149584"><span>Novel Physics with <span class="hlt">Tensor</span> Polarized Deuteron Targets</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Slifer, Karl J.; Long, Elena A.</p> <p>2013-09-01</p> <p>Development of solid spin-1 polarized targets will open the study of <span class="hlt">tensor</span> structure functions to precise measurement, and holds the promise to enable a new generation of polarized scattering experiments. In this talk we will discuss a measurement of the leading twist <span class="hlt">tensor</span> structure function b1, along with prospects for future experiments with a solid <span class="hlt">tensor</span> polarized target. The recently approved JLab experiment E12-13-011 will measure the lead- ing twist <span class="hlt">tensor</span> structure function b1, which provides a unique tool to study partonic effects, while also being sensitive to coherent nuclear properties in the simplest nuclear system. At low x, shadowing effects are expected to dominate b1, while at larger values, b1 provides a clean probe of exotic QCD effects, such as hidden color due to 6-quark configuration. Since the deuteron wave function is relatively well known, any non-standard effects are expected to be readily observable. All available models predict a small or vanishing value of b1 at moderate x. However, the first pioneer measurement of b1 at HERMES revealed a crossover to an anomalously large negative value in the region 0.2 < x < 0.5, albeit with relatively large experimental uncertainty. E12-13-011 will perform an inclusive measurement of the deuteron <span class="hlt">tensor</span> asymmetry in the region 0.16 < x < 0.49, for 0.8 < Q2 < 5.0 GeV2. The UVa solid polarized ND3 target will be used, along with the Hall C spectrometers, and an unpolarized 115 nA beam. This measurement will provide access to the <span class="hlt">tensor</span> quark polarization, and allow a test of the Close-Kumano sum rule, which vanishes in the absence of <span class="hlt">tensor</span> polarization in the quark sea. Until now, <span class="hlt">tensor</span> structure has been largely unexplored, so the study of these quantities holds the potential of initiating a new field of spin physics at Jefferson Lab.</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="http://www.dtic.mil/">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> </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/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/2009SPIE.7259E..1CL','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2009SPIE.7259E..1CL"><span>RADTI: regression analyses of diffusion <span class="hlt">tensor</span> images</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Li, Yimei; Zhu, Hongtu; Chen, Yasheng; Ibrahim, Joseph G.; An, Hongyu; Lin, Weili; Hall, Colin; Shen, Dinggang</p> <p>2009-02-01</p> <p>Diffusion <span class="hlt">tensor</span> image (DTI) is a powerful tool for quantitatively assessing the integrity of anatomical connectivity in white matter in clinical populations. The prevalent methods for group-level analysis of DTI are statistical analyses of invariant measures (e.g., fractional anisotropy) and principal directions across groups. The invariant measures and principal directions, however, do not capture all information in full diffusion <span class="hlt">tensor</span>, which can decrease the statistical power of DTI in detecting subtle changes of white matters. Thus, it is very desirable to develop new statistical methods for analyzing full diffusion <span class="hlt">tensors</span>. In this paper, we develop a set of toolbox, called RADTI, for the analysis of the full diffusion <span class="hlt">tensors</span> as responses and establish their association with a set of covariates. The key idea is to use the recent development of log-Euclidean metric and then transform diffusion <span class="hlt">tensors</span> in a nonlinear space into their matrix logarithms in a Euclidean space. Our regression model is a semiparametric model, which avoids any specific parametric assumptions. We develop an estimation procedure and a test procedure based on score statistics and a resampling method to simultaneously assess the statistical significance of linear hypotheses across a large region of interest. Monte Carlo simulations are used to examine the finite sample performance of the test procedure for controlling the family-wise error rate. We apply our methods to the detection of statistical significance of diagnostic and age effects on the integrity of white matter in a diffusion <span class="hlt">tensor</span> study of human immunodeficiency virus.</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/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://adsabs.harvard.edu/abs/2016PhRvL.116d0401E','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016PhRvL.116d0401E"><span>Local Scale Transformations on the Lattice with <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.; Vidal, G.</p> <p>2016-01-01</p> <p>Consider the partition function of a classical system in two spatial dimensions, or the Euclidean path integral of a <span class="hlt">quantum</span> system in two space-time dimensions, both on a lattice. We show that the <span class="hlt">tensor</span> network renormalization algorithm [G. Evenbly and G. Vidal Phys. Rev. Lett. 115, 180405 (2015)] can be used to implement local scale transformations on these objects, namely, a lattice version of conformal maps. Specifically, we explain how to implement the lattice equivalent of the logarithmic conformal map that transforms the Euclidean plane into a cylinder. As an application, and with the 2D critical Ising model as a concrete example, we use this map to build a lattice version of the scaling operators of the underlying conformal field theory, from which one can extract their scaling dimensions and operator product expansion coefficients.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/26871313','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/26871313"><span>Local Scale Transformations on the Lattice with <span class="hlt">Tensor</span> Network Renormalization.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Evenbly, G; Vidal, G</p> <p>2016-01-29</p> <p>Consider the partition function of a classical system in two spatial dimensions, or the Euclidean path integral of a <span class="hlt">quantum</span> system in two space-time dimensions, both on a lattice. We show that the <span class="hlt">tensor</span> network renormalization algorithm [G. Evenbly and G. Vidal Phys. Rev. Lett. 115, 180405 (2015)] can be used to implement local scale transformations on these objects, namely, a lattice version of conformal maps. Specifically, we explain how to implement the lattice equivalent of the logarithmic conformal map that transforms the Euclidean plane into a cylinder. As an application, and with the 2D critical Ising model as a concrete example, we use this map to build a lattice version of the scaling operators of the underlying conformal field theory, from which one can extract their scaling dimensions and operator product expansion coefficients.</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('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/2017PhLB..771..151A','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017PhLB..771..151A"><span><span class="hlt">Quantum</span> non-equilibrium effects in rigidly-rotating thermal states</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Ambruş, Victor E.</p> <p>2017-08-01</p> <p>Based on known analytic results, the thermal expectation value of the <span class="hlt">stress</span>-energy <span class="hlt">tensor</span> (SET) operator for the massless Dirac field is analysed from a hydrodynamic perspective. Key to this analysis is the Landau decomposition of the SET, with the aid of which we find terms which are not present in the ideal SET predicted by kinetic theory. Moreover, the <span class="hlt">quantum</span> corrections become dominant in the vicinity of the speed of light surface (SOL). While rigidly-rotating thermal states cannot be constructed for the Klein-Gordon field, we perform a similar analysis at the level of <span class="hlt">quantum</span> corrections previously reported in the literature and we show that the Landau frame is well-defined only when the system is enclosed inside a boundary located inside or on the SOL. We discuss the relevance of these results for accretion disks around rapidly-rotating pulsars.</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://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://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('https://eric.ed.gov/?q=diffusion&pg=6&id=ED552116','ERIC'); return false;" href="https://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('http://adsabs.harvard.edu/abs/2002GeoJI.151..755G','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2002GeoJI.151..755G"><span>Controlled source apparent resistivity <span class="hlt">tensors</span> and their relationship to the magnetotelluric impedance <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>Grant Caldwell, T.; Bibby, Hugh M.; Brown, Colin</p> <p>2002-12-01</p> <p>The time-domain surface electric fields produced by a step current in collocated grounded sources can be represented by an apparent resistivity <span class="hlt">tensor</span> defined by the relationship between the measured (time-varying) electric field and a reference field equal to the steady-state current density in a uniform half-space. A magnetic field response <span class="hlt">tensor</span> is similarly defined for the horizontal components of the magnetic field. The `magnetic field apparent resistivity <span class="hlt">tensor</span>' is derived from a linear combination of the contractions of the outer product of the magnetic field response <span class="hlt">tensor</span>. Frequency-domain apparent resistivity <span class="hlt">tensors</span> are derived from the Laplace transforms of the corresponding time-domain electric and magnetic field response <span class="hlt">tensors</span>. Both the frequency and time-domain <span class="hlt">tensors</span> are independent of the source orientation where the sources can be approximated as (infinitesimal) dipoles. A simple combination of the frequency-domain (impulse response) <span class="hlt">tensors</span> can be used to derive the controlled source magnetotelluric (CSMT) impedance <span class="hlt">tensor</span>. The magnetic field apparent resistivity <span class="hlt">tensor</span> is a useful representation of the conductivity structure only where the source-receiver offset is much less than the diffusion or skin depth and behaves in a similar way to the `early-time' apparent resistivity traditionally used to represent time-domain electromagnetic data. Numerical modelling results demonstrate that the (horizontal) magnetic field apparent resistivity is insensitive to the localized 3-D conductivity structures that are typically the target of exploration surveys. In contrast, the electric field apparent resistivity <span class="hlt">tensor</span> depends sensitively upon the conductivity structure and is well behaved over the entire time or frequency range used in long-offset transient electromagnetic or CSMT measurements. By using the electric field apparent resistivity <span class="hlt">tensor</span>, `source effects' that hinder a conventional impedance <span class="hlt">tensor</span> analysis of CSMT data can be avoided</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/19850273','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/19850273"><span>[<span class="hlt">Tensor</span> veli palatini and <span class="hlt">tensor</span> tympani muscles: anatomical, functional and symptomatic links].</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Ramirez Aristeguieta, Luis Miguel; Ballesteros Acuña, Luis Ernesto; Sandoval Ortiz, Germán Pablo</p> <p>2010-01-01</p> <p>Temporomandibular disorders are associated with symptoms such as tinnitus, vertigo, sensation of hearing loss, ear fullness and otalgia. The connection and dysfunction of the <span class="hlt">tensor</span> tympani and <span class="hlt">tensor</span> veli palatini muscles seems to be associated with the aforementioned symptoms. We seek to demonstrate and explain this connection through the morphometry of these structures. We studied 22 paired blocks and 1 left side of human temporal bone. Digital measurements were made of the <span class="hlt">tensor</span> tympani muscles and stapes. The average length of the stapedial muscle was 5.8 mm SD 0.61, and that of the <span class="hlt">tensor</span> tympani was 19.69 mm SD 1.07. Anatomical connections were found in all the samples between the <span class="hlt">tensor</span> veli palatini muscles through a common tendon. There is a need for an interdisciplinary management between physician and specialized dentist in cases of craniofacial pain. 2009 Elsevier España, S.L. All rights reserved.</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/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('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('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> </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/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/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('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> <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('https://www.ncbi.nlm.nih.gov/pubmed/18051037','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/18051037"><span>Geodesic-loxodromes for diffusion <span class="hlt">tensor</span> interpolation and difference measurement.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Kindlmann, Gordon; Estépar, Raúl San José; Niethammer, Marc; Haker, Steven; Westin, Carl-Fredrik</p> <p>2007-01-01</p> <p>In algorithms for processing diffusion <span class="hlt">tensor</span> images, two common ingredients are interpolating <span class="hlt">tensors</span>, and measuring the distance between them. We propose a new class of interpolation paths for <span class="hlt">tensors</span>, termed geodesic-loxodromes, which explicitly preserve clinically important <span class="hlt">tensor</span> attributes, such as mean diffusivity or fractional anisotropy, while using basic differential geometry to interpolate <span class="hlt">tensor</span> orientation. This contrasts with previous Riemannian and Log-Euclidean methods that preserve the determinant. Path integrals of tangents of geodesic-loxodromes generate novel measures of over-all difference between two <span class="hlt">tensors</span>, and of difference in shape and in orientation.</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('http://adsabs.harvard.edu/abs/2017IJMPD..2650073B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017IJMPD..2650073B"><span>Exact scalar-<span class="hlt">tensor</span> cosmological models</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Belinchón, J. A.; Harko, T.; Mak, M. K.</p> <p></p> <p>Scalar-<span class="hlt">tensor</span> gravitational theories are important extensions of standard general relativity, which can explain both the initial inflationary evolution, as well as the late accelerating expansion of the universe. In the present paper, we investigate the cosmological solution of a scalar-<span class="hlt">tensor</span> gravitational theory, in which the scalar field ϕ couples to the geometry via an arbitrary function F(ϕ). The kinetic energy of the scalar field as well as its self-interaction potential V (ϕ) are also included in the gravitational action. By using a standard mathematical procedure, the Lie group approach, and Noether symmetry techniques, we obtain several exact solutions of the gravitational field equations describing the time evolutions of a flat Friedman-Robertson-Walker universe in the framework of the scalar-<span class="hlt">tensor</span> gravity. The obtained solutions can describe both accelerating and decelerating phases during the cosmological expansion of the universe.</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/2001CQGra..18.4997T','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2001CQGra..18.4997T"><span>Gauge field theory coherent states (GCS): IV. Infinite <span class="hlt">tensor</span> product and thermodynamical limit</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Thiemann, T.; Winkler, O.</p> <p>2001-12-01</p> <p>In the canonical approach to Lorentzian <span class="hlt">quantum</span> general relativity in four spacetime dimensions an important step forward has been made by Ashtekar, Isham and Lewandowski some eight years ago through the introduction of a Hilbert space structure, which was later proved to be a faithful representation of the canonical commutation and adjointness relations of the <span class="hlt">quantum</span> field algebra of diffeomorphism invariant gauge field theories by Ashtekar, Lewandowski, Marolf, Mourão and Thiemann. This Hilbert space, together with its generalization due to Baez and Sawin, is appropriate for semi-classical <span class="hlt">quantum</span> general relativity if the spacetime is spatially compact. In the spatially non-compact case, however, an extension of the Hilbert space is needed in order to approximate metrics that are macroscopically nowhere degenerate. For this purpose, in this paper we apply the theory of the infinite <span class="hlt">tensor</span> product (ITP) of Hilbert Spaces, developed by von Neumann more than sixty years ago, to <span class="hlt">quantum</span> general relativity. The cardinality of the number of <span class="hlt">tensor</span> product factors can take the value of any possible Cantor aleph, making this mathematical theory well suited to our problem in which a Hilbert space is attached to each edge of an arbitrarily complicated, generally infinite graph. The new framework opens access to a new arsenal of techniques, appropriate to describe fascinating physics such as <span class="hlt">quantum</span> topology change, semi-classical <span class="hlt">quantum</span> gravity, effective low-energy physics etc from the universal point of view of the ITP. In particular, the study of photons and gravitons propagating on fluctuating <span class="hlt">quantum</span> spacetimes should now be in reach.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2013AGUFM.S24B..08C','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2013AGUFM.S24B..08C"><span>Moment <span class="hlt">Tensor</span> Analysis of Shallow Sources</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Chiang, A.; Dreger, D. S.; Ford, S. R.; Walter, W. R.; Yoo, S.</p> <p>2013-12-01</p> <p>For the nuclear explosion source-type identification problem the uncertainty in a solution is as important as the best fitting parameters. A potential issue for shallow seismic sources that are effectively at the free-surface between the ground and air is that the vanishing traction at the free-surface can cause the associated vertical dip-slip (DS) Green's functions to have vanishing amplitudes (Julian et al., 1998), which in turn results in the indeterminacy of the Mxz and Myz components of the moment <span class="hlt">tensor</span> and bias in the moment <span class="hlt">tensor</span> solution. The effects of the free-surface on the stability of the moment <span class="hlt">tensor</span> method becomes important as we continue to investigate and improve the capabilities of regional full moment <span class="hlt">tensor</span> inversion for source-type identification and discrimination. It is important to understand its effects for discriminating shallow explosive sources in nuclear monitoring, but could also be important in natural systems that have shallow seismicity such as volcanoes and geothermal systems. The HUMMING ALBATROSS quarry blast is an excellent dataset in terms of understanding the effects of free-surface vanishing traction with real data. These chemical explosions are approximately 10 m depth and are recorded at up to several km distances. Therefore the data represents a rather severe source-station geometry in terms of vanishing traction issues. It is possible to obtain a robust full moment <span class="hlt">tensor</span> solution that is comprised dominantly by an isotropic or explosive component, however the data provide the opportunity to evaluate capabilities of moment <span class="hlt">tensor</span> inversion as a function of frequency.</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('http://hdl.handle.net/2060/19790020442','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19790020442"><span>Possibilities and limitations of rod-beam theories. [nonlinear distortion <span class="hlt">tensor</span> and nonlinear <span class="hlt">stress</span> <span class="hlt">tensors</span></span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Peterson, D.</p> <p>1979-01-01</p> <p>Rod-beam theories are founded on hypotheses such as Bernouilli's suggesting flat cross-sections under deformation. These assumptions, which make rod-beam theories possible, also limit the accuracy of their analysis. It is shown that from a certain order upward terms of geometrically nonlinear deformations contradict the rod-beam hypotheses. Consistent application of differential geometry calculus also reveals differences from existing rod theories of higher order. These differences are explained by simple examples.</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('http://adsabs.harvard.edu/abs/2017CQGra..34j5011P','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017CQGra..34j5011P"><span><span class="hlt">Tensor</span> network models of multiboundary wormholes</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Peach, Alex; Ross, Simon F.</p> <p>2017-05-01</p> <p>We study the entanglement structure of states dual to multiboundary wormhole geometries using <span class="hlt">tensor</span> network models. Perfect and random <span class="hlt">tensor</span> networks tiling the hyperbolic plane have been shown to provide good models of the entanglement structure in holography. We extend this by quotienting the plane by discrete isometries to obtain models of the multiboundary states. We show that there are networks where the entanglement structure is purely bipartite, extending results obtained in the large temperature limit. We analyse the entanglement structure in a range of examples.</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/22373465','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/22373465"><span>Blue running of the primordial <span class="hlt">tensor</span> spectrum</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Gong, Jinn-Ouk</p> <p>2014-07-01</p> <p>We examine the possibility of positive spectral index of the power spectrum of the primordial <span class="hlt">tensor</span> perturbation produced during inflation in the light of the detection of the B-mode polarization by the BICEP2 collaboration. We find a blue tilt is in general possible when the slow-roll parameter decays rapidly. We present two known examples in which a positive spectral index for the <span class="hlt">tensor</span> power spectrum can be obtained. We also briefly discuss other consistency tests for further studies on inflationary dynamics.</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/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/2016PhyU...59..141T','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016PhyU...59..141T"><span>Energy-momentum <span class="hlt">tensor</span> of the electromagnetic field in dispersive media</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Toptygin, I. N.; Levina, K.</p> <p>2016-02-01</p> <p>We study the relation between the energy-momentum <span class="hlt">tensor</span> of the electromagnetic field and the group velocity of quasi-monochromatic waves in a nonabsorptive, isotropic, spatially and temporally dispersive dielectric. It is shown that the Abraham force acting on a dielectric is not needed for the momentum conservation law to hold if the dielectric is free of external charges and currents and if the Abraham momentum density is used. The energy-momentum <span class="hlt">tensor</span> turns out to be symmetric, and the Maxwell <span class="hlt">stress</span> <span class="hlt">tensor</span> is expressed either in terms of the momentum density vector and the group velocity or in terms of the energy density and the group velocity. The <span class="hlt">stress</span> <span class="hlt">tensor</span> and the energy density are essentially dependent on the frequency and wave vector derivatives of the functions that describe the electromagnetic properties of the medium (i.e., the dielectric permittivity and the magnetic permeability). The obtained results are applicable to both ordinary and left-handed media. The results are compared with those of other authors. The pressure a wave exerts on the interface between two media is calculated. For both ordinary and left-handed media, either 'radiation pressure' or 'radiation attraction' can occur at the interface, depending on the material parameters of the two media. For liquid dielectrics, the striction effect is considered.</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/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://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('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('http://adsabs.harvard.edu/abs/2010CNSNS..15..823V','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2010CNSNS..15..823V"><span>Nonlinear symmetries on spaces admitting 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>Visinescu, Mihai</p> <p>2010-04-01</p> <p>Nonlinear symmetries corresponding to Killing <span class="hlt">tensors</span> are investigated. The intimate relation between Killing-Yano <span class="hlt">tensors</span> and non-standard supersymmetries is pointed out. The gravitational anomalies are absent if the hidden symmetry is associated with a Killing-Yano <span class="hlt">tensor</span>. In the case of the nonlinear symmetries the dynamical algebras of the Dirac-type operators is more involved and could be organized as infinite dimensional algebras or superalgebras. The general results are applied to some concrete spaces involved in theories of modern physics. As a first example it is considered the 4-dimensional Euclidean Taub-NUT space and its generalizations introduced by Iwai and Katayama. One presents the infinite dimensional superalgebra of Dirac type operators on Taub-NUT space that could be seen as a graded loop superalgebra of the Kac-Moody type. The axial anomaly, interpreted as the index of the Dirac operator, is computed for the generalized Taub-NUT metrics. Finally the existence of the conformal Killing-Yano <span class="hlt">tensors</span> is investigated for some spaces with mixed Sasakian structures.</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('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('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.osti.gov/scitech/biblio/6444602','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/6444602"><span>Extended scalar-<span class="hlt">tensor</span> theory of gravitation</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Borneas, M.</p> <p>1984-08-15</p> <p>A link between several scalar-<span class="hlt">tensor</span> theories of gravitation and Einstein's theory is proposed. It is based on a Lagrangian in which the part depending on the scalar field vanishes under the usual conditions, but under special conditions new aspects of gravitation can be forecast.</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('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/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('https://www.osti.gov/scitech/biblio/21294034','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/21294034"><span>Coherent states in noncommutative <span class="hlt">quantum</span> mechanics</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Ben Geloun, J.; Scholtz, F. G.</p> <p>2009-04-15</p> <p>Gazeau-Klauder coherent states in noncommutative <span class="hlt">quantum</span> mechanics are considered. We find that these states share similar properties to those of ordinary canonical coherent states in the sense that they saturate the related position uncertainty relation, obey a Poisson distribution, and possess a flat geometry. Using the natural isometry between the <span class="hlt">quantum</span> Hilbert space of Hilbert-Schmidt operators and the <span class="hlt">tensor</span> product of the classical configuration space and its dual, we reveal the inherent vector feature of these states.</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('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('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('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> <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://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('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> </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.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://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('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('http://adsabs.harvard.edu/abs/2014RJMP...21..362M','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2014RJMP...21..362M"><span>On positive maps in <span class="hlt">quantum</span> information</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Majewski, W. A.</p> <p>2014-07-01</p> <p>Using the Grothendieck approach to the <span class="hlt">tensor</span> product of locally convex spaces, we review a characterization of positive maps as well as Belavkin-Ohya characterization of PPT states. Moreover, within this scheme, a generalization of the idea of Choi matrices for genuine <span class="hlt">quantum</span> systems will be presented.</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('https://www.ncbi.nlm.nih.gov/pubmed/20715279','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/20715279"><span>Spin-orbit contributions in high-spin nitrenes/carbenes: a hybrid CASSCF/MRMP2 study of zero-field splitting <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>Sugisaki, Kenji; Toyota, Kazuo; Sato, Kazunobu; Shiomi, Daisuke; Kitagawa, Masahiro; Takui, Takeji</p> <p>2010-10-04</p> <p>Zero-field splitting (ZFS) <span class="hlt">tensors</span> (D <span class="hlt">tensors</span>) of organic high-spin oligonitrenes/oligocarbenes up to spin-septet are quantitatively determined on the basis of <span class="hlt">quantum</span> chemical calculations. The spin-orbit contributions, D(SO) <span class="hlt">tensors</span> are calculated in terms of a hybrid CASSCF/MRMP2 approach, which was recently proposed by us. The spin-spin counterparts, D(SS) <span class="hlt">tensors</span> are computed based on McWeeny-Mizuno's equation in conjunction with the RODFT spin densities. The present calculations show that more than 10% of ZFS arises from spin-orbit interactions in the high-spin nitrenes under study. Contributions of spin-bearing site-site interactions are estimated with the aid of a semi-empirical model for the D <span class="hlt">tensors</span> and found to be ca. 5% of the D(SO) <span class="hlt">tensor</span>. The analysis of intermediate states reveal that the largest contributions to the calculated D(SO) <span class="hlt">tensors</span> are attributed to intra-site spin flip excitations and delocalized π and π* orbitals play an important role in the inter-site spin-orbit interactions.</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://adsabs.harvard.edu/abs/2014CQGra..31c5020B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2014CQGra..31c5020B"><span>Gravity induced from <span class="hlt">quantum</span> spacetime</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Beggs, Edwin J.; Majid, Shahn</p> <p>2014-02-01</p> <p>We show that tensoriality constraints in noncommutative Riemannian geometry in the two-dimensional bicrossproduct model <span class="hlt">quantum</span> spacetime algebra [x, t] = λx drastically reduce the moduli of possible metrics g up to normalization to a single real parameter, which we interpret as a time in the past from which all timelike geodesics emerge and a corresponding time in the future at which they all converge. Our analysis also implies a reduction of moduli in n-dimensions and we study a suggested spherically symmetric classical geometry in n = 4 in detail, identifying two one-parameter subcases where the Einstein <span class="hlt">tensor</span> matches that of a perfect fluid for (a) positive pressure, zero density and (b) negative pressure and positive density with ratio w_Q=-{1\\over 2}. The classical geometry is conformally flat and its geodesics motivate new coordinates which we extend to the <span class="hlt">quantum</span> case as a new description of the <span class="hlt">quantum</span> spacetime model as a quadratic algebra. The noncommutative Riemannian geometry is fully solved for n = 2 and includes the <span class="hlt">quantum</span> Levi-Civita connection and a second, nonperturbative, Levi-Civita connection which blows up as λ → 0. We also propose a ‘<span class="hlt">quantum</span> Einstein tensor’ which is identically zero for the main part of the moduli space of connections (as classically in 2D). However, when the <span class="hlt">quantum</span> Ricci <span class="hlt">tensor</span> and metric are viewed as deformations of their classical counterparts there would be an O(λ2) correction to the classical Einstein <span class="hlt">tensor</span> and an O(λ) correction to the classical metric.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/scitech/biblio/22525019','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/22525019"><span>Vector and <span class="hlt">tensor</span> contributions to the curvature perturbation at second order</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Carrilho, Pedro; Malik, Karim A. E-mail: k.malik@qmul.ac.uk</p> <p>2016-02-01</p> <p>We derive the evolution equation for the second order curvature perturbation using standard techniques of cosmological perturbation theory. We do this for different definitions of the gauge invariant curvature perturbation, arising from different splits of the spatial metric, and compare the expressions. The results are valid at all scales and include all contributions from scalar, vector and <span class="hlt">tensor</span> perturbations, as well as anisotropic <span class="hlt">stress</span>, with all our results written purely in terms of gauge invariant quantities. Taking the large-scale approximation, we find that a conserved quantity exists only if, in addition to the non-adiabatic pressure, the transverse traceless part of the anisotropic <span class="hlt">stress</span> <span class="hlt">tensor</span> is also negligible. We also find that the version of the gauge invariant curvature perturbation which is exactly conserved is the one defined with the determinant of the spatial part of the inverse metric.</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://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('http://adsabs.harvard.edu/abs/2010sts..book..107O','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2010sts..book..107O"><span>Minkowski Space and <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>O'Hara, Paul</p> <p></p> <p>A paradigm shift distinguishes general relativity from classical mechanics. In general relativity the energy-momentum <span class="hlt">tensor</span> is the effective cause of the ontological space-time curvature and vice-versa, while in classical physics, the structure of space-time is treated as an accidental cause, serving only as a backdrop against which the laws of physics unfold. This split in turn is inherited by <span class="hlt">quantum</span> mechanics, which is usually developed by changing classical (including special relativity) Hamiltonians into <span class="hlt">quantum</span> wave equations.</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://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://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('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('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('https://www.osti.gov/scitech/biblio/20995324','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/20995324"><span>Pion mass dependence of the nucleon form factors of the energy-momentum <span class="hlt">tensor</span> in the chiral quark-soliton model</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Goeke, K.; Grabis, J.; Ossmann, J.; Schweitzer, P.; Silva, A.; Urbano, D.</p> <p>2007-05-15</p> <p>The nucleon form factors of the energy-momentum <span class="hlt">tensor</span> are studied in the large-N{sub c} limit in the framework of the chiral quark-soliton model for model parameters that simulate physical situations in which pions are heavy. This allows for a direct comparison to lattice <span class="hlt">quantum</span> chromodynamics results.</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> </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://eric.ed.gov/?q=structural+AND+geology&pg=3&id=EJ392776','ERIC'); return false;" href="https://eric.ed.gov/?q=structural+AND+geology&pg=3&id=EJ392776"><span>Limitations of the Concept of <span class="hlt">Stress</span> in Structural Analysis.</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>Edelman, Steven Harold</p> <p>1989-01-01</p> <p>Provides an introduction and explanations of <span class="hlt">stress</span>-strain relationships, measuring <span class="hlt">stress</span>, a goal of structural analysis, and legitimate applications of the concept of <span class="hlt">stress</span>. Diagrams include a derivation of the <span class="hlt">stress</span> <span class="hlt">tensor</span>, graphical representations of <span class="hlt">stress</span>-strain relations, and related problems. (RT)</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> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017EGUGA..19.3047D','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017EGUGA..19.3047D"><span>Elasticity <span class="hlt">tensors</span> symmetry analysis using R</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Danek, Tomasz; Slawinski, Michael</p> <p>2017-04-01</p> <p>In this contribution we present orientation and class classification analysis of few full elasticity <span class="hlt">tensors</span> obtained form seismic measurements. All computations were performed in R environment using both regular and custom made modules. All necessary <span class="hlt">tensor</span> rotations were performed using qaterions and all optimzation procedures were done using global optimization methods. First of all distances to all symmetry classes were optimized and compared using many different norms (e.g. Forbenius, operator etc.). Than we used MC method to analyse measurement errors impact on obtained results. In the last step of this project we presented some consideration regarding the possible methods of most probable symmetry class determination. This research was supported by the Polish National Science Center under contract No. DEC-2013/11/B/ST10/0472.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=4691604','PMC'); return false;" href="https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=4691604"><span>Saliency Mapping Enhanced by Structure <span class="hlt">Tensor</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>He, Zhiyong; Chen, Xin; Sun, Lining</p> <p>2015-01-01</p> <p>We propose a novel efficient algorithm for computing visual saliency, which is based on the computation architecture of Itti model. As one of well-known bottom-up visual saliency models, Itti method evaluates three low-level features, color, intensity, and orientation, and then generates multiscale activation maps. Finally, a saliency map is aggregated with multiscale fusion. In our method, the orientation feature is replaced by edge and corner features extracted by a linear structure <span class="hlt">tensor</span>. Following it, these features are used to generate contour activation map, and then all activation maps are directly combined into a saliency map. Compared to Itti method, our method is more computationally efficient because structure <span class="hlt">tensor</span> is more computationally efficient than Gabor filter that is used to compute the orientation feature and our aggregation is a direct method instead of the multiscale operator. Experiments on Bruce's dataset show that our method is a strong contender for the state of the art. PMID:26788050</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/26788050','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/26788050"><span>Saliency Mapping Enhanced by Structure <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>He, Zhiyong; Chen, Xin; Sun, Lining</p> <p>2015-01-01</p> <p>We propose a novel efficient algorithm for computing visual saliency, which is based on the computation architecture of Itti model. As one of well-known bottom-up visual saliency models, Itti method evaluates three low-level features, color, intensity, and orientation, and then generates multiscale activation maps. Finally, a saliency map is aggregated with multiscale fusion. In our method, the orientation feature is replaced by edge and corner features extracted by a linear structure <span class="hlt">tensor</span>. Following it, these features are used to generate contour activation map, and then all activation maps are directly combined into a saliency map. Compared to Itti method, our method is more computationally efficient because structure <span class="hlt">tensor</span> is more computationally efficient than Gabor filter that is used to compute the orientation feature and our aggregation is a direct method instead of the multiscale operator. Experiments on Bruce's dataset show that our method is a strong contender for the state of the art.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/1996SoPh..164..389M','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/1996SoPh..164..389M"><span>Singular Points of the Polarization <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>Molodensky, M. M.; Starkova, L. I.</p> <p>1996-03-01</p> <p>The problem to compute the magnetic field above the chromosphere using data of the vector τ = B t/Bt that gives the projected field direction can be solved with different approximations. The field of direction vectors τ is, however, not the only field accessible to observations. The Stokes parameters, which are components of the radiation <span class="hlt">tensor</span>, can be measured at each point of the image plane. The directions of the eigenvectors of the radiation <span class="hlt">tensor</span> define two mutually orthogonal systems of integral curves in the image plane. These families of curves have singular points, which are generally of different type than those of the vector field. When the morphology of Hα chromospheric fibrils are used to infer the topology of the magnetic field, a similar problem is met, suggesting that singular points should also be present there.</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('http://adsabs.harvard.edu/abs/2013AmJPh..81..498B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2013AmJPh..81..498B"><span><span class="hlt">Tensors</span>: A guide for undergraduate students</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Battaglia, Franco; George, Thomas F.</p> <p>2013-07-01</p> <p>A guide on <span class="hlt">tensors</span> is proposed for undergraduate students in physics or engineering that ties directly to vector calculus in orthonormal coordinate systems. We show that once orthonormality is relaxed, a dual basis, together with the contravariant and covariant components, naturally emerges. Manipulating these components requires some skill that can be acquired more easily and quickly once a new notation is adopted. This notation distinguishes multi-component quantities in different coordinate systems by a differentiating sign on the index labelling the component rather than on the label of the quantity itself. This tiny stratagem, together with simple rules openly stated at the beginning of this guide, allows an almost automatic, easy-to-pursue procedure for what is otherwise a cumbersome algebra. By the end of the paper, the reader will be skillful enough to tackle many applications involving <span class="hlt">tensors</span> of any rank in any coordinate system, without index-manipulation obstacles standing in the way.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017JHEP...06..036K','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017JHEP...06..036K"><span>Random matrices 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; Kumar, K. V. Pavan; Sanyal, Sambuddha</p> <p>2017-06-01</p> <p>We further explore the connection between holographic O( n) <span class="hlt">tensor</span> models and random matrices. First, we consider the simplest non-trivial uncolored <span class="hlt">tensor</span> model and show that the results for the density of states, level spacing and spectral form factor are qualitatively identical to the colored case studied in arXiv:1612.06330. We also explain an overall 16-fold degeneracy by identifying various symmetries, some of which were unavailable in SYK and the colored models. Secondly, and perhaps more interestingly, we systematically identify the Spectral Mirror Symmetry and the Time-Reversal Symmetry of both the colored and uncolored models for all values of n, and use them to identify the Andreev ensembles that control their random matrix behavior. We find that the ensembles that arise exhibit a refined version of Bott periodicity in n.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/scitech/biblio/20695994','SCIGOV-STC'); return false;" href="https://www.osti.gov/scitech/biblio/20695994"><span><span class="hlt">Tensor</span> coupling and pseudospin symmetry in nuclei</span></a></p> <p><a target="_blank" href="http://www.osti.gov/scitech">SciTech Connect</a></p> <p>Alberto, P.; Castro, A.S. de; Lisboa, R.; Malheiro, M.</p> <p>2005-03-01</p> <p>In this work we study the contribution of the isoscalar <span class="hlt">tensor</span> coupling to the realization of pseudospin symmetry in nuclei. Using realistic values for the <span class="hlt">tensor</span> coupling strength, we show that this coupling reduces noticeably the pseudospin splittings, especially for single-particle levels near the Fermi surface. By using an energy decomposition of the pseudospin energy splittings, we show that the changes in these splittings come mainly through the changes induced in the lower radial wave function for the low-lying pseudospin partners and through changes in the expectation value of the pseudospin-orbit coupling term for surface partners. This allows us to confirm the conclusion already reached in previous studies, namely that the pseudospin symmetry in nuclei is of a dynamical nature.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2015PhRvD..91h5031B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015PhRvD..91h5031B"><span><span class="hlt">Tensor</span> gauge fields of N =8 supergravity</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Bandos, Igor; Ortín, Tomás</p> <p>2015-04-01</p> <p>We study the <span class="hlt">tensor</span> gauge fields ("notophs") of ungauged N =8 ,D =4 supergravity in superspace. These are described by 2-form potentials B2G in the adjoint representation of G =E7 (+7 ). The consistency of the natural candidates for the superspace constraints for their field strengths H3G fixes the form of the generalized Bianchi identities D H3G=… and also requires the potentials B2G /H with indices of G /H =E7 (+7 )/S U (8 ) generators to be dual to the scalars of the N =8 ,D =4 supergravity multiplet. In contrast, the field strengths of the 2-form potentials corresponding to the S U (8 ) generators are dual to fermionic bilinears, so that these potentials are auxiliary rather than physical fields. Their presence, however, is essential to formulate a <span class="hlt">tensor</span> hierarchy of N =8 ,D =4 supergravity consistent with its U-duality group E7 (+7 ).</p> </li> <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('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/17009699','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/17009699"><span>Uncertainty in diffusion <span class="hlt">tensor</span> based fibre tracking.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Hahn, H K; Klein, J; Nimsky, C; Rexilius, J; Peitgen, H O</p> <p>2006-01-01</p> <p>Diffusion <span class="hlt">tensor</span> imaging and related fibre tracking techniques have the potential to identify major white matter tracts afflicted by an individual pathology or tracts at risk for a given surgical approach. However, the reliability of these techniques is known to be limited by image distortions, image noise, low spatial resolution, and the problem of identifying crossing fibres. This paper intends to bridge the gap between the requirements of neurosurgical applications and basic research on fibre tracking uncertainty. We acquired echo planar diffusion <span class="hlt">tensor</span> data from both 1.5 T and 3.0 T scanners. For fibre tracking, an extended deflection-based algorithm is employed with enhanced robustness to impaired fibre integrity such as caused by diffuse or infiltrating pathological processes. Moreover, we present a method to assess and visualize the uncertainty of fibre reconstructions based on variational complex Gaussian noise, which provides an alternative to the bootstrap method. We compare fibre tracking results with and without variational noise as well as with artificially decreased image resolution and signal-to-noise. Using our fibre tracking technique, we found a high robustness to decreased image resolution and signal-to-noise. Still, the effects of image quality on the tracking result will depend on the employed fibre tracking algorithm and must be handled with care, especially when being used for neurosurgical planning or resection guidance. An advantage of the variational noise approach over the bootstrap technique is that it is applicable to any given set of diffusion <span class="hlt">tensor</span> images. We conclude that the presented approach allows for investigating the uncertainty of diffusion <span class="hlt">tensor</span> imaging based fibre tracking and might offer a perspective to overcome the problem of size underestimation observed by existing techniques.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016JHEP...06..060H','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016JHEP...06..060H"><span><span class="hlt">Tensor</span> integrand reduction via Laurent expansion</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Hirschi, Valentin; Peraro, Tiziano</p> <p>2016-06-01</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 N inja. 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 N inja 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 N inja library and interfaced it to M adL oop, which is part of the public M adG raph5_ aMC@NLO framework. We performed a detailed performance study, comparing against other public reduction tools, namely C utT ools, S amurai, IREGI, PJF ry++ and G olem95. We find that N inja 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 N inja. 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 N inja'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/21960133','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/21960133"><span>Diffusion <span class="hlt">tensor</span> imaging in carpal tunnel syndrome.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Taşdelen, Neslihan; Gürses, Bengi; Kiliçkesmez, Özgür; Firat, Zeynep; Karlikaya, Geysu; Tercan, Mustafa; Uluğ, Aziz Müfit; Gürmen, Ahmet Nevzat</p> <p>2012-01-01</p> <p>We aimed to investigate the efficacy of diffusion <span class="hlt">tensor</span> imaging in the diagnosis of carpal tunnel syndrome and to obtain a quantitative parameter that may contribute to the diagnosis. The median nerves in 57 wrists of 38 patients diagnosed as carpal tunnel syndrome and 30 wrists of 24 normal subjects were prospectively evaluated with a 3T Philips scanner, using standard 8-channel SENSE head coil. Diffusion <span class="hlt">tensor</span> imaging was performed using spin echo-echo planar imaging. For anatomical reference, a T1-weighted sequence was acquired. Fractional anisotropy and apparent diffusion coefficient measurements were done focally at the carpal tunnel level and from whole median nerve. In carpal tunnel syndrome patients, both focal carpal tunnel and whole nerve measurements demonstrated statistically significantly lower fractional anisotropy values than normal subjects (P < 0.001). No statistically significant difference was observed in apparent diffusion coefficient measurements. The cut-off value obtained by receiver operator characteristics analysis was 0.554 for focal carpal tunnel fractional anisotropy (sensitivity, 80%; specificity, 80%) and 0.660 for whole nerve fractional anisotropy (sensitivity, 82%; specificity, 80%) measurement. Diffusion <span class="hlt">tensor</span> imaging may contribute to the diagnosis of carpal tunnel syndrome on the basis of fractional anisotropy measurements.</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.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.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> </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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