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Sample records for quantum stress tensor

  1. Particle creation from the quantum stress tensor

    NASA Astrophysics Data System (ADS)

    Firouzjaee, Javad T.; Ellis, George F. R.

    2015-05-01

    Among the different methods to derive particle creation, finding the quantum stress tensor expectation value gives a covariant quantity which can be used for examining the backreaction issue. However this tensor also includes vacuum polarization in a way that depends on the vacuum chosen. Here we review different aspects of particle creation by looking at energy conservation and at the quantum stress tensor. We show that in the case of general spherically symmetric black holes that have a dynamical horizon, as occurs in a cosmological context, one cannot have pair creation on the horizon because this violates energy conservation. This confirms the results obtained in other ways in a previous paper [J. T. Firouzjaee and G. F. R. Ellis, Gen. Relativ. Gravit. 47, 6 (2015)]. Looking at the expectation value of the quantum stress tensor with three different definitions of the vacuum state, we study the nature of particle creation and vacuum polarization in black hole and cosmological models, and the associated stress-energy tensors. We show that the thermal temperature that is calculated from the particle flux given by the quantum stress tensor is compatible with the temperature determined by the affine null parameter approach. Finally, we show that in the spherically symmetric dynamic case, we can neglect the backscattering term and only consider the s-wave term near the future apparent horizon.

  2. Completely regular quantum stress tensor with w<-1

    SciTech Connect

    Kahya, E. O.; Onemli, V. K.; Woodard, R. P.

    2010-01-15

    For many quantum field theory computations in cosmology it is not possible to use the flat space trick of obtaining full, interacting states by evolving free states over infinite times. State wave functionals must be specified at finite times and, although the free states suffice to obtain the lowest order effects, higher order corrections necessarily involve changes of the initial state. Failing to correctly change the initial state can result in effective field equations which diverge on the initial value surface, or which contain tedious sums of terms that redshift like inverse powers of the scale factor. In this paper we verify a conjecture from 2004 that the lowest order initial state correction can indeed absorb the initial value divergences and all the redshifting terms of the two-loop expectation value (in free, Bunch-Davies vacuum) of the stress tensor of a massless, minimally coupled scalar with a quartic self-interaction on a nondynamical de Sitter background.

  3. Completely regular quantum stress tensor with w<-1

    NASA Astrophysics Data System (ADS)

    Kahya, E. O.; Onemli, V. K.; Woodard, R. P.

    2010-01-01

    For many quantum field theory computations in cosmology it is not possible to use the flat space trick of obtaining full, interacting states by evolving free states over infinite times. State wave functionals must be specified at finite times and, although the free states suffice to obtain the lowest order effects, higher order corrections necessarily involve changes of the initial state. Failing to correctly change the initial state can result in effective field equations which diverge on the initial value surface, or which contain tedious sums of terms that redshift like inverse powers of the scale factor. In this paper we verify a conjecture from 2004 that the lowest order initial state correction can indeed absorb the initial value divergences and all the redshifting terms of the two-loop expectation value (in free, Bunch-Davies vacuum) of the stress tensor of a massless, minimally coupled scalar with a quartic self-interaction on a nondynamical de Sitter background.

  4. Probability distributions for quantum stress tensors in four dimensions

    NASA Astrophysics Data System (ADS)

    Fewster, Christopher J.; Ford, L. H.; Roman, Thomas A.

    2012-06-01

    We treat the probability distributions for quadratic quantum fields, averaged with a Lorentzian test function, in four-dimensional Minkowski vacuum. These distributions share some properties with previous results in two-dimensional spacetime. Specifically, there is a lower bound at a finite negative value, but no upper bound. Thus arbitrarily large positive energy density fluctuations are possible. We are not able to give closed form expressions for the probability distribution, but rather use calculations of a finite number of moments to estimate the lower bounds, the asymptotic forms for large positive argument, and possible fits to the intermediate region. The first 65 moments are used for these purposes. All of our results are subject to the caveat that these distributions are not uniquely determined by the moments. We apply the asymptotic form of the electromagnetic energy density distribution to estimate the nucleation rates of black holes and of Boltzmann brains.

  5. Quantum corrections to the stress-energy tensor in thermodynamic equilibrium with acceleration

    NASA Astrophysics Data System (ADS)

    Becattini, F.; Grossi, E.

    2015-08-01

    We show that the stress-energy tensor has additional terms with respect to the ideal form in states of global thermodynamic equilibrium in flat spacetime with nonvanishing acceleration and vorticity. These corrections are of quantum origin and their leading terms are second order in the gradients of the thermodynamic fields. Their relevant coefficients can be expressed in terms of correlators of the stress-energy tensor operator and the generators of the Lorentz group. With respect to previous assessments, we find that there are more second-order coefficients and that all thermodynamic functions including energy density receive acceleration and vorticity dependent corrections. Notably, also the relation between ρ and p , that is, the equation of state, is affected by acceleration and vorticity. We have calculated the corrections for a free real scalar field—both massive and massless—and we have found that they increase, particularly for a massive field, at very high acceleration and vorticity and very low temperature. Finally, these nonideal terms depend on the explicit form of the stress-energy operator, implying that different stress-energy tensors of the scalar field—canonical or improved—are thermodynamically inequivalent.

  6. Quantum integrability of quadratic Killing tensors

    SciTech Connect

    Duval, C.; Valent, G.

    2005-05-01

    Quantum integrability of classical integrable systems given by quadratic Killing tensors on curved configuration spaces is investigated. It is proven that, using a 'minimal' quantization scheme, quantum integrability is ensured for a large class of classic examples.

  7. Virial theorem for an inhomogeneous medium, boundary conditions for the wave functions, and stress tensor in quantum statistics.

    PubMed

    Bobrov, V B; Trigger, S A; van Heijst, G J F; Schram, P P J M

    2010-07-01

    On the basis of the stationary Schrödinger equation, the virial theorem in an inhomogeneous external field for the canonical ensemble is proved. It is shown that the difference in the form of virial theorem is conditioned by the value of the wave-function derivative on the surface of the volume, surrounding the system under consideration. The stress tensor in such a system is determined by the average values of the wave-function space derivatives.

  8. Virial theorem for an inhomogeneous medium, boundary conditions for the wave functions, and stress tensor in quantum statistics.

    PubMed

    Bobrov, V B; Trigger, S A; van Heijst, G J F; Schram, P P J M

    2010-07-01

    On the basis of the stationary Schrödinger equation, the virial theorem in an inhomogeneous external field for the canonical ensemble is proved. It is shown that the difference in the form of virial theorem is conditioned by the value of the wave-function derivative on the surface of the volume, surrounding the system under consideration. The stress tensor in such a system is determined by the average values of the wave-function space derivatives. PMID:20866550

  9. 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.

  10. Tensor Networks and Quantum Error Correction

    NASA Astrophysics Data System (ADS)

    Ferris, Andrew J.; Poulin, David

    2014-07-01

    We establish several relations between quantum error correction (QEC) and tensor network (TN) methods of quantum 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 quantum codes and decoding algorithms that generalize and improve upon quantum polar codes and successive cancellation decoding in a natural way.

  11. Quantum theory with bold operator tensors.

    PubMed

    Hardy, Lucien

    2015-08-01

    In this paper, we present a formulation of quantum theory in terms of bold operator tensors. A circuit is built up of operations where an operation corresponds to a use of an apparatus. We associate collections of operator tensors (which together comprise a bold operator) with these apparatus uses. We give rules for combining bold operator tensors such that, for a circuit, they give a probability distribution over the possible outcomes. If we impose certain physicality constraints on the bold operator tensors, then we get exactly the quantum 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 quantum field theory.

  12. Quantum tensor product structures are observable induced.

    PubMed

    Zanardi, Paolo; Lidar, Daniel A; Lloyd, Seth

    2004-02-13

    It is argued that the partition of a quantum system into subsystems is dictated by the set of operationally accessible interactions and measurements. The emergence of a multipartite tensor product structure of the state space and the associated notion of quantum entanglement are then relative and observable induced. We develop a general algebraic framework aimed to formalize this concept.

  13. The operator tensor formulation of quantum theory.

    PubMed

    Hardy, Lucien

    2012-07-28

    In this paper, we provide what might be regarded as a manifestly covariant presentation of discrete quantum theory. A typical quantum experiment has a bunch of apparatuses placed so that quantum 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 quantum systems inputted into it and zero or more quantum 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 tensor formulation of quantum theory, each operation corresponds to an operator tensor. For example, the operation B(b(2)a(3))(a(1)) corresponds to the operator tensor B(b(2)a(3))(a(1)). Further, the probability for a general circuit is given by replacing operations with corresponding operator tensors 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 tensors must be physical (namely, they must have positive input transpose and satisfy a certain normalization condition).

  14. Radiation Forces and Torques without Stress (Tensors)

    ERIC Educational Resources Information Center

    Bohren, Craig F.

    2011-01-01

    To understand radiation forces and torques or to calculate them does not require invoking photon or electromagnetic field momentum transfer or stress tensors. 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…

  15. On Endomorphisms of Quantum Tensor Space

    NASA Astrophysics Data System (ADS)

    Lehrer, Gustav Isaac; Zhang, Ruibin

    2008-12-01

    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 quantum {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 quantum alternator in H 3( q), and the endomorphism algebra is the classical realisation of the Temperley-Lieb algebra on tensor 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 tensor powers when q is a root of unity.

  16. Stress tensor correlators in three dimensional gravity

    NASA Astrophysics Data System (ADS)

    Bagchi, Arjun; Grumiller, Daniel; Merbis, Wout

    2016-03-01

    We calculate holographically arbitrary n -point correlators of the boundary stress tensor in three-dimensional Einstein gravity with negative or vanishing cosmological constant. We provide explicit expressions up to 5-point (connected) correlators and show consistency with the Galilean conformal field theory Ward identities and recursion relations of correlators, which we derive. This provides a novel check of flat space holography in three dimensions.

  17. Covariant statistical mechanics and the stress-energy tensor.

    PubMed

    Becattini, F

    2012-06-15

    After recapitulating the covariant formalism of equilibrium statistical mechanics in special relativity and extending it to the case of a nonvanishing spin tensor, we show that the relativistic stress-energy tensor at thermodynamical equilibrium can be obtained from a functional derivative of the partition function with respect to the inverse temperature four-vector β. For usual thermodynamical equilibrium, the stress-energy tensor turns out to be the derivative of the relativistic thermodynamic potential current with respect to the four-vector β, i.e., T(μν)=-∂Φ(μ)/∂β(ν). This formula establishes a relation between the stress-energy tensor and the entropy current at equilibrium, possibly extendable to nonequilibrium hydrodynamics. PMID:23004277

  18. Covariant statistical mechanics and the stress-energy tensor.

    PubMed

    Becattini, F

    2012-06-15

    After recapitulating the covariant formalism of equilibrium statistical mechanics in special relativity and extending it to the case of a nonvanishing spin tensor, we show that the relativistic stress-energy tensor at thermodynamical equilibrium can be obtained from a functional derivative of the partition function with respect to the inverse temperature four-vector β. For usual thermodynamical equilibrium, the stress-energy tensor turns out to be the derivative of the relativistic thermodynamic potential current with respect to the four-vector β, i.e., T(μν)=-∂Φ(μ)/∂β(ν). This formula establishes a relation between the stress-energy tensor and the entropy current at equilibrium, possibly extendable to nonequilibrium hydrodynamics.

  19. Anisotropy of Local Stress Tensor Leads to Line Tension

    NASA Astrophysics Data System (ADS)

    Shao, Mingzhe; Wang, Jianjun; Zhou, Xin

    2015-04-01

    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 stress tensor 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 stress tensor is considered.

  20. Covariant diagonalization of the perfect fluid stress-energy tensor

    NASA Astrophysics Data System (ADS)

    Garat, Alcides

    2015-02-01

    We introduce new tetrads that manifestly and covariantly diagonalize the stress-energy tensor for a perfect fluid with vorticity at every spacetime point. This new tetrad can be applied to introduce simplification in the analysis of astrophysical relativistic problems where vorticity is present through the Carter-Lichnerowicz equation. We also discuss the origin of inertia in this special case from the standpoint of our new local tetrads.

  1. Stress tensor for a scalar field in a spatially varying background potential: Divergences, "renormalization", anomalies, and Casimir forces

    NASA Astrophysics Data System (ADS)

    Milton, Kimball A.; Fulling, Stephen A.; Parashar, Prachi; Kalauni, Pushpa; Murphy, Taylor

    2016-04-01

    Motivated by a desire to understand quantum fluctuation energy densities and stress within a spatially varying dielectric medium, we examine the vacuum expectation value for the stress tensor 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 stress tensor 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 stress tensor exhibits the expected trace anomaly. The renormalized stress tensor 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 stress tensor had been computed outside of the wall, whereas now we compute all components of the stress tensor in the interior of the wall. The full finite stress tensor 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).

  2. The solid phase stress tensor in porous media mechanics and the Hill-Mandel condition

    NASA Astrophysics Data System (ADS)

    Gray, William G.; Schrefler, Bernhard A.; Pesavento, Francesco

    2009-03-01

    An assessment of the stress tensors used currently for the modeling of partially saturated porous media is made which includes concepts like total stress, solid phase stress, and solid pressure. Thermodynamically constrained averaging theory is used to derive the solid phase stress tensor. It is shown that in the upscaling procedure the Hill conditions are satisfied, which is not trivial. The stress tensor is then compared to traditional stress measures. The physical meaning of two forms of solid pressure and of the Biot coefficient is clarified. Finally, a Bishop-Skempton like form of the stress tensor is obtained and a form of the total stress tensor that does not make use of the effective stress concept.

  3. Stress-tensor OPE in {N}=2 superconformal theories

    NASA Astrophysics Data System (ADS)

    Liendo, Pedro; Ramírez, Israel; Seo, Jihye

    2016-02-01

    We carry out a detailed superspace analysis of the OPE of two {N}=2 stress-tensor multiplets. Knowledge of the multiplets appearing in the expansion, together with the two-dimensional chiral algebra description of {N}=2 SCFTs, imply an analytic bound on the central charge c. This bound is valid for any {N}=2 SCFT regardless of its matter content and flavor symmetries, and is saturated by the simplest Argyres-Douglas fixed point. We also present a partial conformal block analysis for the scalar superconformal primary of the multiplet.

  4. Stress-energy tensor for trans-Planckian cosmology

    NASA Astrophysics Data System (ADS)

    Lemoine, Martin; Lubo, Musongela; Martin, Jérôme; Uzan, Jean-Philippe

    2002-01-01

    This article presents the derivation of the stress-energy tensor of a free scalar field with a general nonlinear dispersion relation in curved spacetime. This dispersion relation is used as a phenomelogical description of the short distance structure of spacetime following the conventional approach of trans-Planckian modes in black hole physics and in cosmology. This stress-energy tensor is then used to discuss both the equation of state of trans-Planckian modes in cosmology and the magnitude of their back reaction during inflation. It is shown that gravitational waves of trans-Planckian momenta but subhorizon frequencies cannot account for the form of cosmic vacuum energy density observed at present, contrary to a recent claim. The back reaction effects during inflation are confirmed to be important and generic for those dispersion relations that are liable to induce changes in the power spectrum of metric fluctuations. Finally, it is shown that in pure de Sitter inflation there is no modification of the power spectrum except for a possible magnification of its overall amplitude independently of the dispersion relation.

  5. Release of program Win-Tensor 4.0 for tectonic stress inversion: statistical expression of stress parameters

    NASA Astrophysics Data System (ADS)

    Delvaux, D.

    2012-04-01

    The Win-Tensor program is an interactive computer program for fracture analysis and crustal stress reconstruction, freely distributed to the scientific and academic community and widely used by structural geologists. It was developed with a constant feed-back from the users and is regularly upgraded. Version 4.0 released in January 2012 provides as a new feature the standard deviation of the horizontal stress axes (SHmax/SHmin) and the stress regime Index R'. The latter expresses the relative stress magnitudes and the nature of the vertical stress in a continuous scale, ranging from 1 to 3. Computation of the standard deviations is based on the examination of all possible reduced stress tensors for a particular stress solution obtained from the inversion of fault-slip or focal mechanism data. They are defined by combining the possible values of each individual stress axes (sigma 1, sigma 2, sigma 3) and the stress ratio R = (sigma2-sigma3)/(sigma1-sigma3). For each possible reduced tensors, the horizontal paleostress directions (SHmax/SHmin) and regime (R') are computed and the related 1 sigma standard deviations determined. This way, the 4 dimensions of the reduced stress tensor are reduced to a two dimensional expression with is commonly used to depict the horizontal stress trajectories as in the World Stress Map project. This procedure has been implemented for the three different methods for reconstructing the reduced stress tensors in Win-Tensor: PBT Right Dihedron and Rotational Optimisation. The advantages of this statistical expression of stress parameters are demonstrated using practical examples. Win-Tensor program can be downloaded from the Tensor web site: http://www.damiendelvaux.be/Tensor/tensor-index.html

  6. Metric fluctuations of an evaporating black hole from backreaction of stress tensor fluctuations

    SciTech Connect

    Hu, B. L.; Roura, Albert

    2007-12-15

    This paper delineates the first steps in a systematic quantitative study of the spacetime fluctuations induced by quantum fields in an evaporating black hole under the stochastic gravity program. The central object of interest is the noise kernel, which is the symmetrized two-point quantum correlation function of the stress tensor operator. As a concrete example we apply it to the study of the spherically symmetric sector of metric perturbations around an evaporating black hole background geometry. For macroscopic black holes we find that those fluctuations grow and eventually become important when considering sufficiently long periods of time (of the order of the evaporation time), but well before the Planckian regime is reached. In addition, the assumption of a simple correlation between the fluctuations of the energy flux crossing the horizon and far from it, which was made in earlier work on spherically symmetric induced fluctuations, is carefully scrutinized and found to be invalid. Our analysis suggests the existence of an infinite amplitude for the fluctuations when trying to localize the horizon as a three-dimensional hypersurface, as in the classical case, and, as a consequence, a more accurate picture of the horizon as possessing a finite effective width due to quantum fluctuations. This is supported by a systematic analysis of the noise kernel in curved spacetime smeared with different functions under different conditions; the details are collected in the appendixes. This case study shows a pathway for probing quantum metric fluctuations near the horizon and understanding their physical meaning.

  7. Theory of electron g-tensor in bulk and quantum-well semiconductors

    NASA Astrophysics Data System (ADS)

    Lau, Wayne H.; Flatte', Michael E.

    2004-03-01

    We present quantitative calculations for the electron g-tensors in bulk and quantum-well semiconductors based on a generalized P.p envelope function theory solved in a fourteen-band restricted basis set. The dependences of g-tensor 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-tensors 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 quantum-well semiconductors due to the additional electric quantization along the growth direction. The influence of quantum confinement on the electron g-tensors in QWs is studied by examining the dependence of electron g-tensors on well width. Excellent agreement between these calculated electron g-tensors 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).

  8. Stress tensor and focal mechanisms in the Dead Sea basin

    NASA Astrophysics Data System (ADS)

    Hofstetter, A.; Dorbath, C.; Dorbath, L.; Braeuer, B.; Weber, M. H.

    2015-12-01

    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 that occurred in the Dead Sea basin. The observed seismicity in the Dead Sea basin was divided into 9 regions according to the spatial distribution of the earthquakes and the known tectonic features. The large number of recording stations and the good 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 stress tensor. For 159 earthquakes out of the 494 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 stress axes are well constrained presenting minimal variability in the inversion of the data, which is in good agreement with the Arava fault on the eastern 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 sigma1 and sigma2 or the switching of sigma2 and sigma3as major horizontal stress directions. This observed switching of stress axes allows having dip-slip and normal mechanisms in a region that is dominated by strike-slip motion.

  9. Stress tensor and focal mechanisms in the Dead Sea basin

    NASA Astrophysics Data System (ADS)

    Hofstetter, A.; Dorbath, C.; Dorbath, L.; Braeuer, B.; Weber, M.

    2016-04-01

    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 stress tensor. 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 stress 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 stress directions. This observed switching of stress axes allows having dip-slip and normal mechanisms in a region that is dominated by strike-slip motion.

  10. Hadamard renormalization of the stress-energy tensor for a quantized scalar field in a general spacetime of arbitrary dimension

    SciTech Connect

    Decanini, Yves; Folacci, Antoine

    2008-08-15

    We develop the Hadamard renormalization of the stress-energy tensor for a massive scalar field theory defined on a general spacetime of arbitrary dimension. Our formalism could be helpful in treating some aspects of the quantum physics of extra spatial dimensions. More precisely, for spacetime dimensions up to six, we explicitly describe the Hadamard renormalization procedure and for spacetime dimensions from 7 to 11, we provide the framework permitting the interested reader to perform this procedure explicitly in a given spacetime. We complete our study (i) by considering the ambiguities of the Hadamard renormalization of the stress-energy tensor and the corresponding ambiguities for the trace anomaly, (ii) by providing the expressions of the gravitational counterterms involved in the renormalization process, and (iii) by discussing the connections between Hadamard renormalization and renormalization in the effective action. All our results are expanded on standard bases for Riemann polynomials constructed from group theoretical considerations and thus given on irreducible forms.

  11. Use of non-fault fractures in stress tensor reconstruction using the Mohr Circle with the Win-tensor program

    NASA Astrophysics Data System (ADS)

    Delvaux, Damien

    2016-04-01

    Paleostress inversion of geological fault-slip data is usually done using the directional part of the applied stress tensor 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 stress 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 stress 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-Tensor program, and tested it with natural and synthetic data sets from different stress 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

  12. Flavour fields in steady state: stress tensor and free energy

    NASA Astrophysics Data System (ADS)

    Banerjee, Avik; Kundu, Arnab; Kundu, Sandipan

    2016-02-01

    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 stress tensor 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.

  13. Improvement of stress-energy tensor using space-time symmetries

    NASA Astrophysics Data System (ADS)

    Bandyopadhyay, Akash

    2001-05-01

    In 1970 Callan, Coleman, and Jackiw found that it is always possible to improve the symmetric stress-energy tensor of a renormalizable relativistic field theory over (3+1)-dimensional flat space-time manifold. The improved stress-energy tensor defines the same field energy- momentum and angular momentum as the conventional tensor, and it is traceless for a non-interacting field theory when all coupling constants are physically dimensionless. The question for existence of an improved stress-energy tensor for a scale invariant relativistic field theory on a (1+1)-dimensional flat space-time manifold has been a long standing open problem for almost 30 years. In this thesis, I develop the weakest set of necessary and sufficient conditions for existence of a conserved symmetric traceless stress-energy tensor for a scale invariant relativistic field theory over a d-dimensional flat space-time manifold. This improved tensor, which defines the same conserved charges as the canonical tensor, has been explicitly constructed for arbitrary space-time dimensions including d = 2 intrinsically from the flat space-time field theory without coupling it with gravity. As an example, I derive the improved tensor of (1+1)- dimensional Liouville field theory. We discuss two remarkable results: (1)full conformal symmetry over the flat space-time is sufficient but not necessary for the existence of the improved tensor; (2)quite surprisingly, the improved stress-energy tensor exists in all space-time dimensions for a free massless Abelian U(1) gauge theory provided the gauge symmetry has been broken in favor of Lorentz gauge for d ≠ 2, 4.

  14. Performance Optimization of Tensor Contraction Expressions for Many Body Methods in Quantum Chemistry

    SciTech Connect

    Krishnamoorthy, Sriram; Bernholdt, David E; Pitzer, R. M.; Sadayappan, Ponnuswamy

    2009-01-01

    Complex tensor contraction expressions arise in accurate electronic structure models in quantum chemistry, such as the coupled cluster method. This paper addresses two complementary aspects of performance optimization of such tensor 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 tensor contraction expressions can result in a reduction of the total number of operations required to evaluate the tensor contractions. The first part of the paper describes an effective algorithm for operation minimization with common subexpression identification and demonstrates its effectiveness on tensor contraction expressions for coupled cluster equations. The second part of the paper highlights the importance of data layout transformation in the optimization of tensor 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 tensors is described, and experimental performance data is provided that demonstrates its effectiveness.

  15. Performance Optimization of Tensor Contraction Expressions for Many Body Methods in Quantum Chemistry

    SciTech Connect

    Hartono, Albert; Lu, Qingda; henretty, thomas; Krishnamoorthy, Sriram; zhang, huaijian; Baumgartner, Gerald; Bernholdt, David E.; Nooijen, Marcel; Pitzer, Russell M.; Ramanujam, J.; Sadayappan, Ponnuswamy

    2009-11-12

    Complex tensor contraction expressions arise in accurate electronic structure models in quantum chemistry, such as the coupled cluster method. This paper addresses two complementary aspects of performance optimization of such tensor 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 tensor contraction expressions can result in a reduction of the total number of operations required to evaluate the tensor contractions. The first part of the paper describes an effective algorithm for operation minimization with common subexpression identification and demonstrates its effectiveness on tensor contraction expressions for coupled cluster equations. The second part of the paper highlights the importance of data layout transformation in the optimization of tensor 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 tensors is described and experimental performance data is provided that demonstrates its effectiveness.

  16. Performance optimization of tensor contraction expressions for many-body methods in quantum chemistry.

    PubMed

    Hartono, Albert; Lu, Qingda; Henretty, Thomas; Krishnamoorthy, Sriram; Zhang, Huaijian; Baumgartner, Gerald; Bernholdt, David E; Nooijen, Marcel; Pitzer, Russell; Ramanujam, J; Sadayappan, P

    2009-11-12

    Complex tensor contraction expressions arise in accurate electronic structure models in quantum chemistry, such as the coupled cluster method. This paper addresses two complementary aspects of performance optimization of such tensor 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 tensor contraction expressions can result in a reduction of the total number of operations required to evaluate the tensor contractions. The first part of the paper describes an effective algorithm for operation minimization with common subexpression identification and demonstrates its effectiveness on tensor contraction expressions for coupled cluster equations. The second part of the paper highlights the importance of data layout transformation in the optimization of tensor 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 tensors is described, and experimental performance data is provided that demonstrates its effectiveness. PMID:19888780

  17. Stress tensor of a quark moving through N=4 thermal plasma

    SciTech Connect

    Friess, Joshua J.; Gubser, Steven S.; Michalogiorgakis, Georgios; Pufu, Silviu S.

    2007-05-15

    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 stress tensor in the boundary gauge theory. Components of the stress tensor 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.

  18. Approximate stress-energy tensor of the massless spin-1/2 field in Schwarzschild spacetime

    SciTech Connect

    Matyjasek, Jerzy

    2005-01-15

    The approximate stress-energy tensor of the conformally invariant massless spin-1/2 field in the Hartle-Hawking state in the Schwarzschild spacetime is constructed. It is shown that by solving the conservation equation in conformal space and utilizing the regularity conditions in a physical metric one obtains the stress-energy tensor that is in good agreement with the numerical calculations. The backreaction of the quantized field upon the spacetime metric is briefly discussed.

  19. Conservation laws and stress-energy-momentum tensors for systems with background fields

    SciTech Connect

    Gratus, Jonathan; Obukhov, Yuri N.; Tucker, Robin W.

    2012-10-15

    This article attempts to delineate the roles played by non-dynamical background structures and Killing symmetries in the construction of stress-energy-momentum tensors 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 stress-energy-momentum tensor derived from a Noether current and the Einstein-Hilbert stress-energy-momentum tensor 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 tensors particularly in the context of electrodynamics in media. These tensors 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 stress-energy-momentum tensors are emphasised. Black-Right-Pointing-Pointer The Abraham and Minkowski electromagnetic tensors 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.

  20. Flat-space holography and stress tensor of Kerr black hole

    NASA Astrophysics Data System (ADS)

    Baghchesaraei, Omid; Fareghbal, Reza; Izadi, Yousef

    2016-09-01

    We propose a stress tensor 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 stress tensor of the four-dimensional Kerr-AdS black hole. The proposed stress tensor 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 tensor 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.

  1. Effective gravitational wave stress-energy tensor in alternative theories of gravity

    SciTech Connect

    Stein, Leo C.; Yunes, Nicolas

    2011-03-15

    The inspiral of binary systems in vacuum is controlled by the stress-energy of gravitational radiation and any other propagating degrees of freedom. For gravitational waves, the dominant contribution is characterized by an effective stress-energy tensor at future null infinity. We employ perturbation theory and the short-wavelength approximation to compute this stress-energy tensor in a wide class of alternative theories. We find that this tensor is generally a modification of that first computed by Isaacson, where the corrections can dominate over the general relativistic term. In a wide class of theories, however, these corrections identically vanish at asymptotically flat, future, null infinity, reducing the stress-energy tensor to Isaacson's. We exemplify this phenomenon by first considering dynamical Chern-Simons modified gravity, which corrects the action via a scalar field and the contraction of the Riemann tensor and its dual. We then consider a wide class of theories with dynamical scalar fields coupled to higher-order curvature invariants and show that the gravitational wave stress-energy tensor still reduces to Isaacson's. The calculations presented in this paper are crucial to perform systematic tests of such modified gravity theories through the orbital decay of binary pulsars or through gravitational wave observations.

  2. Short distance and initial state effects in inflation: Stress tensor and decoherence

    SciTech Connect

    Anderson, Paul R.; Molina-Paris, Carmen; Mottola, Emil

    2005-08-15

    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 quantum scalar fields in Robertson-Walker (RW) spacetimes, subject to the requirement that their ultraviolet behavior be consistent with renormalizability of the covariantly conserved stress tensor 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 stress tensor 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.

  3. Scalar and tensor perturbations in loop quantum cosmology: high-order corrections

    SciTech Connect

    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

    2015-10-01

    Loop quantum 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 quantum 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 quantum corrections. We calculate the power spectra, spectral indices, and running of the spectral indices for both scalar and tensor perturbations, whereby the tensor-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 tensor spectra exhibit a deviation from the usual shape at large scales. Then, using the Planck, BAO and SN data we obtain new constraints on quantum gravitational effects from LQC corrections, and find that such effects could be within the detection of the forthcoming experiments.

  4. High-efficiency quantum steganography based on the tensor product of Bell states

    NASA Astrophysics Data System (ADS)

    Xu, ShuJiang; Chen, XiuBo; Niu, XinXin; Yang, YiXian

    2013-09-01

    In this paper, we first propose a hidden rule among the secure message, the initial tensor product of two Bell states and the final tensor product when respectively applying local unitary transformations to the first particle of the two initial Bell states, and then present a high-efficiency quantum steganography protocol under the control of the hidden rule. In the proposed quantum steganography scheme, a hidden channel is established to transfer a secret message within any quantum secure direct communication (QSDC) scheme that is based on 2-level quantum states and unitary transformations. The secret message hiding/unhiding process is linked with the QSDC process only by unitary transformations. To accurately describe the capacity of a steganography scheme, a quantitative measure, named embedding efficiency, is introduced in this paper. The performance analysis shows that the proposed steganography scheme achieves a high efficiency as well as a good imperceptibility. Moreover, it is shown that this scheme can resist all serious attacks including the intercept-resend attack, measurement-resend attack, auxiliary particle attack and even the Denial of Service attack. To improve the efficiency of the proposed scheme, the hidden rule is extended based on the tensor product of multiple Bell states.

  5. Vacuum stress-energy tensor of a massive scalar field in a wormhole spacetime

    SciTech Connect

    Bezerra, V. B.; Bezerra de Mello, E. R.; Khusnutdinov, N. R.; Sushkov, S. V.

    2010-04-15

    The vacuum average value of the stress-energy tensor 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 tensor does not violate the null energy condition near the throat. Therefore, the vacuum polarization cannot self-consistently support the wormhole.

  6. Positive Tensor Network Approach for Simulating Open Quantum Many-Body Systems.

    PubMed

    Werner, A H; Jaschke, D; Silvi, P; Kliesch, M; Calarco, T; Eisert, J; Montangero, S

    2016-06-10

    Open quantum many-body systems play an important role in quantum 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 quantum many-body dynamics using tensor networks. It is based on representing mixed quantum 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 quantum systems ranging from few to many bodies.

  7. Positive Tensor Network Approach for Simulating Open Quantum Many-Body Systems

    NASA Astrophysics Data System (ADS)

    Werner, A. H.; Jaschke, D.; Silvi, P.; Kliesch, M.; Calarco, T.; Eisert, J.; Montangero, S.

    2016-06-01

    Open quantum many-body systems play an important role in quantum 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 quantum many-body dynamics using tensor networks. It is based on representing mixed quantum 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 quantum systems ranging from few to many bodies.

  8. Simple Derivation of the Maxwell Stress Tensor and Electrostrictive Effects in Crystals

    ERIC Educational Resources Information Center

    Juretschke, H. J.

    1977-01-01

    Shows that local equilibrium and energy considerations in an elastic dielectric crystal lead to a simple derivation of the Maxwell stress tensor in anisotropic dielectric solids. The resulting equilibrium stress-strain relations are applied to determine the deformations of a charged parallel plate capacitor. (MLH)

  9. The non-uniqueness of the atomistic stress tensor and its relationship to the generalized Beltrami representation

    NASA Astrophysics Data System (ADS)

    Admal, Nikhil Chandra; Tadmor, E. B.

    2016-08-01

    The non-uniqueness of the atomistic stress tensor is a well-known issue when defining continuum fields for atomistic systems. In this paper, we study the non-uniqueness of the atomistic stress tensor stemming from the non-uniqueness of the potential energy representation. In particular, we show using rigidity theory that the distribution associated with the potential part of the atomistic stress tensor can be decomposed into an irrotational part that is independent of the potential energy representation, and a traction-free solenoidal part. Therefore, we have identified for the atomistic stress tensor a discrete analog of the continuum generalized Beltrami representation (a version of the vector Helmholtz decomposition for symmetric tensors). We demonstrate the validity of these analogies using a numerical test. A program for performing the decomposition of the atomistic stress tensor called MDStressLab is available online at

  10. Multidimensional supersymmetric quantum mechanics: spurious states for the tensor sector two Hamiltonian.

    PubMed

    Chou, Chia-Chun; Kouri, Donald J

    2013-04-25

    We show that there exist spurious states for the sector two tensor Hamiltonian in multidimensional supersymmetric quantum mechanics. For one-dimensional supersymmetric quantum 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 quantum 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 quantum system and also generate several spurious states for a two-dimensional anharmonic oscillator system and for the hydrogen atom.

  11. Multidimensional supersymmetric quantum mechanics: spurious states for the tensor sector two Hamiltonian.

    PubMed

    Chou, Chia-Chun; Kouri, Donald J

    2013-04-25

    We show that there exist spurious states for the sector two tensor Hamiltonian in multidimensional supersymmetric quantum mechanics. For one-dimensional supersymmetric quantum 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 quantum 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 quantum system and also generate several spurious states for a two-dimensional anharmonic oscillator system and for the hydrogen atom. PMID:23531015

  12. Determination of the residual stress tensor in textured zirconium alloy by neutron diffraction

    NASA Astrophysics Data System (ADS)

    Sumin, V. V.; Papushkin, I. V.; Vasin, R. N.; Venter, А. M.; Balagurov, А. М.

    2012-02-01

    Results of neutron diffraction studies of crystallographic texture and residual stress tensor components in cold-worked and annealed cylindrical components made from E-110 zirconium alloy are presented. Those components are used as plugs in the fuel elements of the VVER-type reactors; the resident residual stresses influence the durability and safety of the fuel elements. The experiments were carried out on the neutron diffractometers at Dubna (the IBR-2 pulsed reactor) and Berlin Helmholtz-Zentrum (the BER II research reactor). It is shown that the samples have fiber texture that is changed considerably with annealing. The type I residual stress tensors for both samples were calculated by the BulkPathGEO model. The cold worked component has 136-166 MPa tensile residual stress in the radial direction and zero stress along the axial direction. Residual stress values in the annealed component are close to zero.

  13. Green-Naghdi rate of the Kirchhoff stress and deformation rate: the elasticity tensor

    NASA Astrophysics Data System (ADS)

    Bellini, Chiara; Federico, Salvatore

    2015-06-01

    The elasticity tensor providing the power-conjugation of the Green-Naghdi rate of the Kirchhoff stress 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 tensor 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 tensor 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 tensor 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 tensor with the symmetric deformation rate tensor. In order to avoid carrying this unnecessary skew-symmetric contribution in the computations, we employ a tensor identity that naturally symmetrises the second pair of feet of the elasticity tensor. We demonstrated the validity and robustness of the implementation of the user-defined material based on this tensor 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.

  14. Theoretical study of lithium ionic conductors by electronic stress tensor density and electronic kinetic energy density.

    PubMed

    Nozaki, Hiroo; Fujii, Yosuke; Ichikawa, Kazuhide; Watanabe, Taku; Aihara, Yuichi; Tachibana, Akitomo

    2016-07-01

    We analyze the electronic structure of lithium ionic conductors, Li3PO4 and Li3PS4, using the electronic stress tensor density and kinetic energy density with special focus on the ionic bonds among them. We find that, as long as we examine the pattern of the eigenvalues of the electronic stress tensor density, we cannot distinguish between the ionic bonds and bonds among metalloid atoms. We then show that they can be distinguished by looking at the morphology of the electronic interface, the zero surface of the electronic kinetic energy density. © 2016 Wiley Periodicals, Inc.

  15. Elliptic Relaxation of a Tensor Representation for the Redistribution Terms in a Reynolds Stress Turbulence Model

    NASA Technical Reports Server (NTRS)

    Carlson, J. R.; Gatski, T. B.

    2002-01-01

    A formulation to include the effects of wall proximity in a second-moment closure model that utilizes a tensor representation for the redistribution terms in the Reynolds stress equations is presented. The wall-proximity effects are modeled through an elliptic relaxation process of the tensor expansion coefficients that properly accounts for both correlation length and time scales as the wall is approached. Direct numerical simulation data and Reynolds stress solutions using a full differential approach are compared for the case of fully developed channel flow.

  16. A stress tensor and QTAIM perspective on the substituent effects of biphenyl subjected to torsion.

    PubMed

    Jiajun, D; Maza, J R; Xu, Y; Xu, T; Momen, R; Kirk, S R; Jenkins, S

    2016-10-30

    The Quantum Theory of Atoms in Molecules (QTAIM) defines quantities in 3D space that can be easily obtained from routine quantum chemical calculations. The present investigation shows that local properties can be related quantitatively to measures traditionally connected to experimental data, such as Hammett constants. We consider the specific case of substituted biphenyl to quantify the effects of a torsion φ, 0.0° ≤ φ ≤ 180.0°, of the C-C bond linking the two phenyl rings for C12 H9 -x, where x = N(CH3 )2 , NH2 , CH3 , CHO, CN, NO2, on the entire molecule. QTAIM interpreted Hammett constants, aΔH(rb ) are introduced and constructed using the difference between the H(rb ) value of C12 H9 -x and the C12 H9 -H, biphenyl which is the reference molecule, with a constant of proportionality a. This investigation unexpectedly yields very good or good agreement for the x groups with the Hammett para-, meta-, and ortho-substituent constants and is checked against para-substituted benzene. We then proceed to present the interpreted substituent constants of seven new biphenyl substituent groups, where tabulated Hammett substituent constant values are not available; y = SiH3 , ZnCl, COOCH3 , SO2 NH2 , SO2 OH, COCl, CB3 . Consistency is found for the QTAIM interpreted biphenyl substituent constants of the seven new groups y independently using the stress tensor polarizability Pσ . In addition, a selection of future applications is discussed that highlight the usefulness of this approach. © 2016 Wiley Periodicals, Inc. PMID:27546220

  17. Variational tensor network renormalization in imaginary time: Two-dimensional quantum compass model at finite temperature

    NASA Astrophysics Data System (ADS)

    Czarnik, Piotr; Dziarmaga, Jacek; Oleś, Andrzej M.

    2016-05-01

    Progress in describing thermodynamic phase transitions in quantum systems is obtained by noticing that the Gibbs operator e-β H for a two-dimensional (2D) lattice system with a Hamiltonian H can be represented by a three-dimensional tensor network, the third dimension being the imaginary time (inverse temperature) β . Coarse graining the network along β results in a 2D projected entangled-pair operator (PEPO) with a finite bond dimension D . The coarse graining is performed by a tree tensor network of isometries. The isometries are optimized variationally, taking into account full tensor environment, to maximize the accuracy of the PEPO. The algorithm is applied to the isotropic quantum compass model on an infinite square lattice near a symmetry-breaking phase transition at finite temperature. From the linear susceptibility in the symmetric phase and the order parameter in the symmetry-broken phase, the critical temperature is estimated at Tc=0.0606 (4 ) J , where J is the isotropic coupling constant between S =1/2 pseudospins.

  18. Reliability of methods to separate stress tensors from heterogeneous fault-slip data

    NASA Astrophysics Data System (ADS)

    Liesa, Carlos L.; Lisle, Richard J.

    2004-03-01

    The reliability of methods for separating palaeostress tensors from heterogeneous fault-slip data is evaluated. The methods of Etchecopar et al. (1981), Yamaji (2000), and the cluster procedure of Nemcok and Lisle (1995) are assessed but the results can probably be extrapolated to other methods based on similar assumptions. Heterogeneous fault-slip data sets, artificially generated by mixing two natural homogeneous data sets, have been used to evaluate both the role of the relative dominance (in number of faults taken from each tensor) and the difference between the parent tensors. The results obtained from a natural heterogeneous data set were compared with additional field data to evaluate and constrain the tensor separation process as well. Results suggest that attempts to devise a fully automatic separation procedure for distinguishing homogeneous data sets from heterogeneous ones will be unsuccessful because the researcher will always be required to take some part in the correct choice of the tensors. In this sense, additional structural data such as geometrical characteristics of the faults (e.g. conjugate or quasi-conjugate Andersonian systems), stylolites or tension gashes will be very useful for the correct separation of stress tensors from fault-slip data.

  19. Slow-roll inflation in loop quantum cosmology of scalar-tensor theories of gravity

    NASA Astrophysics Data System (ADS)

    Han, Yu

    2015-07-01

    The slow-roll inflation of scalar-tensor theories (STTs) of gravity in the context of loop quantum 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 tensor-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.

  20. Replica exchange molecular dynamics optimization of tensor network states for quantum many-body systems.

    PubMed

    Liu, Wenyuan; Wang, Chao; Li, Yanbin; Lao, Yuyang; Han, Yongjian; Guo, Guang-Can; Zhao, Yong-Hua; He, Lixin

    2015-03-01

    Tensor network states (TNS) methods combined with the Monte Carlo (MC) technique have been proven a powerful algorithm for simulating quantum many-body systems. However, because the ground state energy is a highly non-linear function of the tensors, it is easy to get stuck in local minima when optimizing the TNS of the simulated physical systems. To overcome this difficulty, we introduce a replica-exchange molecular dynamics optimization algorithm to obtain the TNS ground state, based on the MC sampling technique, by mapping the energy function of the TNS to that of a classical mechanical system. The method is expected to effectively avoid local minima. We make benchmark tests on a 1D Hubbard model based on matrix product states (MPS) and a Heisenberg J1-J2 model on square lattice based on string bond states (SBS). The results show that the optimization method is robust and efficient compared to the existing results.

  1. Notes on Translational and Rotational Properties of Tensor Fields in Relativistic Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    Dvoeglazov, V. V.

    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 tensor 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 quantum 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 tensor 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 quantum mechanics. The relations of this theory with the scalar-tensor theories of gravitation and f(R) are discussed. Particular attention has been paid to the correct definitions of the energy-momentum tensor 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.

  2. Parameterization of subgrid-scale stress by the velocity gradient tensor

    NASA Technical Reports Server (NTRS)

    Lund, Thomas S.; Novikov, E. A.

    1993-01-01

    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 stress is a function of the strain and rotation rate tensors. Extensions of the Caley-Hamilton theorem can then be used to write the assumed functional dependence explicitly in the form of a tensor 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.

  3. Separation of deviatoric stress tensors from heterogeneous calcite twin data using a statistical mixture model

    NASA Astrophysics Data System (ADS)

    Yamaji, Atsushi

    2016-04-01

    It is essential for the techniques of paleostress analysis to separate stresses 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 stress tensors, but also estimates the number of tensors 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 stress 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 stress tensor. 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 stresses 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 stress tensors that were assumed to generate the data sets. The natural data were inverted to give two stresses that appeared appropriate for the tectonic setting of the area where the data were obtained.

  4. Efficient tree tensor network states (TTNS) for quantum chemistry: Generalizations of the density matrix renormalization group algorithm

    NASA Astrophysics Data System (ADS)

    Nakatani, Naoki; Chan, Garnet Kin-Lic

    2013-04-01

    We investigate tree tensor network states for quantum chemistry. Tree tensor 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 tensor network states encode a tree entanglement structure, allowing for a more flexible description of general molecules. We describe an optimal tree tensor network state algorithm for quantum 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 tensor 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 tensor 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 tensor network states correlates 110 electrons in 110 active orbitals.

  5. Efficient tree tensor network states (TTNS) for quantum chemistry: generalizations of the density matrix renormalization group algorithm.

    PubMed

    Nakatani, Naoki; Chan, Garnet Kin-Lic

    2013-04-01

    We investigate tree tensor network states for quantum chemistry. Tree tensor 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 tensor network states encode a tree entanglement structure, allowing for a more flexible description of general molecules. We describe an optimal tree tensor network state algorithm for quantum 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 tensor 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 tensor 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 tensor network states correlates 110 electrons in 110 active orbitals.

  6. g tensor modulation resonance and single-spin manipulation in semiconductor quantum dots

    NASA Astrophysics Data System (ADS)

    Pingenot, Joseph

    2005-03-01

    We explore how electric fields can be used to drive single spin resonance in quantum dots without AC magnetic fields. We calculate the g tensor for a single electron in a semiconductor quantum dot as a function of electric field along the growth direction of the dot. The calculations are based on an eight-band envelope-function formalism[1]. The growth-direction g factor is relatively insensitive to this electric field, but for InAs/GaAs dots with transition energies around 1.2 eV the in-plane g factor changes by 20% for an electric field of 150kV/cm. For a DC magnetic field oriented at 45 degrees to the growth direction the spin precession axis for an electron changes by 6 degrees from zero electric field to 150 kV/cm. Thus an AC pseudo-magnetic field almost 10% the size of the DC magnetic field can be generated. This is sufficient to drive g-tensor modulation resonance[2] in the dot and perform single-spin manipulation. 1. C. E. Pryor and M. E. Flatt'e, cond-mat/0410678. 2. Y. Kato, et al., Science 299, 1201 (2003).

  7. Altimetry data and the elastic stress tensor of subduction zones

    NASA Technical Reports Server (NTRS)

    Caputo, Michele

    1987-01-01

    The maximum shear stress (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 stress 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 stress for both cases, and is located at a depth related to the diameter of the surface mass anomaly.

  8. Stress tensor for GYM in 4 p dimensions and viability of GYM-Higgs in four dimensions

    NASA Astrophysics Data System (ADS)

    O'Brien, G. M.; Tchrakian, D. H.

    1986-02-01

    We present the stress tensor for GYM systems in 4 p dimensions and give a method to compute this tensor 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.

  9. Calculations of the stress tensor under Symmetric cylindrical shock wave loading

    SciTech Connect

    Chikhradze, N. M.; Lomidze, I.; Marquis, F. D. S.; Staudhammer, Karl P.; Japaridze, L. A.; Peikrishvili, A. B.

    2001-01-01

    The calculation of the components of the stress tensor 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 stress-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 stress tensor and the solution of this set, for this specific case, gives all the components of the stress tensor.

  10. Stress-energy tensor correlators in N-dimensional hot flat spaces via the generalized zeta-function method

    NASA Astrophysics Data System (ADS)

    Cho, H. T.; Hu, B. L.

    2012-09-01

    We calculate the expectation values of the stress-energy bitensor defined at two different spacetime points x, x‧ of a massless, minimally coupled scalar field with respect to a quantum state at finite temperature T in a flat N-dimensional spacetime by means of the generalized zeta-function method. These correlators, also known as the noise kernels, give the fluctuations of energy and momentum density of a quantum field which are essential for the investigation of the physical effects of negative energy density in certain spacetimes or quantum states. They also act as the sources of the Einstein-Langevin equations in stochastic gravity which one can solve for the dynamics of metric fluctuations as in spacetime foams. In terms of constitutions these correlators are one rung above (in the sense of the correlation—BBGKY or Schwinger-Dyson—hierarchies) the mean (vacuum and thermal expectation) values of the stress-energy tensor which drive the semiclassical Einstein equation in semiclassical gravity. The low- and the high-temperature expansions of these correlators are also given here: at low temperatures, the leading order temperature dependence goes like TN while at high temperatures they have a T2 dependence with the subleading terms exponentially suppressed by e-T. We also discuss the singular behavior of the correlators in the x‧ → x coincident limit as was done before for massless conformal quantum fields. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical in honour of Stuart Dowker’s 75th birthday devoted to ‘Applications of zeta functions and other spectral functions in mathematics and physics’.

  11. Characteristics of the residual stress tensor as a function of length scale in simulations of stably stratified turbulence

    NASA Astrophysics Data System (ADS)

    de Braganca Alves, Felipe Augusto; de Bruyn Kops, Stephen

    2015-11-01

    A priori analysis of the relationships between the deviatoric residual stress tensor τr and kinematic tensors is made for stably stratified Boussinesq turbulence. Two data sets from direct numerical simulation are used for the analyses: the decaying Taylor-Green simulations of Riley and de Bruyn Kops (2003), and the forced homogeneous stratified turbulence simulations of Almalkie and de Bruyn Kops (2012) resolved on up to 8192 × 8192 × 4096 grid points. The data sets are filtered using a Gaussian kernel with filter widths up to the buoyancy scale. Through tensor decomposition theorems described in Thompson et al. (2010) the relationship between the strain rate tensor and the residual stress is quantified for each filter width and case. This is also done for the tensor formed by the Lie product between the strain rate and rate of rotation tensors. The role of each tensor, seen as a part of the residual stress tensor, is analyzed, in particular with respect to filtered kinetic energy budget equation. The authors acknowledge the support from CAPES grant BEX 13649/13-2, DoD HPCMP Frontier Project FPCFD-FY14-007 and ONR grant N00014-15-1-2248.

  12. Proton chemical shift tensors determined by 3D ultrafast MAS double-quantum NMR spectroscopy.

    PubMed

    Zhang, Rongchun; Mroue, Kamal H; Ramamoorthy, Ayyalusamy

    2015-10-14

    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-quantum (SQ) chemical shift correlation experiment. Herein, we propose a three-dimensional (3D) (1)H double-quantum (DQ) chemical shift/CSA/SQ chemical shift correlation experiment to extract the CS tensors of proton sites whose signals are not well resolved along the single-quantum 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 tensors, both tensors 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

  13. Proton chemical shift tensors determined by 3D ultrafast MAS double-quantum NMR spectroscopy

    SciTech Connect

    Zhang, Rongchun; Mroue, Kamal H.; Ramamoorthy, Ayyalusamy

    2015-10-14

    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-quantum (SQ) chemical shift correlation experiment. Herein, we propose a three-dimensional (3D) {sup 1}H double-quantum (DQ) chemical shift/CSA/SQ chemical shift correlation experiment to extract the CS tensors of proton sites whose signals are not well resolved along the single-quantum 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 tensors, both tensors can be extracted by numerical fitting. We believe that this robust and elegant single-channel proton-based 3D experiment provides useful atomistic

  14. The antiferromagnetic cross-coupled spin ladder: Quantum fidelity and tensor networks approach

    NASA Astrophysics Data System (ADS)

    Chen, Xi-Hao; Cho, Sam Young; Zhou, Huan-Qiang; Batchelor, Murray T.

    2016-05-01

    We investigate the phase diagram of the cross-coupled Heisenberg spin ladder with antiferromagnetic couplings. For this model, the results for the existence of the columnar dimer phase, which was predicted on the basis of weak coupling field theory renormalization group arguments, have been conflicting. The numerical work on this model has been based on various approaches, including exact diagonalization, series expansions and density-matrix renormalization group calculations. Using the recently-developed tensor network states and groundstate fidelity approach for quantum spin ladders, we find no evidence for the existence of the columnar dimer phase. We also provide an argument based on the symmetry of the Hamiltonian, which suggests that the phase diagram for antiferromagnetic couplings consists of a single line separating the rung-singlet and the Haldane phases.

  15. Reduced Stress Tensor and Dissipation and the Transport of Lamb Vector

    NASA Technical Reports Server (NTRS)

    Wu, Jie-Zhi; Zhou, Ye; Wu, Jian-Ming

    1996-01-01

    We develop a methodology to ensure that the stress tensor, 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 stress model can always be replaced by a reduced one before putting it into computation. Furthermore, we show how the modeling of Reynolds stress tensor 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 stress transport equation.

  16. Method for estimating the stress field from seismic moment tensor data based on the flow rule in plasticity theory

    NASA Astrophysics Data System (ADS)

    Matsumoto, S.

    2016-09-01

    The stress field is a key factor controlling earthquake occurrence and crustal evolution. In this study, we propose an approach for determining the stress field in a region using seismic moment tensors, based on the classical equation in plasticity theory. Seismic activity is a phenomenon that relaxes crustal stress 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 tensor is proportional to the deviatoric stress tensor. Simple mathematical manipulation enables the development of an inversion method for estimating the stress field in a region. The method is tested on shallow earthquakes occurring on Kyushu Island, Japan.

  17. Spin-S kagome quantum antiferromagnets in a field with tensor networks

    NASA Astrophysics Data System (ADS)

    Picot, Thibaut; Ziegler, Marc; Orús, Román; Poilblanc, Didier

    2016-02-01

    Spin-S Heisenberg quantum antiferromagnets on the kagome lattice offer, when placed in a magnetic field, a fantastic playground to observe exotic phases of matter with (magnetic analogs of) superfluid, charge, bond, or nematic orders, or a coexistence of several of the latter. In this context, we have obtained the (zero-temperature) phase diagrams up to S =2 directly in the thermodynamic limit owing to infinite projected entangled pair states, a tensor network numerical tool. We find incompressible phases characterized by a magnetization plateau versus field and stabilized by spontaneous breaking of point group or lattice translation symmetry(ies). The nature of such phases may be semiclassical, as the plateaus at the 1/3th ,(1-2/9S)th, and (1-1/9S)th of the saturated magnetization (the latter followed by a macroscopic magnetization jump), or fully quantum as the spin-1/2 1/9 plateau exhibiting a coexistence of charge and bond orders. Upon restoration of the spin rotation U (1 ) symmetry, a finite compressibility appears, although lattice symmetry breaking persists. For integer spin values we also identify spin gapped phases at low enough fields, such as the S =2 (topologically trivial) spin liquid with no symmetry breaking, neither spin nor lattice.

  18. Full elastic strain and stress tensor measurements from individual dislocation cells in copper through-Si vias

    SciTech Connect

    Levine, Lyle E.; Okoro, Chukwudi A.; Xu, Ruqing

    2015-09-30

    We report non-destructive measurements of the full elastic strain and stress tensors 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 tensors 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 tensor and stress tensor components.

  19. Full elastic strain and stress tensor measurements from individual dislocation cells in copper through-Si vias

    DOE PAGESBeta

    Levine, Lyle E.; Okoro, Chukwudi A.; Xu, Ruqing

    2015-09-30

    We report non-destructive measurements of the full elastic strain and stress tensors 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 tensors 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 tensor and stress tensor components.« less

  20. Full elastic strain and stress tensor measurements from individual dislocation cells in copper through-Si vias

    PubMed Central

    Levine, Lyle E.; Okoro, Chukwudi; Xu, Ruqing

    2015-01-01

    Nondestructive measurements of the full elastic strain and stress tensors 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 tensors 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 tensor and stress tensor components. PMID:26594371

  1. Preface to the special issue on "Regional moment tensors and stress field in South and Central America"

    NASA Astrophysics Data System (ADS)

    Audemard, Franck; Zahradnik, Jiri; Assumpção, Marcelo

    2016-11-01

    This special issue follows from the Symposium "Regional Moment Tensor 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 tensors, focal mechanisms and the stress field in Central and South America. The study areas of each paper are indicated in the index Map of Fig. 1.

  2. Geomechanical simulation of the stress tensor rotation caused by injection of cold water in a deep geothermal reservoir

    NASA Astrophysics Data System (ADS)

    Jeanne, Pierre; Rutqvist, Jonny; Dobson, Patrick F.; Garcia, Julio; Walters, Mark; Hartline, Craig; Borgia, Andrea

    2015-12-01

    We present a three-dimensional thermohydromechanical numerical study of the evolution and distribution of the stress tensor 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 stress regime, we calculated local changes in the stress regime around injection wells. Our results were compared with previously published studies in which the stress state was inferred from inverting the focal plane mechanism of seismic events. Our main finding is that changes in stress tensor 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 stress reduction is larger and propagates far below the injection well. At the same time, the horizontal stress increases, mostly because of stress redistribution below and above the cooling area. These two phenomena cause the rotation of the stress tensor and the appearance of a strike-slip regime above, inside, and below the cooling area. The cooling and the associated rotation of the stress regime can play a significant role in the observed long-term deepening of the microseismicity below active injection wells.

  3. Quantum-gravitational effects on gauge-invariant scalar and tensor perturbations during inflation: The de Sitter case

    NASA Astrophysics Data System (ADS)

    Brizuela, David; Kiefer, Claus; Krämer, Manuel

    2016-05-01

    We present detailed calculations for quantum-gravitational corrections to the power spectra of gauge-invariant scalar and tensor 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 quantum-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.

  4. The signature of the magnetorotational instability in the Reynolds and Maxwell stress tensors in accretion discs

    NASA Astrophysics Data System (ADS)

    Pessah, Martin E.; Chan, Chi-Kwan; Psaltis, Dimitrios

    2006-10-01

    The magnetorotational instability is thought to be responsible for the generation of magnetohydrodynamic turbulence that leads to enhanced outward angular momentum transport in accretion discs. Here, we present the first formal analytical proof showing that, during the exponential growth of the instability, the mean (averaged over the disc scaleheight) Reynolds stress is always positive, the mean Maxwell stress is always negative, and hence the mean total stress is positive and leads to a net outward flux of angular momentum. More importantly, we show that the ratio of the Maxwell to the Reynolds stresses during the late times of the exponential growth of the instability is determined only by the local shear and does not depend on the initial spectrum of perturbations or the strength of the seed magnetic field. Even though we derived this property of the stress tensors for the exponential growth of the instability in incompressible flows, numerical simulations of shearing boxes show that this characteristic is qualitatively preserved under more general conditions, even during the saturated turbulent state generated by the instability.

  5. Critical study and discrimination of different formulations of electromagnetic force density and consequent stress tensors inside matter

    NASA Astrophysics Data System (ADS)

    Jazayeri, Amir M.; Mehrany, Khashayar

    2014-04-01

    By examination of the exerted electromagnetic (EM) force on boundary of an object in a few examples, we look into the compatibility of the stress tensors 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 stress tensor accords with special relativity. The Minkowski sress tensor is also consistent with special relativity. It is worth noting that the mathematical expression of the Minkowski stress tensor can be quite different from the well-known form of this stress tensor in the literature. We show that the Einstein-Laub stress tensor 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.

  6. On universality of stress-energy tensor correlation functions in supergravity [rapid communication

    NASA Astrophysics Data System (ADS)

    Buchel, Alex

    2005-03-01

    Using the Minkowski space AdS/CFT prescription we explicitly compute in the low-energy limit the two-point correlation function of the boundary stress-energy tensor 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.

  7. Renormalized stress tensor in Kerr space-time: Numerical results for the Hartle-Hawking vacuum

    SciTech Connect

    Duffy, Gavin; Ottewill, Adrian C.

    2008-01-15

    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 stress tensor 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.

  8. Crustal stress field in the Greek region inferred from inversion of moment tensor solutions

    NASA Astrophysics Data System (ADS)

    Konstantinou, Konstantinos; Mouslopoulou, Vasiliki; Liang, Wen-Tzong; Heidbach, Oliver; Oncken, Onno; Suppe, John

    2016-04-01

    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 tensor databases in order to extract focal mechanism solutions that will be used to infer crustal stresses 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 stress inversion over a grid whose node spacing is 0.35 degrees for the purpose of recovering the three principal stress axes and the stress 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 stress field model is then compared to the GPS-derived strain field revealing an excellent agreement between the two datasets. Additionally, maximum and minimum stress 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.

  9. Generalized Galileons: All scalar models whose curved background extensions maintain second-order field equations and stress tensors

    SciTech Connect

    Deffayet, C.; Deser, S.; Esposito-Farese, G.

    2009-09-15

    We extend to curved backgrounds all flat-space scalar field models that obey purely second-order equations, while maintaining their second-order dependence on both field and metric. This extension simultaneously restores to second order the, originally higher derivative, stress tensors as well. The process is transparent and uniform for all dimensions.

  10. Tensor numerical methods in quantum chemistry: from Hartree-Fock to excitation energies.

    PubMed

    Khoromskaia, Venera; Khoromskij, Boris N

    2015-12-21

    We resume the recent successes of the grid-based tensor 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 tensor calculus for the 3D Hartree potential using 1D complexity operations, and have evolved to entirely grid-based tensor-structured 3D Hartree-Fock eigenvalue solver. It benefits from tensor 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 tensor 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 tensor-structured numerical quadratures. The tensor 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 tensor-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 tensor 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. PMID:26016539

  11. Body versus surface forces in continuum mechanics: Is the Maxwell stress tensor a physically objective Cauchy stress?

    NASA Astrophysics Data System (ADS)

    Rinaldi, Carlos; Brenner, Howard

    2002-03-01

    The Maxwell stress tensor (MST) TM 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 fM =def. ∇.TM, where fM(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 TM is not uniquely defined via the preceding relationship from knowledge of fM, we point out in this paper that the interpretation of TM as being a physical stress 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 stresses 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.

  12. Tensor numerical methods in quantum chemistry: from Hartree-Fock to excitation energies

    NASA Astrophysics Data System (ADS)

    Khoromskaia, Venera; Khoromskij, Boris N.

    We resume the recent successes of the grid-based tensor 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, led to entirely grid-based tensor-structured 3D Hartree-Fock eigenvalue solver. It benefits from tensor 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\\times n\\times n $ Cartesian grids. The algorithm for calculating TEI tensor in a form of the Cholesky decomposition is based on multiple factorizations using algebraic 1D ``density fitting`` scheme. The basis functions are not restricted to separable Gaussians, since the analytical integration is substituted by high-precision tensor-structured numerical quadratures. The tensor approaches to post-Hartree-Fock calculations for the MP2 energy correction and for the Bethe-Salpeter excited states, based on using low-rank factorizations and the reduced basis method, were recently introduced. Another direction is related to the recent attempts to develop a tensor-based Hartree-Fock numerical scheme for finite lattice-structured systems, where one of the numerical challenges is the summation of electrostatic potentials of a large number of nuclei. The 3D grid-based tensor method for calculation of a potential sum on a $L\\times L\\times L$ 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.

  13. Stueckelberg massive electromagnetism in curved spacetime: Hadamard renormalization of the stress-energy tensor and the Casimir effect

    NASA Astrophysics Data System (ADS)

    Belokogne, Andrei; Folacci, Antoine

    2016-02-01

    We discuss Stueckelberg massive electromagnetism on an arbitrary four-dimensional curved spacetime and, in particular, (i) the gauge invariance of the classical theory and its covariant quantization; (ii) the wave equations for the massive spin-1 field Aμ , for the auxiliary Stueckelberg scalar field Φ and for the ghost fields C and C*; (iii) Ward identities; (iv) the Hadamard representation of the various Feynman propagators and the covariant Taylor series expansions of the corresponding coefficients. This permits us to construct, for a Hadamard quantum state, the expectation value of the renormalized stress-energy tensor associated with the Stueckelberg theory. We provide two alternative but equivalent expressions for this result. The first one is obtained by removing the contribution of the "Stueckelberg ghost" Φ and only involves state-dependent and geometrical quantities associated with the massive vector field Aμ. The other one involves contributions coming from both the massive vector field and the auxiliary Stueckelberg scalar field, and it has been constructed in such a way that, in the zero-mass limit, the massive vector field contribution reduces smoothly to the result obtained from Maxwell's theory. As an application of our results, we consider the Casimir effect outside a perfectly conducting medium with a plane boundary. We discuss the results obtained using Stueckelberg but also de Broglie-Proca electromagnetism, and we consider the zero-mass limit of the vacuum energy in both theories. We finally compare the de Broglie-Proca and Stueckelberg formalisms and highlight the advantages of the Stueckelberg point of view, even if, in our opinion, the de Broglie-Proca and Stueckelberg approaches of massive electromagnetism are two faces of the same field theory.

  14. Reviewing the active stress field in Central Asia by using a modified stress tensor approach

    NASA Astrophysics Data System (ADS)

    Karagianni, I.; Papazachos, C. B.; Scordilis, E. M.; Karakaisis, G. F.

    2015-04-01

    Central Asia and its surroundings constitute a geodynamically complicated region, where almost all types of tectonic patterns can be observed. A triple junction, collision, and subduction zones, as well as extended fault systems of all types prevail in different parts of this region and compose one of the most interesting and complex geotectonic environments on Earth. This complicated setting is also associated with intense deformation, resulting in a large number of high seismicity zones, where numerous strong earthquakes occur, also extending, in some cases, to intermediate depths. Several previous studies have focused on specific seismotectonic zones in order to assess the active tectonic setting and the associated stress regime. We attempt to provide a unified but detailed picture of the stress field variability for the entire central Asia region, using the well-known inversion method proposed by Gephart and Forsyth (1984), modified in the present work on the basis of Fisher statistics. For this application, we employ a large number of focal mechanisms, spatially separated in 138 data groups. Τhe proposed modified algorithm (FD-BSM) examines the Fisher distribution of all possible stress principal axes solutions and select the one that: (a) shows the smallest angle variation from the Fisher mean in all three principal distributions and (b) minimizes the difference between the theoretical and observed slip vectors of the employed fault plane solution data. Synthetic tests and comparison of the corresponding results with real data show that, in cases where the stress regime is not clearly uniform or the number of available data is rather small, the models selected by the modified approach (FD-BSM) are more robust and show better spatial coherence compared to the initial Gephart and Forsyth (1984) method or alternative techniques such as the method of Michael (1984, 1987) as adapted by Vavrycuk (2014).

  15. A QTAIM and stress tensor investigation of the torsion path of a light-driven fluorene molecular rotary motor.

    PubMed

    Hu, Ming Xing; Xu, Tianlv; Momen, Roya; Huan, Guo; Kirk, Steven R; Jenkins, Samantha; Filatov, Michael

    2016-11-01

    The utility of the QTAIM/stress tensor analysis method for characterizing the photoisomerization of light driven molecular rotary machines is investigated on the example of the torsion path in fluorene molecular motor. The scalar and vector descriptors of QTAIM/stress tensor reveal additional information on the bonding interactions between the rotating units of the motor, which cannot be obtained from the analysis of the ground and excited state potential energy surfaces. The topological features of the fluorene motor molecular graph display that, upon the photoexcitation a certain increase in the torsional stiffness of the rotating bond can be attributed to the increasing topological stability of the rotor carbon atom attached to the rotation axle. The established variations in the torsional stiffness of the rotating bond may cause transfer of certain fraction of the torsional energy to other internal degrees of freedom, such as the pyramidalization distortion. © 2016 Wiley Periodicals, Inc. PMID:27671359

  16. Analysis of structural correlations in a model binary 3D liquid through the eigenvalues and eigenvectors of the atomic stress tensors.

    PubMed

    Levashov, V A

    2016-03-01

    It is possible to associate with every atom or molecule in a liquid its own atomic stress tensor. These atomic stress tensors can be used to describe liquids' structures and to investigate the connection between structural and dynamic properties. In particular, atomic stresses allow to address atomic scale correlations relevant to the Green-Kubo expression for viscosity. Previously correlations between the atomic stresses of different atoms were studied using the Cartesian representation of the stress tensors 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 stress tensors. 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 stress 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 stress tensors. We also found correlations between the eigenvalues of the same atomic stress tensor. For the studied system, with purely repulsive interactions between the particles, the eigenvalues of every atomic stress tensor 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. PMID:26957166

  17. Analysis of structural correlations in a model binary 3D liquid through the eigenvalues and eigenvectors of the atomic stress tensors.

    PubMed

    Levashov, V A

    2016-03-01

    It is possible to associate with every atom or molecule in a liquid its own atomic stress tensor. These atomic stress tensors can be used to describe liquids' structures and to investigate the connection between structural and dynamic properties. In particular, atomic stresses allow to address atomic scale correlations relevant to the Green-Kubo expression for viscosity. Previously correlations between the atomic stresses of different atoms were studied using the Cartesian representation of the stress tensors 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 stress tensors. 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 stress 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 stress tensors. We also found correlations between the eigenvalues of the same atomic stress tensor. For the studied system, with purely repulsive interactions between the particles, the eigenvalues of every atomic stress tensor 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.

  18. Assessment of rock mechanical behavior considering stress dependent stiffness of the cracked domain within crack tensor-based approach

    NASA Astrophysics Data System (ADS)

    Takemura, T.; Panaghi, K.; Golshani, A.; Takahashi, M.; Sato, M.

    2015-12-01

    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 stress 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 tensor-based formulation in describing stress-strain behavior of cracked rock is a case in point in which the fourth-rank crack tensor 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 tensor 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.

  19. Direct Measurements of Quantum Kinetic Energy Tensor in Stable and Metastable Water near the Triple Point: An Experimental Benchmark.

    PubMed

    Andreani, Carla; Romanelli, Giovanni; Senesi, Roberto

    2016-06-16

    This study presents the first direct and quantitative measurement of the nuclear momentum distribution anisotropy and the quantum kinetic energy tensor 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 quantum 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 quantum effects in water and represent reference experimental values for theoretical investigations. PMID:27214268

  20. Direct Measurements of Quantum Kinetic Energy Tensor in Stable and Metastable Water near the Triple Point: An Experimental Benchmark.

    PubMed

    Andreani, Carla; Romanelli, Giovanni; Senesi, Roberto

    2016-06-16

    This study presents the first direct and quantitative measurement of the nuclear momentum distribution anisotropy and the quantum kinetic energy tensor 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 quantum 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 quantum effects in water and represent reference experimental values for theoretical investigations.

  1. Internal Crack Propagation in a Continuously Cast Austenitic Stainless Steel Analyzed by Actual Residual Stress Tensor Distributions

    NASA Astrophysics Data System (ADS)

    Saito, Youichi; Tanaka, Shun-Ichiro

    2016-04-01

    Initiation, propagation, and termination of internal cracks in a continuously cast austenitic stainless steel has been investigated with emphasis on stress loading of the solidified shell during casting. Cracks were formed at the center of the slab, parallel to the width of the cast, and were observed near the narrow faces. Optimized two-dimensional X-ray diffraction method was employed to measure residual stress tensor distributions around the cracks in the as-cast slab with coarse and strongly preferentially oriented grains. The tensor distributions had a sharp peak, as high as 430 MPa, at the crack end neighboring the columnar grains. On the other hand, lower values were measured at the crack end neighboring the equiaxed grains, where the local temperatures were higher during solidification. The true residual stress distributions were determined by evaluating the longitudinal elastic constant for each measured position, resulting in more accurate stress values than before. Electron probe micro-analysis at the terminal crack position showed that Ni, Ti, and Si were concentrated at the boundaries of the equiaxed grains, where the tensile strength was estimated to be lower than at the primary grains. A model of the crack formation and engineering recommendations to reduce crack formation are proposed.

  2. The polarized interface between quadrupolar insulators: Maxwell stress tensor, surface tension, and potential.

    PubMed

    Slavchov, Radomir I; Dimitrova, Iglika M; Ivanov, Tzanko

    2015-10-21

    The quadrupolar Maxwell electrostatic equations predict several qualitatively different results compared to Poisson's classical equation in their description of the properties of a dielectric interface. All interfaces between dielectrics possess surface dipole moment which results in a measurable surface potential jump. The surface dipole moment is conjugated to the bulk quadrupole moment density (the quadrupolarization) similarly to Gauss's relation between surface charge and bulk polarization. However, the classical macroscopic Maxwell equations completely neglect the quadrupolarization of the medium. Therefore, the electrostatic potential distribution near an interface of intrinsic dipole moment can be correctly described only within the quadrupolar macroscopic equations of electrostatics. They predict that near the polarized interface a diffuse dipole layer exists, which bears many similarities to the diffuse charge layer near a charged surface, in agreement with existing molecular dynamics simulation data. It turns out that when the quadrupole terms are kept in the multipole expansion of the laws of electrostatics, the solutions for the potential and the electric field are continuous functions at the surface. A well-defined surface electric field exists, interacting with the adsorbed dipoles. This allows for a macroscopic description of the surface dipole-surface dipole and the surface dipole-bulk quadrupole interactions. They are shown to have considerable contribution to the interfacial tension-of the order of tens of mN/m! To evaluate it, the Maxwell stress tensor in quadrupolar medium is deduced, including the electric field gradient action on the quadrupoles, as well as quadrupolar image force and quadrupolar electrostriction. The dependence of the interfacial tension on the external normal electric field (the dielectrocapillary curve) is predicted and the dielectric susceptibility of the dipolar double layer is related to the quadrupolarizabilities of

  3. The polarized interface between quadrupolar insulators: Maxwell stress tensor, surface tension, and potential.

    PubMed

    Slavchov, Radomir I; Dimitrova, Iglika M; Ivanov, Tzanko

    2015-10-21

    The quadrupolar Maxwell electrostatic equations predict several qualitatively different results compared to Poisson's classical equation in their description of the properties of a dielectric interface. All interfaces between dielectrics possess surface dipole moment which results in a measurable surface potential jump. The surface dipole moment is conjugated to the bulk quadrupole moment density (the quadrupolarization) similarly to Gauss's relation between surface charge and bulk polarization. However, the classical macroscopic Maxwell equations completely neglect the quadrupolarization of the medium. Therefore, the electrostatic potential distribution near an interface of intrinsic dipole moment can be correctly described only within the quadrupolar macroscopic equations of electrostatics. They predict that near the polarized interface a diffuse dipole layer exists, which bears many similarities to the diffuse charge layer near a charged surface, in agreement with existing molecular dynamics simulation data. It turns out that when the quadrupole terms are kept in the multipole expansion of the laws of electrostatics, the solutions for the potential and the electric field are continuous functions at the surface. A well-defined surface electric field exists, interacting with the adsorbed dipoles. This allows for a macroscopic description of the surface dipole-surface dipole and the surface dipole-bulk quadrupole interactions. They are shown to have considerable contribution to the interfacial tension-of the order of tens of mN/m! To evaluate it, the Maxwell stress tensor in quadrupolar medium is deduced, including the electric field gradient action on the quadrupoles, as well as quadrupolar image force and quadrupolar electrostriction. The dependence of the interfacial tension on the external normal electric field (the dielectrocapillary curve) is predicted and the dielectric susceptibility of the dipolar double layer is related to the quadrupolarizabilities of

  4. The polarized interface between quadrupolar insulators: Maxwell stress tensor, surface tension, and potential

    NASA Astrophysics Data System (ADS)

    Slavchov, Radomir I.; Dimitrova, Iglika M.; Ivanov, Tzanko

    2015-10-01

    The quadrupolar Maxwell electrostatic equations predict several qualitatively different results compared to Poisson's classical equation in their description of the properties of a dielectric interface. All interfaces between dielectrics possess surface dipole moment which results in a measurable surface potential jump. The surface dipole moment is conjugated to the bulk quadrupole moment density (the quadrupolarization) similarly to Gauss's relation between surface charge and bulk polarization. However, the classical macroscopic Maxwell equations completely neglect the quadrupolarization of the medium. Therefore, the electrostatic potential distribution near an interface of intrinsic dipole moment can be correctly described only within the quadrupolar macroscopic equations of electrostatics. They predict that near the polarized interface a diffuse dipole layer exists, which bears many similarities to the diffuse charge layer near a charged surface, in agreement with existing molecular dynamics simulation data. It turns out that when the quadrupole terms are kept in the multipole expansion of the laws of electrostatics, the solutions for the potential and the electric field are continuous functions at the surface. A well-defined surface electric field exists, interacting with the adsorbed dipoles. This allows for a macroscopic description of the surface dipole-surface dipole and the surface dipole-bulk quadrupole interactions. They are shown to have considerable contribution to the interfacial tension—of the order of tens of mN/m! To evaluate it, the Maxwell stress tensor in quadrupolar medium is deduced, including the electric field gradient action on the quadrupoles, as well as quadrupolar image force and quadrupolar electrostriction. The dependence of the interfacial tension on the external normal electric field (the dielectrocapillary curve) is predicted and the dielectric susceptibility of the dipolar double layer is related to the quadrupolarizabilities of

  5. Piezo-optic tensor of crystals from quantum-mechanical calculations

    SciTech Connect

    Erba, A. Dovesi, R.; Ruggiero, M. T.; Korter, T. M.

    2015-10-14

    An automated computational strategy is devised for the ab initio determination of the full fourth-rank piezo-optic tensor 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 tensor 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.

  6. Piezo-optic tensor of crystals from quantum-mechanical calculations.

    PubMed

    Erba, A; Ruggiero, M T; Korter, T M; Dovesi, R

    2015-10-14

    An automated computational strategy is devised for the ab initio determination of the full fourth-rank piezo-optic tensor 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 tensor 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 CaWO4, which have recently been experimentally reconstructed. Present calculations unambiguously determine the absolute sign (positive) of the π61 constant, confirm the reliability of 6 out of 10 experimentally determined constants and provide new, more accurate values for the remaining 4 constants.

  7. Exact tensor hypercontraction: a universal technique for the resolution of matrix elements of local finite-range N-body potentials in many-body quantum problems.

    PubMed

    Parrish, Robert M; Hohenstein, Edward G; Schunck, Nicolas F; Sherrill, C David; Martínez, Todd J

    2013-09-27

    Configuration-space matrix elements of N-body potentials arise naturally and ubiquitously in the Ritz-Galerkin solution of many-body quantum problems. For the common specialization of local, finite-range potentials, we develop the exact tensor hypercontraction method, which provides a quantized renormalization of the coordinate-space form of the N-body potential, allowing for a highly separable tensor 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. PMID:24116775

  8. Neutron stress measurement of triaxial residual stress tensors in an aerospace weldment before and after post-weld heat-treatment

    SciTech Connect

    Winholtz, R.A.; Krawitz, A.D.

    1996-12-31

    Triaxial stress tensors and their corresponding principal stresses were determined with neutron diffraction, before and after post-weld heat-treatment, at 14 positions in and near a circumferential weld in a subscale model cylinder of the NASA-Advanced Solid Rocket Motor. No principal stress directions were assumed in making the measurements. The principal stresses range from {minus}393 to +1,045 MPa in the as-welded condition and decreased to a range of {minus}212 to +421 MPa after post-weld heat-treatment. The largest as-welded tensile stresses were located around the cap pass heat affected zone in the interior of the material and were aligned with the hoop direction of the cylinder.

  9. (77)Se chemical shift tensor of L-selenocystine: experimental NMR measurements and quantum chemical investigations of structural effects.

    PubMed

    Struppe, Jochem; Zhang, Yong; Rozovsky, Sharon

    2015-03-01

    The genetically encoded amino acid selenocysteine and its dimeric form, selenocystine, are both utilized by nature. They are found in active sites of selenoproteins, enzymes that facilitate a diverse range of reactions, including the detoxification of reactive oxygen species and regulation of redox pathways. Due to selenocysteine and selenocystine's specialized biological roles, it is of interest to examine their (77)Se NMR properties and how those can in turn be employed to study biological systems. We report the solid-state (77)Se NMR measurements of the L-selenocystine chemical shift tensor, which provides the first experimental chemical shift tensor information on selenocysteine-containing systems. Quantum chemical calculations of L-selenocystine models were performed to help understand various structural effects on (77)Se L-selenocystine's chemical shift tensor. The effects of protonation state, protein environment, and substituent of selenium-bonded carbon on the isotropic chemical shift were found to be in a range of ca. 10-20 ppm. However, the conformational effect was found to be much larger, spanning ca. 600 ppm for the C-Se-Se-C dihedral angle range of -180° to +180°. Our calculations show that around the minimum energy structure with a C-Se-Se-C dihedral angle of ca. -90°, the energy costs to alter the dihedral angle in the range from -120° to -60° are within only 2.5 kcal/mol. This makes it possible to realize these conformations in a protein or crystal environment. (77)Se NMR was found to be a sensitive probe to such changes and has an isotropic chemical shift range of 272 ± 30 ppm for this energetically favorable conformation range. The energy-minimized structures exhibited calculated isotropic shifts that lay within 3-9% of those reported in previous solution NMR studies. The experimental solid-state NMR isotropic chemical shift is near the lower bound of this calculated range for these readily accessible conformations. These results suggest

  10. Anomalous Conductivity Tensor and Quantum Oscillations in the Dirac Semimetal Na3Bi

    NASA Astrophysics Data System (ADS)

    Xiong, Jun; Kushwaha, Satya; Krizan, Jason; Liang, Tian; Cava, Robert J.; Ong, Nai Phuan

    2015-03-01

    Na3Bi is a 3D Dirac semimetal with protected nodes. Angle-resolved photoemission experiments have observed these massless Dirac fermions in the bulk band, but transport experiments have been hampered by the extreme air sensitivity of Na3Bi crystals. Transport experiments can potentially address interesting issues such as charge pumping between the separated Weyl nodes when the time-reversal symmetry is broken by a strong magnetic field. Here we report a transport measurement that reveals robust anomalies in both the conductivity and resistivity tensors. The resistivity ρxx is B-linear up to 35 T, while the Hall angle exhibits an unusual profile approaching a step-function. In addition, we have also observed a prominent beating pattern in the Shubnikov de Haas (SdH) oscillations indicating the existence of two nearly equal SdH frequencies when the Fermi energy falls inside the non-trivial gap-inverted regime. Supported by NSF-MRSEC (DMR 0819860), Army Research Office (ARO W911NF-11-1-0379) and MURI Grant (ARO W911NF-12-1-0461).

  11. Seismic activity and stress tensor inversion at Las Tres Vírgenes Volcanic and Geothermal Field (México)

    NASA Astrophysics Data System (ADS)

    Antayhua-Vera, Yanet; Lermo-Samaniego, Javier; Quintanar-Robles, Luis; Campos-Enríquez, Oscar

    2015-10-01

    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 stress tensor to understand the local and regional stress 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. Stress inversion showed NW-SE, E-W and NE-SW extensional orientations (Shmin), in agreement with the local tectonic stress field; while NE-SW compressional orientations (SHmax) are correlated with the regional tectonic stress field.

  12. Efficient elastic reverse-time migration for the decomposed P-wavefield using stress tensor in the time domain

    NASA Astrophysics Data System (ADS)

    Ha, Jiho; Shin, Sungryul; Shin, Changsoo; Chung, Wookeen

    2015-05-01

    Because complex mixed waves are typically generated in elastic media, wavefield decomposition is required for such media to obtain migration images accurately. In isotropic media, this is achieved according to the Helmholtz decomposition theorem; in particular, the divergence operator is commonly applied to P-wavefield decomposition. In this study, two types of elastic reverse-time migration algorithms are proposed for decomposition of the P-wavefield without requiring the divergence operator. The first algorithm involves formulation of the stress tensor by spatially differentiated displacement according to the stress-strain relationship and is utilized to construct an imaging condition for the decomposed P-wavefield. We demonstrate this approach through numerical testing. The second algorithm allows us to obtain emphasized interfaces through the application of the absolute value function to decomposed wavefield in imaging condition. Because reverse-time migration can be defined by a zero-lag cross-correlation relationship between the partial-derivative wavefield and the observed wavefield data, we derive the virtual source to construct the partial-derivative wavefield based on a 2D staggered-grid finite-difference modeling method in the time domain. The explicitly computed partial-derivative wavefield from virtual sources with the stress tensor is in agreement with the partial-derivative wavefield directly computed from residual by between with and without a perturbation point in the subsurface. Moreover, the back-propagation technique is used to enhance the computational efficiency. To validate our two types of imaging conditions, numerical tests are conducted. The migration images created according to our imaging conditions can represent the subsurface structure accurately. Thus, we can confirm the feasibility of obtaining migration images of the decomposed P-wavefield without requiring the application of the divergence operator.

  13. A dynamic regularized gradient model of the subgrid-scale stress tensor for large-eddy simulation

    NASA Astrophysics Data System (ADS)

    Vollant, A.; Balarac, G.; Corre, C.

    2016-02-01

    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) stress tensor to take into account the effect of scales smaller than the filter size. In this work, a new model is proposed for the SGS stress 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 stress tensor 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.

  14. Possible paleo-stress tensor configurations derived from fault-slip data in eastern Vermont and western New Hampshire

    NASA Astrophysics Data System (ADS)

    Hardcastle, Kenneth C.

    1989-04-01

    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 stress 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 tensor. 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.

  15. All-electron formalism for total energy strain derivatives and stress tensor components for numeric atom-centered orbitals

    NASA Astrophysics Data System (ADS)

    Knuth, Franz; Carbogno, Christian; Atalla, Viktor; Blum, Volker; Scheffler, Matthias

    2015-05-01

    We derive and implement the strain derivatives of the total energy of solids, i.e., the analytic stress tensor 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.

  16. Present-day stress tensors along the southern Caribbean plate boundary zone from inversion of focal mechanism solutions: A successful trial

    NASA Astrophysics Data System (ADS)

    Audemard M., Franck A.; Castilla, Raymi

    2016-11-01

    This paper presents a compilation of 16 present-day stress tensors along the southern Caribbean plate boundary zone (PBZ), and particularly in western and along northern Venezuela. As a trial, these new stress tensors 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 tensors are compared to those 59 tensors 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 stress tensors, one derived from geological data and the other one from seismological data, compare very well throughout the PBZ in terms of both stress orientation and shape of the stress tensor. 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 stress (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 stress ellipsoid derived from the Etchecopar et al.'s method better characterize whether the stress regime is transpressional or compressional, or even very rarely trantensional at local scale. The orientation and space variation of this regional stress field in western Venezuela results from the addition of the two major neighbouring interplate maximum horizontal stress orientations (

  17. Tensor Network Renormalization.

    PubMed

    Evenbly, G; Vidal, G

    2015-10-30

    We introduce a coarse-graining transformation for tensor networks that can be applied to study both the partition function of a classical statistical system and the Euclidean path integral of a quantum many-body system. The scheme is based upon the insertion of optimized unitary and isometric tensors (disentanglers and isometries) into the tensor 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 tensors), 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.

  18. Lunisolar tidal and tidal load elastic stress tensor components within the Earth's mantle and their influence on earthquake occurrences

    NASA Astrophysics Data System (ADS)

    Varga, Peter; Grafarend, Erik

    2016-04-01

    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 stress tensor 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 stress 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.

  19. Next-to-leading term of the renormalized stress-energy tensor of the quantized massive scalar field in Schwarzschild spacetime. The back reaction

    SciTech Connect

    Matyjasek, Jerzy; Tryniecki, Dariusz

    2009-04-15

    The next-to-leading term of the renormalized stress-energy tensor of the quantized massive field with an arbitrary curvature coupling in the spacetime of the Schwarzschild black hole is constructed. It is achieved by functional differentiation of the DeWitt-Schwinger effective action involving coincidence limit of the Hadamard-Minakshisundaram-DeWitt-Seely coefficients a{sub 3} and a{sub 4}. It is shown, by comparison with the existing numerical results, that inclusion of the second-order term leads to substantial improvement of the approximation of the exact stress-energy tensor even in the closest vicinity of the event horizon. The back reaction of the quantized field upon the Schwarzschild black hole is briefly discussed.

  20. HYPODD Relocations and Stress Tensor Inversion Analyses of Local Earthquake Clusters in the Sea of Marmara

    NASA Astrophysics Data System (ADS)

    Korkusuz Öztürk, Yasemin; Meral Özel, Nurcan

    2016-04-01

    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 stresses 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 stress analyses will make an important contribution to a

  1. White Matter Changes in Posttraumatic Stress Disorder Following Mild Traumatic Brain Injury: A Prospective Longitudinal Diffusion Tensor Imaging Study

    PubMed Central

    Li, Li; Sun, Gang; Liu, Kai; Li, Min; Li, Bo; Qian, Shao-Wen; Yu, Li-Li

    2016-01-01

    Background: The ability to predict posttraumatic stress 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 tensor 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

  2. Quantum volume

    NASA Astrophysics Data System (ADS)

    Ryabov, V. A.

    2015-08-01

    Quantum systems in a mechanical embedding, the breathing mode of a small particles, optomechanical system, etc. are far not the full list of examples in which the volume exhibits quantum behavior. Traditional consideration suggests strain in small systems as a result of a collective movement of particles, rather than the dynamics of the volume as an independent variable. The aim of this work is to show that some problem here might be essentially simplified by introducing periodic boundary conditions. At this case, the volume is considered as the independent dynamical variable driven by the internal pressure. For this purpose, the concept of quantum volume based on Schrödinger’s equation in 𝕋3 manifold is proposed. It is used to explore several 1D model systems: An ensemble of free particles under external pressure, quantum manometer and a quantum breathing mode. In particular, the influence of the pressure of free particle on quantum oscillator is determined. It is shown also that correction to the spectrum of the breathing mode due to internal degrees of freedom is determined by the off-diagonal matrix elements of the quantum stress. The new treatment not using the “force” theorem is proposed for the quantum stress tensor. In the general case of flexible quantum 3D dynamics, quantum deformations of different type might be introduced similarly to monopole mode.

  3. Anisotropy of the Reynolds stress tensor in the wakes of wind turbine arrays in Cartesian arrangements with counter-rotating rotors

    NASA Astrophysics Data System (ADS)

    Hamilton, Nicholas; Cal, Raúl Bayoán

    2015-01-01

    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 stress - 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 stress anisotropy tensor (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 tensor yields principle components and corresponding coordinate system transformations. Characteristic spheroids representing the balance of components in the normalized anisotropy tensor 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 stress anisotropy tensor 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 stress anisotropy tensor and terms from the mean

  4. Determining changes in the state of stress associated with an earthquake via combined focal mechanism and moment tensor analysis: Application to the 2013 Awaji Island earthquake, Japan

    NASA Astrophysics Data System (ADS)

    Matsumoto, Satoshi; Katao, Hiroshi; Iio, Yoshihisa

    2015-05-01

    One approach that can be used to evaluate the potential for an earthquake occurrence is the detection of the stress concentration at an earthquake fault. While the stress fields for pre- and post-seismic event stages differ, this change cannot provide information regarding the potential for an earthquake. Here, we propose a detection method for states of stress that uses focal mechanism data from microearthquakes. The state of stress can be defined both by the background stress and by a moment tensor equivalent to the stress concentration. We applied this method to actual focal mechanism data from the 2013 Awaji Island earthquake (M6.3), Japan, and the results showed the presence of stress concentration around the earthquake fault before the mainshock. In addition, the regional differential stress was shown to be about 13 MPa. The magnitude of the obtained stress concentration in the focal area and the high dip angle of the mainshock fault imply that the faulting occurred in the crust where it was overpressurized to a level near the lithostatic pressure.

  5. Tensor Network Contractions for #SAT

    NASA Astrophysics Data System (ADS)

    Biamonte, Jacob D.; Morton, Jason; Turner, Jacob

    2015-09-01

    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 quantum systems experienced advancements due to the development of tensor network algorithms and associated quantum physics-inspired techniques. By these methods, we give an algorithm using an axiomatic tensor contraction language for n-variable #SAT instances with complexity where c is the number of COPY-tensors, g is the number of gates, and d is the maximal degree of any COPY-tensor. Thus, n-variable counting problems can be solved efficiently when their tensor network expression has at most COPY-tensors 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 tensor based algorithmic tools and provides an alternative insight on these problems which have a long history in statistical physics and computer science.

  6. Tectonic stress inversion of large multi-phase fracture data sets: application of Win-Tensor to reveal the brittle tectonic history of the Lufilan Arc, DRC

    NASA Astrophysics Data System (ADS)

    Delvaux, Damien; Kipata, Louis; Sintubin, Manuel

    2013-04-01

    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 stress 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 stress 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 stresses mark the transition towards rift-related extension. More details in Kipata, Delvaux et al.(2013), Geologica Belgica 16/1-2: 001-017 Win-Tensor can be downloaded at: http://users.skynet.be/damien.delvaux/Tensor/tensor-index.html

  7. Mixed weak-perturbative solution method for Maxwell's equations of diffusion with Müller's partial stress tensor in the low velocity limit

    NASA Astrophysics Data System (ADS)

    Faliagas, A. C.

    2016-03-01

    Maxwell's theory of multicomponent diffusion and subsequent extensions are based on systems of mass and momentum conservation equations. The partial stress tensor, 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 stress tensor. 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.

  8. MATLAB Tensor Toolbox

    SciTech Connect

    Kolda, Tamara G.; Bader, Brett W.

    2006-08-03

    This software provides a collection of MATLAB classes for tensor manipulations that can be used for fast algorithm prototyping. The tensor class extends the functionality of MATLAB's multidimensional arrays by supporting additional operations such as tensor multiplication. We have also added support for sparse tensor, tensors in Kruskal or Tucker format, and tensors stored as matrices (both dense and sparse).

  9. Multiple seismogenic processes for high-frequency earthquakes at Katmai National Park, Alaska: Evidence from stress tensor inversions of fault-plane solutions

    USGS Publications Warehouse

    Moran, S.C.

    2003-01-01

    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 stress tensor in different regions within the park. Earthquakes removed by several kilometers from the volcanic axis occur in a stress 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, stress tensors 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.

  10. Probabilistic waveform inversion for 22 earthquake moment tensors in Hungary: new constraints on the tectonic stress pattern inside the Pannonian basin

    NASA Astrophysics Data System (ADS)

    Wéber, Zoltán

    2016-01-01

    We have successfully estimated the full moment tensors 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 tensor 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 tensor 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 tensor 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

  11. CAST: Contraction Algorithm for Symmetric Tensors

    SciTech Connect

    Rajbhandari, Samyam; NIkam, Akshay; Lai, Pai-Wei; Stock, Kevin; Krishnamoorthy, Sriram; Sadayappan, Ponnuswamy

    2014-09-22

    Tensor contractions represent the most compute-intensive core kernels in ab initio computational quantum chemistry and nuclear physics. Symmetries in these tensor 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 tensors. We introduce a novel approach that avoids data redistribution in contracting symmetric tensors 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 quantum chemistry method. We also present a novel approach to tensor 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.

  12. Tensor Algebra Library for NVidia Graphics Processing Units

    SciTech Connect

    Liakh, Dmitry

    2015-03-16

    This is a general purpose math library implementing basic tensor algebra operations on NVidia GPU accelerators. This software is a tensor algebra library that can perform basic tensor algebra operations, including tensor contractions, tensor products, tensor 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 tensor algebra operation on a specific GPU. The tensors participating in a particular tensor 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 quantum many-body theory (e.g., in electronic structure theory).

  13. Tensor Algebra Library for NVidia Graphics Processing Units

    2015-03-16

    This is a general purpose math library implementing basic tensor algebra operations on NVidia GPU accelerators. This software is a tensor algebra library that can perform basic tensor algebra operations, including tensor contractions, tensor products, tensor 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 ofmore » the corresponding tensor algebra operation on a specific GPU. The tensors participating in a particular tensor 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 quantum many-body theory (e.g., in electronic structure theory).« less

  14. R-Matrices and the Tensor Product Graph Method

    NASA Astrophysics Data System (ADS)

    Gould, Mark D.; Zhang, Yao-Zhong

    2002-11-01

    A systematic method for constructing trigonometric R-matrices corresponding to the (multiplicity-free) tensor product of any two affinizable representations of a quantum algebra or superalgebra has been developed by the Brisbane group and its collaborators. This method has been referred to as the Tensor Product Graph Method. Here we describe applications of this method to untwisted and twisted quantum affine superalgebras.

  15. R-Matrices and the Tensor Product Graph Method

    NASA Astrophysics Data System (ADS)

    Gould, Mark D.; Zhang, Yao-Zhong

    A systematic method for constructing trigonometric R-matrices corresponding to the (multiplicity-free) tensor product of any two affinizable representations of a quantum algebra or superalgebra has been developed by the Brisbane group and its collaborators. This method has been referred to as the Tensor Product Graph Method. Here we describe applications of this method to untwisted and twisted quantum affine superalgebras.

  16. Tensor-product state approach to spin-1/2 square J1-J2 antiferromagnetic Heisenberg model: Evidence for deconfined quantum criticality

    NASA Astrophysics Data System (ADS)

    Wang, Ling; Gu, Zheng-Cheng; Verstraete, Frank; Wen, Xiao-Gang

    2016-08-01

    The ground state phase of a spin-1/2 J1-J2 antiferromagnetic Heisenberg model on a square lattice around the maximally frustrated regime (J2˜0.5 J1 ) has been debated for decades. Here we study this model using the cluster update algorithm for tensor-product states (TPSs). The ground state energies at finite sizes and in the thermodynamic limit (with finite size scaling) are in good agreement with exact diagonalization study. Through finite size scaling of the spin correlation function, we find the critical point J2c1=0.572 (5 ) J1 and critical exponents ν =0.50 (8 ) ,ηs=0.28 (6 ) . In the range of 0.572 quantum critical point at J2c1. Remarkably, all the observed critical exponents are consistent with the J -Q model.

  17. Quantum electronic stress: density-functional-theory formulation and physical manifestation.

    PubMed

    Hu, Hao; Liu, Miao; Wang, Z F; Zhu, Junyi; Wu, Dangxin; Ding, Hepeng; Liu, Zheng; Liu, Feng

    2012-08-01

    The concept of quantum electronic stress (QES) is introduced and formulated within density functional theory to elucidate extrinsic electronic effects on the stress 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 quantum analog of classical Hooke's law. Two distinct QES manifestations are demonstrated quantitatively by density functional theory calculations: (1) in the form of bulk stress induced by charge carriers and (2) in the form of surface stress induced by quantum confinement. Implications of QES in some physical phenomena are discussed to underlie its importance.

  18. Measurement of the residual stress tensor on the surface of a specimen by layer removal and interferometry: uncertainty analysis

    NASA Astrophysics Data System (ADS)

    Palma, J.; Rivero, R.; Lira, I.; François, M.

    2009-11-01

    A new method for measuring the principal residual stresses on the surface of a thin metallic specimen is presented. The novelty of the method resides in a combination of the layer removal technique by chemical etching and of electronic speckle pattern interferometry to measure the ensuing deformation. It is shown that the loci of constant deflection with respect to the original plane surface are conic sections. An interferometer sensitive to out-of-plane displacements was used, yielding fringe patterns that reproduced those curves. Immediate visualization of the orientation and relative magnitude of the principal stresses within the removed layer was then possible. A fit of the measured deformation to the theoretical shape, together with knowledge of the initial and final thickness of the specimen and of the elastic properties of the material (a cold-rolled low-carbon steel sheet), allowed estimating the principal stresses. It is shown that the critical factor that determines the uncertainty of these estimates is the thickness of the removed layer.

  19. The Topology of Symmetric Tensor Fields

    NASA Technical Reports Server (NTRS)

    Levin, Yingmei; Batra, Rajesh; Hesselink, Lambertus; Levy, Yuval

    1997-01-01

    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 tensor fields. A second-order tensor 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 tensor field. The simplify and often complex tensor field and to capture its important features, the tensor is decomposed into an isotopic tensor and a deviator. A tensor 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 tensor field, while the isotopic part provides a uniform bias. Degenerate points are basic constituents of tensor fields. In 2-D tensor 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 tensor, 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 stress tensors reveal that the basic addie-viscosity assuptions have their validity in turbulence modeling under certain conditions.

  20. Electrode-stress-induced nanoscale disorder in Si quantum electronic devices

    NASA Astrophysics Data System (ADS)

    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.

    2016-06-01

    Disorder in the potential-energy landscape presents a major obstacle to the more rapid development of semiconductor quantum 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 stresses 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 quantum well within a Si/SiGe heterostructure. Electrode stress presents both challenges to the design of devices and opportunities associated with the lateral manipulation of electronic energy levels.

  1. Stress-directed compositional patterning of SiGe substrates for lateral quantum barrier manipulation

    SciTech Connect

    Ghosh, Swapnadip; Kaiser, Daniel; Sinno, Talid E-mail: meister@unm.edu; Bonilla, Jose; Han, Sang M. E-mail: meister@unm.edu

    2015-08-17

    While vertical stacking of quantum well and dot structures is well established in heteroepitaxial semiconductor materials, manipulation of quantum barriers in the lateral directions poses a significant engineering challenge. Here, we demonstrate lateral quantum barrier manipulation in a crystalline SiGe alloy using structured mechanical fields to drive compositional redistribution. To apply stress, 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 stress. 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 “stress transfer” process is studied in detail using multiscale computer simulations that demonstrate its robustness across a wide range of applied stresses and annealing temperatures. While the “Si nanodot” structures formed here are not intrinsically useful as quantum structures, it is anticipated that the stress transfer process may be modified by judicious control of the SiGe film thickness and indenter array pattern to form more technologically useful structures.

  2. Seismic Activity Related to the 2002-2003 Mt. Etna Volcano Eruption (Italy): Fault Plane Solutions and Stress Tensor Computation

    NASA Astrophysics Data System (ADS)

    Barberi, G.; Cammarata, L.; Cocina, O.; Maiolino, V.; Musumeci, C.; Privitera, E.

    2003-04-01

    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 stress 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

  3. Tensor gauge condition and tensor field decomposition

    NASA Astrophysics Data System (ADS)

    Zhu, Ben-Chao; Chen, Xiang-Song

    2015-10-01

    We discuss various proposals of separating a tensor field into pure-gauge and gauge-invariant components. Such tensor field decomposition is intimately related to the effort of identifying the real gravitational degrees of freedom out of the metric tensor in Einstein’s general relativity. We show that as for a vector field, the tensor field decomposition has exact correspondence to and can be derived from the gauge-fixing approach. The complication for the tensor field, however, is that there are infinitely many complete gauge conditions in contrast to the uniqueness of Coulomb gauge for a vector field. The cause of such complication, as we reveal, is the emergence of a peculiar gauge-invariant pure-gauge construction for any gauge field of spin ≥ 2. We make an extensive exploration of the complete tensor gauge conditions and their corresponding tensor field decompositions, regarding mathematical structures, equations of motion for the fields and nonlinear properties. Apparently, no single choice is superior in all aspects, due to an awkward fact that no gauge-fixing can reduce a tensor field to be purely dynamical (i.e. transverse and traceless), as can the Coulomb gauge in a vector case.

  4. Cadmium sulfide quantum dots induce oxidative stress and behavioral impairments in the marine clam Scrobicularia plana.

    PubMed

    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

    2015-07-01

    Cadmium sulfide (CdS) quantum 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 quantum 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 quantum dots showed that 52% of CdS quantum 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 quantum dots). However, significant changes in biochemical responses were observed in clams exposed to CdS quantum 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 quantum dots. The results show that oxidative stress and behavior biomarkers are sensitive predictors of CdS quantum 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. PMID:25772261

  5. Cadmium sulfide quantum dots induce oxidative stress and behavioral impairments in the marine clam Scrobicularia plana.

    PubMed

    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

    2015-07-01

    Cadmium sulfide (CdS) quantum 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 quantum 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 quantum dots showed that 52% of CdS quantum 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 quantum dots). However, significant changes in biochemical responses were observed in clams exposed to CdS quantum 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 quantum dots. The results show that oxidative stress and behavior biomarkers are sensitive predictors of CdS quantum 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.

  6. Tensor network decompositions in the presence of a global symmetry

    SciTech Connect

    Singh, Sukhwinder; Pfeifer, Robert N. C.; Vidal, Guifre

    2010-11-15

    Tensor 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 tensor network decompositions and algorithms. This is achieved by considering tensors that are invariant under the action of the group G. Each symmetric tensor decomposes into two types of tensors: degeneracy tensors, containing all the degrees of freedom, and structural tensors, which only depend on the symmetry group. In numerical calculations, the use of symmetric tensors ensures the preservation of the symmetry, allows selection of a specific symmetry sector, and significantly reduces computational costs. On the other hand, the resulting tensor network can be interpreted as a superposition of exponentially many spin networks. Spin networks are used extensively in loop quantum gravity, where they represent states of quantum geometry. Our work highlights their importance in the context of tensor network algorithms as well, thus setting the stage for cross-fertilization between these two areas of research.

  7. Motion of a mirror under infinitely fluctuating quantum vacuum stress

    NASA Astrophysics Data System (ADS)

    Wang, Qingdi; Unruh, William G.

    2014-04-01

    The actual value of the quantum vacuum energy density is generally regarded as irrelevant in nongravitational physics. However, this paper presents a nongravitational system where this value does have physical significance. The system is a mirror with an internal degree of freedom that interacts with a scalar field. We find that the force exerted on the mirror by the field vacuum undergoes wild fluctuations with a magnitude proportional to the value of the vacuum energy density, which is mathematically infinite. This infinite fluctuating force gives infinite instantaneous acceleration of the mirror. We show that this infinite fluctuating force and infinite instantaneous acceleration make sense because they will not result in infinite fluctuation of the mirror's position. On the contrary, the mirror's fluctuating motion will be confined in a small region due to two special properties of the quantum vacuum: (1) the vacuum friction that resists the mirror's motion and (2) the strong anticorrelation of vacuum fluctuations that constantly changes the direction of the mirror's infinite instantaneous acceleration and thus cancels the effect of infinities to make the fluctuation of the mirror's position finite.

  8. High-Precision Locations and the Stress Field from Instrumental Seismicity, Moment Tensors, and Short-Period Mechanisms through the Mina Deflection, Central Walker Lane

    NASA Astrophysics Data System (ADS)

    Ruhl, C. J.; Smith, K. D.

    2012-12-01

    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 tensor (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

  9. Visualization of second order tensor fields and matrix data

    NASA Technical Reports Server (NTRS)

    Delmarcelle, Thierry; Hesselink, Lambertus

    1992-01-01

    We present a study of the visualization of 3-D second order tensor fields and matrix data. The general problem of visualizing unsymmetric real or complex Hermitian second order tensor fields can be reduced to the simultaneous visualization of a real and symmetric second order tensor 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 tensor 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 tensor data by generalizing the vector notion of streamline to the tensor concept of hyperstreamline. We stress 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 tensor fields.

  10. Primordial tensor modes of the early Universe

    NASA Astrophysics Data System (ADS)

    Martínez, Florencia Benítez; Olmedo, Javier

    2016-06-01

    We study cosmological tensor perturbations on a quantized background within the hybrid quantization approach. In particular, we consider a flat, homogeneous and isotropic spacetime and small tensor inhomogeneities on it. We truncate the action to second order in the perturbations. The dynamics is ruled by a homogeneous scalar constraint. We carry out a canonical transformation in the system where the Hamiltonian for the tensor perturbations takes a canonical form. The new tensor modes now admit a standard Fock quantization with a unitary dynamics. We then combine this representation with a generic quantum scheme for the homogeneous sector. We adopt a Born-Oppenheimer ansatz for the solutions to the constraint operator, previously employed to study the dynamics of scalar inhomogeneities. We analyze the approximations that allow us to recover, on the one hand, a Schrödinger equation similar to the one emerging in the dressed metric approach and, on the other hand, the ones necessary for the effective evolution equations of these primordial tensor modes within the hybrid approach to be valid. Finally, we consider loop quantum cosmology as an example where these quantization techniques can be applied and compare with other approaches.

  11. A Communication-Optimal Framework for Contracting Distributed Tensors

    SciTech Connect

    Rajbhandari, Samyam; NIkam, Akshay; Lai, Pai-Wei; Stock, Kevin; Krishnamoorthy, Sriram; Sadayappan, Ponnuswamy

    2014-11-16

    Tensor contractions are extremely compute intensive generalized matrix multiplication operations encountered in many computational science fields, such as quantum chemistry and nuclear physics. Unlike distributed matrix multiplication, which has been extensively studied, limited work has been done in understanding distributed tensor contractions. In this paper, we characterize distributed tensor contraction algorithms on torus networks. We develop a framework with three fundamental communication operators to generate communication-efficient contraction algorithms for arbitrary tensor contractions. We show that for a given amount of memory per processor, our framework is communication optimal for all tensor contractions. We demonstrate performance and scalability of our framework on up to 262,144 cores of BG/Q supercomputer using five tensor contraction examples.

  12. Kinetic-energy-momentum tensor in electrodynamics

    NASA Astrophysics Data System (ADS)

    Sheppard, Cheyenne J.; Kemp, Brandon A.

    2016-01-01

    We show that the Einstein-Laub formulation of electrodynamics is invalid since it yields a stress-energy-momentum (SEM) tensor 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 tensors 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 tensor transforms. Within each analysis, the Einstein-Laub formulation violates special relativity, which invalidates the Einstein-Laub SEM tensor.

  13. Quantum dress for a naked singularity

    NASA Astrophysics Data System (ADS)

    Casals, Marc; Fabbri, Alessandro; Martínez, Cristián; Zanelli, Jorge

    2016-09-01

    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 quantum stress-energy tensor 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.

  14. Tensor sufficient dimension reduction

    PubMed Central

    Zhong, Wenxuan; Xing, Xin; Suslick, Kenneth

    2015-01-01

    Tensor is a multiway array. With the rapid development of science and technology in the past decades, large amount of tensor observations are routinely collected, processed, and stored in many scientific researches and commercial activities nowadays. The colorimetric sensor array (CSA) data is such an example. Driven by the need to address data analysis challenges that arise in CSA data, we propose a tensor dimension reduction model, a model assuming the nonlinear dependence between a response and a projection of all the tensor predictors. The tensor dimension reduction models are estimated in a sequential iterative fashion. The proposed method is applied to a CSA data collected for 150 pathogenic bacteria coming from 10 bacterial species and 14 bacteria from one control species. Empirical performance demonstrates that our proposed method can greatly improve the sensitivity and specificity of the CSA technique. PMID:26594304

  15. Quantum field theory in spaces with closed timelike curves

    NASA Astrophysics Data System (ADS)

    Boulware, David G.

    1992-11-01

    Gott spacetime has closed timelike curves, but no locally anomalous stress 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 quantum field theory is constructed using these eigenfunctions. The resultant interacting quantum 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 stress tensor 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 stress tensor is regular and cannot prevent the formation of the Cauchy horizon.

  16. Entanglement, tensor networks and black hole horizons

    NASA Astrophysics Data System (ADS)

    Molina-Vilaplana, J.; Prior, J.

    2014-11-01

    We elaborate on a previous proposal by Hartman and Maldacena on a tensor 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 tensor 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 quantum quench are also analyzed. To this end, a full tensor network representation of the action of local unitary operations on the bridge state is proposed. This amounts to a tensor network which grows in size by adding succesive layers of bridge states. Finally, we discuss on the holographic interpretation of the tensor network through a notion of distance within the network which emerges from its entanglement distribution.

  17. Positivity of linear maps under tensor powers

    NASA Astrophysics Data System (ADS)

    Müller-Hermes, Alexander; Reeb, David; Wolf, Michael M.

    2016-01-01

    We investigate linear maps between matrix algebras that remain positive under tensor powers, i.e., under tensoring 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 "tensor-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 tensor-stable positive map that is not completely positive yields an upper bound on the quantum 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 quantum capacity, and that moreover it is a strong converse rate for this task.

  18. Tree Tensor Network State with Variable Tensor Order: An Efficient Multireference Method for Strongly Correlated Systems.

    PubMed

    Murg, V; Verstraete, F; Schneider, R; Nagy, P R; Legeza, Ö

    2015-03-10

    We study the tree-tensor-network-state (TTNS) method with variable tensor orders for quantum chemistry. TTNS is a variational method to efficiently approximate complete active space (CAS) configuration interaction (CI) wave functions in a tensor 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 tensors 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 tensor network topology based on quantum 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.

  19. Bandgap tuning with thermal residual stresses induced in a quantum dot.

    PubMed

    Kong, Eui-Hyun; Joo, Soo-Hyun; Park, Hyun-Jin; Song, Seungwoo; Chang, Yong-June; Kim, Hyoung Seop; Jang, Hyun Myung

    2014-09-24

    Lattice distortion induced by residual stresses can alter electronic and mechanical properties of materials significantly. Herein, a novel way of the bandgap tuning in a quantum dot (QD) by lattice distortion is presented using 4-nm-sized CdS QDs grown on a TiO2 particle as an application example. The bandgap tuning (from 2.74 eV to 2.49 eV) of a CdS QD is achieved by suitably adjusting the degree of lattice distortion in a QD via the tensile residual stresses which arise from the difference in thermal expansion coefficients between CdS and TiO2. The idea of bandgap tuning is then applied to QD-sensitized solar cells, achieving ≈60% increase in the power conversion efficiency by controlling the degree of thermal residual stress. Since the present methodology is not limited to a specific QD system, it will potentially pave a way to unexplored quantum effects in various QD-based applications. PMID:24832671

  20. Orthogonal tensor decompositions

    SciTech Connect

    Tamara G. Kolda

    2000-03-01

    The authors explore the orthogonal decomposition of tensors (also known as multi-dimensional arrays or n-way arrays) using two different definitions of orthogonality. They present numerous examples to illustrate the difficulties in understanding such decompositions. They conclude with a counterexample to a tensor extension of the Eckart-Young SVD approximation theorem by Leibovici and Sabatier [Linear Algebra Appl. 269(1998):307--329].

  1. Ground state fidelity from tensor network representations.

    PubMed

    Zhou, Huan-Qiang; Orús, Roman; Vidal, Guifre

    2008-02-29

    For any D-dimensional quantum lattice system, the fidelity between two ground state many-body wave functions is mapped onto the partition function of a D-dimensional classical statistical vertex lattice model with the same lattice geometry. The fidelity per lattice site, analogous to the free energy per site, is well defined in the thermodynamic limit and can be used to characterize the phase diagram of the model. We explain how to compute the fidelity per site in the context of tensor network algorithms, and demonstrate the approach by analyzing the two-dimensional quantum Ising model with transverse and parallel magnetic fields. PMID:18352611

  2. Tensor hypercontraction. II. Least-squares renormalization

    NASA Astrophysics Data System (ADS)

    Parrish, Robert M.; Hohenstein, Edward G.; Martínez, Todd J.; Sherrill, C. David

    2012-12-01

    The least-squares tensor hypercontraction (LS-THC) representation for the electron repulsion integral (ERI) tensor is presented. Recently, we developed the generic tensor hypercontraction (THC) ansatz, which represents the fourth-order ERI tensor as a product of five second-order tensors [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 tensor 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 quantum chemistry.

  3. Tensor hypercontraction. II. Least-squares renormalization.

    PubMed

    Parrish, Robert M; Hohenstein, Edward G; Martínez, Todd J; Sherrill, C David

    2012-12-14

    The least-squares tensor hypercontraction (LS-THC) representation for the electron repulsion integral (ERI) tensor is presented. Recently, we developed the generic tensor hypercontraction (THC) ansatz, which represents the fourth-order ERI tensor as a product of five second-order tensors [E. G. Hohenstein, R. M. Parrish, and T. J. Martínez, J. Chem. Phys. 137, 044103 (2012)]. 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 tensor 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∕r(12) 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 quantum chemistry. PMID:23248986

  4. Quantum Efficiency Loss after PID Stress: Wavelength Dependence on Cell Surface and Cell Edge

    SciTech Connect

    Oh, Jaewon; Bowden, Stuart; TamizhMani, GovindaSamy; Hacke, Peter

    2015-06-14

    It is known that the potential induced degradation (PID) stress of conventional p-base solar cells affects power, shunt resistance, junction recombination, and quantum 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 stress 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 stress testing, a new but simple test setup that does not require laminated cell coupon has been developed and is used in this investigation.

  5. Faster identification of optimal contraction sequences for tensor networks.

    PubMed

    Pfeifer, Robert N C; Haegeman, Jutho; Verstraete, Frank

    2014-09-01

    The efficient evaluation of tensor expressions involving sums over multiple indices is of significant importance to many fields of research, including quantum many-body physics, loop quantum gravity, and quantum chemistry. The computational cost of evaluating an expression may depend strongly on the order in which the index sums are evaluated, and determination of the operation-minimizing contraction sequence for a single tensor network (single term, in quantum chemistry) is known to be NP-hard. The current preferred solution is an exhaustive search, using either an iterative depth-first approach with pruning or dynamic programming and memoization, but these approaches are impractical for many of the larger tensor network ansätze encountered in quantum many-body physics. We present a modified search algorithm with enhanced pruning which exhibits a performance increase of several orders of magnitude while still guaranteeing identification of an optimal operation-minimizing contraction sequence for a single tensor network. A reference implementation for matlab, compatible with the ncon() and multienv() network contractors of arXiv:1402.0939 and Evenbly and Pfeifer, Phys. Rev. B 89, 245118 (2014), respectively, is supplied.

  6. Faster identification of optimal contraction sequences for tensor networks

    NASA Astrophysics Data System (ADS)

    Pfeifer, Robert N. C.; Haegeman, Jutho; Verstraete, Frank

    2014-09-01

    The efficient evaluation of tensor expressions involving sums over multiple indices is of significant importance to many fields of research, including quantum many-body physics, loop quantum gravity, and quantum chemistry. The computational cost of evaluating an expression may depend strongly on the order in which the index sums are evaluated, and determination of the operation-minimizing contraction sequence for a single tensor network (single term, in quantum chemistry) is known to be NP-hard. The current preferred solution is an exhaustive search, using either an iterative depth-first approach with pruning or dynamic programming and memoization, but these approaches are impractical for many of the larger tensor network ansätze encountered in quantum many-body physics. We present a modified search algorithm with enhanced pruning which exhibits a performance increase of several orders of magnitude while still guaranteeing identification of an optimal operation-minimizing contraction sequence for a single tensor network. A reference implementation for matlab, compatible with the ncon() and multienv() network contractors of arXiv:1402.0939 and Evenbly and Pfeifer, Phys. Rev. B 89, 245118 (2014),10.1103/PhysRevB.89.245118, respectively, is supplied.

  7. Conformal killing tensors and covariant Hamiltonian dynamics

    SciTech Connect

    Cariglia, M.; Gibbons, G. W.; Holten, J.-W. van; Horvathy, P. A.; Zhang, P.-M.

    2014-12-15

    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 tensors 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, quantum dots, the Hénon-Heiles and Holt systems, respectively, providing us with Killing tensors of rank that ranges from one to six.

  8. Tensor modes on the string theory landscape

    NASA Astrophysics Data System (ADS)

    Westphal, Alexander

    2013-04-01

    We attempt an estimate for the distribution of the tensor mode fraction r over the landscape of vacua in string theory. The dynamics of eternal inflation and quantum 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 tensor 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.

  9. Visualizing Tensor Normal Distributions at Multiple Levels of Detail.

    PubMed

    Abbasloo, Amin; Wiens, Vitalis; Hermann, Max; Schultz, Thomas

    2016-01-01

    Despite the widely recognized importance of symmetric second order tensor fields in medicine and engineering, the visualization of data uncertainty in tensor fields is still in its infancy. A recently proposed tensorial normal distribution, involving a fourth order covariance tensor, provides a mathematical description of how different aspects of the tensor field, such as trace, anisotropy, or orientation, vary and covary at each point. However, this wealth of information is far too rich for a human analyst to take in at a single glance, and no suitable visualization tools are available. We propose a novel approach that facilitates visual analysis of tensor covariance at multiple levels of detail. We start with a visual abstraction that uses slice views and direct volume rendering to indicate large-scale changes in the covariance structure, and locations with high overall variance. We then provide tools for interactive exploration, making it possible to drill down into different types of variability, such as in shape or orientation. Finally, we allow the analyst to focus on specific locations of the field, and provide tensor glyph animations and overlays that intuitively depict confidence intervals at those points. Our system is demonstrated by investigating the effects of measurement noise on diffusion tensor MRI, and by analyzing two ensembles of stress tensor fields from solid mechanics. PMID:26529741

  10. Quantum field theory in spaces with closed time-like curves

    NASA Astrophysics Data System (ADS)

    Boulware, D. G.

    Gott spacetime has closed timelike curves, but no locally anomalous stress-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 quantum field theory is constructed using these eigenfunctions. The resultant interacting quantum 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 stress tensor 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 stress tensor is regular and cannot prevent the formation of the Cauchy horizon.

  11. Tensor perturbations in a general class of Palatini theories

    SciTech Connect

    Jiménez, Jose Beltrán; Heisenberg, Lavinia; Olmo, Gonzalo J. E-mail: laviniah@kth.se

    2015-06-01

    We study a general class of gravitational theories formulated in the Palatini approach and derive the equations governing the evolution of tensor 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 tensor perturbations equations (including anisotropic stresses) 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 tensor perturbations. As a general result, we show that both tensor perturbations coincide in the absence of anisotropic stresses.

  12. Superconducting tensor gravity gradiometer

    NASA Technical Reports Server (NTRS)

    Paik, H. J.

    1981-01-01

    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 tensor. A dewar flask capable of maintaining helium in a liquid state for a year's duration is under development by NASA, and a superconducting tensor 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.

  13. Tensor network characterization of superconducting circuits

    NASA Astrophysics Data System (ADS)

    Duclos-Cianci, Guillaume; Poulin, David; Najafi-Yazdi, Alireza

    Superconducting circuits are promising candidates in the development of reliable quantum 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 tensor 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.

  14. Quantum fluctuations of radiation pressure

    SciTech Connect

    Wu, Chun-Hsien; Ford, L. H.

    2001-08-15

    Quantum fluctuations of electromagnetic radiation pressure are discussed. We use an approach based on the quantum stress tensor to calculate the fluctuations in velocity and position of a mirror subjected to electromagnetic radiation. Our approach reveals that radiation pressure fluctuations in the case of a coherent state are due to a cross term between vacuum and state dependent terms in a stress tensor operator product. Thus observation of these fluctuations would entail experimental confirmation of this cross term. We first analyze the pressure fluctuations on a single, perfectly reflecting mirror, and then study the case of an interferometer. This involves a study of the effects of multiple bounces in one arm, as well as the correlations of the pressure fluctuations between arms of the interferometer. In all cases, our results are consistent with those previously obtained by Caves using different methods. We argue that the agreement between the different methods supports the reality of the cross term and justifies the methods used in its evaluation.

  15. Physical states in the canonical tensor model from the perspective of random tensor networks

    NASA Astrophysics Data System (ADS)

    Narain, Gaurav; Sasakura, Naoki; Sato, Yuki

    2015-01-01

    Tensor models, generalization of matrix models, are studied aiming for quantum gravity in dimensions larger than two. Among them, the canonical tensor model is formulated as a totally constrained system with first-class constraints, the algebra of which resembles the Dirac algebra of general relativity. When quantized, the physical states are defined to be vanished by the quantized constraints. In explicit representations, the constraint equations are a set of partial differential equations for the physical wave-functions, which do not seem straightforward to be solved due to their non-linear character. In this paper, after providing some explicit solutions for N = 2 , 3, we show that certain scale-free integration of partition functions of statistical systems on random networks (or random tensor networks more generally) provides a series of solutions for general N. Then, by generalizing this form, we also obtain various solutions for general N. Moreover, we show that the solutions for the cases with a cosmological constant can be obtained from those with no cosmological constant for increased N. This would imply the interesting possibility that a cosmological constant can always be absorbed into the dynamics and is not an input parameter in the canonical tensor model. We also observe the possibility of symmetry enhancement in N = 3, and comment on an extension of Airy function related to the solutions.

  16. The regional moment tensor of the 5 May 2014 Chiang Rai earthquake (Mw = 6.5), Northern Thailand, with its aftershocks and its implication to the stress and the instability of the Phayao Fault Zone

    NASA Astrophysics Data System (ADS)

    Noisagool, Sutthipong; Boonchaisuk, Songkhun; Pornsopin, Patinya; Siripunvaraporn, Weerachai

    2016-09-01

    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 tensor (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 stress inversion was applied to these 30 focal mechanisms to determine the stresses of the region, the Mohr's diagram, and the principal fault planes. The retrieved maximum stress 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 stress 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

  17. Killing and conformal Killing tensors

    NASA Astrophysics Data System (ADS)

    Heil, Konstantin; Moroianu, Andrei; Semmelmann, Uwe

    2016-08-01

    We introduce an appropriate formalism in order to study conformal Killing (symmetric) tensors on Riemannian manifolds. We reprove in a simple way some known results in the field and obtain several new results, like the classification of conformal Killing 2-tensors on Riemannian products of compact manifolds, Weitzenböck formulas leading to non-existence results, and construct various examples of manifolds with conformal Killing tensors.

  18. Computer Tensor Codes to Design the War Drive

    NASA Astrophysics Data System (ADS)

    Maccone, C.

    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 Quantum 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 tensor 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 tensor 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 tensors, especially by using different metric signatures, different metric determinant signs, different definitions of the basic Riemann and Ricci tensors, 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 tensor 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 Tensor Code to design the Warp Drive.

  19. Notes on super Killing tensors

    NASA Astrophysics Data System (ADS)

    Howe, P. S.; Lindström, U.

    2016-03-01

    The notion of a Killing tensor is generalised to a superspace setting. Conserved quantities associated with these are defined for superparticles and Poisson brackets are used to define a supersymmetric version of the even Schouten-Nijenhuis bracket. Superconformal Killing tensors in flat superspaces are studied for spacetime dimensions 3,4,5,6 and 10. These tensors are also presented in analytic superspaces and super-twistor spaces for 3,4 and 6 dimensions. Algebraic structures associated with superconformal Killing tensors are also briefly discussed.

  20. A hierarchy of topological tensor network states

    SciTech Connect

    Buerschaper, Oliver; Mombelli, Juan Martin; Aguado, Miguel

    2013-01-15

    We present a hierarchy of quantum many-body states among which many examples of topological order can be identified by construction. We define these states in terms of a general, basis-independent framework of tensor networks based on the algebraic setting of finite-dimensional Hopf C*-algebras. At the top of the hierarchy we identify ground states of new topological lattice models extending Kitaev's quantum double models [Ann. Phys. 303, 2 (2003)]. For these states we exhibit the mechanism responsible for their non-zero topological entanglement entropy by constructing an entanglement renormalization flow. Furthermore, we argue that the hierarchy states are related to each other by the condensation of topological charges.

  1. Particle Production by Tidal Forces, and the Energy - Tensor

    NASA Astrophysics Data System (ADS)

    Massacand, Christophe Maurice Jean-Baptiste

    The quantum production of spinless particles, < n_{k}(t)>, and of energy-momentum-stress, < T^{{a}{b}}(P) >, by the tidal forces of classical curved space-time are investigated in this thesis. In a first part we consider the test case of 1+1 dimensions. Our computations are finite step by step, the predicted evolution of the energy-momentum tensor < T^{ a b} > and of the spectral energy density e_{k}< n_{k }> are consistent with each other throughout curved space-time, < T^ { a b}> is covariantly conserved and has the standard trace anomaly R/24 pi for massless particles. The two chiralities, right-goers versus left-goers, are decoupled, the total < T^{{a} {b}}> is the sum of the chiral parts. We apply our methods to four problems: (1) The Rindler problem. (2) An inhomogeneous patch of curvature produces a burst of energy-momentum and of particles. (3) We compute the quantum production of energy density and pressure for a quantum field in external Friedmann-Robertson -Walker space-times in 1+1 dimensions. (4) We consider the gravitational field of a collapsing shell of classical matter in 3+1 dimensions, and we compute the production of Hawking radiation everywhere inside a linear wave guide in the radial direction. In a second part, we compute the energy density and pressures from a quantum scalar field propagating in the external field of a (3+1)-dimensional, spherically symmetric, static geometry with flat spatial sections. We consider only the (l = 0)-sector of the scalar field. The initial state of the quantum field is the gauge invariant vacuum on one of these hypersurface. Our computations are finite step by step. For the pressures we use the covariant conservation of T^{mu nu} and its four-dimensional trace. We apply our results to the case of the gravitational potential due to an homogeneous spherical body. At late times, i.e. when all switch-on effects are far away from the body, the results are that a static cloud of energy and pressure is formed inside

  2. Reduced white matter integrity in the cingulum and anterior corona radiata in posttraumatic stress disorder in male combat veterans: A diffusion tensor imaging study

    PubMed Central

    Sanjuan, Pilar Margaret; Thoma, Robert; Claus, Eric Daniel; Mays, Nicci; Caprihan, Arvind

    2014-01-01

    Posttraumatic stress (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. PMID:24074963

  3. Competition between the tensor light shift and nonlinear Zeeman effect

    SciTech Connect

    Chalupczak, W.; Wojciechowski, A.; Pustelny, S.; Gawlik, W.

    2010-08-15

    Many precision measurements (e.g., in spectroscopy, atomic clocks, quantum-information processing, etc.) suffer from systematic errors introduced by the light shift. In our experimental configuration, however, the tensor 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 tensor light shift is demonstrated.

  4. Extended tensor products and generalization of the notion of entanglement

    NASA Astrophysics Data System (ADS)

    Khrennikov, Andrei; Rosinger, Elemer E.

    2012-03-01

    Motivated by the novel applications of the mathematical formalism of quantum theory and its generalizations in cognitive science, psychology, social and political sciences, and economics, we extend the notion of the tensor 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 tensor products of non-Archimedean (e.g., p-adic) and complex Hilbert spaces.

  5. Tensor Target Polarization at TRIUMF

    NASA Astrophysics Data System (ADS)

    Smith, G.

    2014-10-01

    The first measurements of tensor observables in πvec d scattering experiments were performed in the mid-80's at TRIUMF, and later at SIN/PSI. The full suite of tensor observables accessible in πvec d elastic scattering were measured: T20, T21, and T22. The vector analyzing power iT11 was also measured. These results led to a better understanding of the three-body theory used to describe this reaction. A direct measurement of the target tensor polarization was also made independent of the usual NMR techniques by exploiting the (nearly) model-independent result for the tensor analyzing power at 90°cm in the πvec d → 2p reaction. This method was also used to check efforts to enhance the tensor polarization by RF burning of the NMR spectrum. A brief description of the methods developed to measure and analyze these experiments is provided.

  6. Quantum reverse hypercontractivity

    SciTech Connect

    Cubitt, Toby; Kastoryano, Michael; Montanaro, Ashley; Temme, Kristan

    2015-10-15

    We develop reverse versions of hypercontractive inequalities for quantum channels. By generalizing classical techniques, we prove a reverse hypercontractive inequality for tensor 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 quantum generalization of non-interactive correlation distillation.

  7. The quantum hydrodynamic model for semiconductor devices

    SciTech Connect

    Gardner, C.L. )

    1994-04-01

    The classical hydrodynamic equations can be extended to include quantum effects by incorporating the first quantum corrections. The full three-dimensional quantum 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 stress tensor have additional quantum terms. These quantum 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 quantum 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 quantum well.

  8. Stress influenced trapping processes in Si based multi-quantum well structures and heavy ions implanted Si

    SciTech Connect

    Ciurea, Magdalena Lidia Lazanu, Sorina

    2014-10-06

    Multi-quantum well structures and Si wafers implanted with heavy iodine and bismuth ions are studied in order to evaluate the influence of stress 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 'stress-induced' ones, the last having a Gaussian-shaped temperature dependence of the cross section. The stress 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.

  9. MATLAB tensor classes for fast algorithm prototyping.

    SciTech Connect

    Bader, Brett William; Kolda, Tamara Gibson

    2004-10-01

    Tensors (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 tensor manipulations that can be used for fast algorithm prototyping. The tensor class extends the functionality of MATLAB's multidimensional arrays by supporting additional operations such as tensor multiplication. The tensor as matrix class supports the 'matricization' of a tensor, i.e., the conversion of a tensor to a matrix (and vice versa), a commonly used operation in many algorithms. Two additional classes represent tensors stored in decomposed formats: cp tensor and tucker tensor. We descibe all of these classes and then demonstrate their use by showing how to implement several tensor algorithms that have appeared in the literature.

  10. Apoptosis and necrosis induced by novel realgar quantum dots in human endometrial cancer cells via endoplasmic reticulum stress signaling pathway

    PubMed Central

    Wang, Huan; Liu, Zhengyun; Gou, Ying; Qin, Yu; Xu, Yaze; Liu, Jie; Wu, Jin-Zhu

    2015-01-01

    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 quantum 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 quantum 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 stress by RQDs were further confirmed by increased expression of GADD153 and GRP78 at both mRNA and protein levels. ER stress 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 stress leading to apoptotic cell death and necrosis. PMID:26357474

  11. Stress-determined nucleation sites above GaAs-capped arrays of InAs quantum dots

    NASA Astrophysics Data System (ADS)

    Latini, V.; Placidi, E.; Arciprete, F.; Tisbi, E.; Patella, F.; Magri, R.

    2016-09-01

    We studied the stress field at the surface of GaAs capping layers of variable thicknesses burying InAs quantum dot arrays using the Finite Element method to solve numerically the equations of the elastic field. The aim is to determine the stress-determined favorable sites for dot nucleation. We show that: (i) depending on the cap thickness, dot distances, and array orientation, sudden transitions in the stress-strain fields occur, leading from a vertical alignment of the dots to an anti-aligned correlation. We find that just few determined positions are favorable for dot nucleation and exclude some other sites previously indicated as favorable in the literature; (ii) the critical thicknesses at which the switch between the vertical alignment and the anti-aligned positions occurs depend on the distance between the dots in a square array and on the ratio between the two different distances if the arrays are rectangular; (iii) the transitions occur within a few nanometer range of the capping layer thickness, and the elastic field undergoes large changes in its properties before and after the transition. This behavior has been revealed by a very accurate fit of the tangential stress field using appropriate fit functions. The fit and parameter functions allow to easily reproduce the stress field in different contexts and are useful in growth simulation models. The results suggest that by properly engineering the capping layer thicknesses in the layers of a stack, it is possible to obtain different three-dimensional quantum dot lattices starting from an initial fixed dot array. Our results are in agreement with the available experimental data.

  12. FAST TRACK COMMUNICATION The Bel-Robinson tensor for topologically massive gravity

    NASA Astrophysics Data System (ADS)

    Deser, S.; Franklin, J.

    2011-02-01

    We construct, and establish the (covariant) conservation of, a 4-index 'super stress tensor' for topologically massive gravity. Separately, we discuss its invalidity in quadratic curvature models and suggest a generalization.

  13. Moment tensors of ten witwatersrand mine tremors

    USGS Publications Warehouse

    McGarr, A.

    1992-01-01

    Ground motions, recorded both underground and on the surface in two of the South African Gold mining districts, were inverted to determine complete moment tensors for 10 mining-induced tremors in the magnitude range 1.9 to 3.3. The resulting moment tensors 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 stress for which the maximum principal stress is oriented vertically. ?? 1992 Birkha??user Verlag.

  14. Quantum hyperbolic geometry in loop quantum gravity with cosmological constant

    NASA Astrophysics Data System (ADS)

    Dupuis, Maïté; Girelli, Florian

    2013-06-01

    Loop quantum gravity (LQG) is an attempt to describe the quantum 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 quantum groups can be used to introduce Λ into the game. Not much is known when defining LQG with a quantum group. Tensor operators can be used to construct observables in any type of discrete quantum gauge theory with a classical/quantum gauge group. We illustrate this by constructing explicitly geometric observables for LQG defined with a quantum group and show for the first time that they encode a quantized hyperbolic geometry. This is a novel argument pointing out the usefulness of quantum groups as encoding a nonzero cosmological constant. We conclude by discussing how tensor operators provide the right formalism to unlock the LQG formulation with a nonzero cosmological constant.

  15. Effect of tensor interaction in the Dirac-attractive radial problem under pseudospin symmetry limit

    SciTech Connect

    Hamzavi, M.; Eshghi, M.; Ikhdair, S. M.

    2012-08-15

    We approximately investigated pseudospin symmetric solutions of the Dirac equation for attractive radial potential, including a Coulomb-like tensor interaction under pseudospin symmetry limit for any spin-orbit quantum number {kappa}. By using the parametric generalization of the Nikiforov-Uvarov method, the energy eigenvalues equation and the corresponding wave functions have been obtained in closed forms. Some numerical results are also given. We presented tensor interaction removes degeneracy between two states in pseudospin doublets.

  16. A Framework for Load Balancing of Tensor Contraction Expressions via Dynamic Task Partitioning

    SciTech Connect

    Lai, Pai-Wei; Stock, Kevin; Rajbhandari, Samyam; Krishnamoorthy, Sriram; Sadayappan, Ponnuswamy

    2013-11-17

    In this paper, we introduce the Dynamic Load-balanced Tensor Contractions (DLTC), a domain-specific library for efficient task parallel execution of tensor contraction expressions, a class of computation encountered in quantum 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 tensor contraction expressions on parallel computers using examples from coupled cluster methods.

  17. Development of the Tensoral Computer Language

    NASA Technical Reports Server (NTRS)

    Ferziger, Joel; Dresselhaus, Eliot

    1996-01-01

    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 Tensoral, designed to remove this barrier. The Tensoral language provides a framework in which efficient generic data manipulations can be easily coded and implemented. First of all, Tensoral is general. The fundamental objects in Tensoral represent tensor fields and the operators that act on them. The numerical implementation of these tensors and operators is completely and flexibly programmable. New mathematical constructs and operators can be easily added to the Tensoral system. Tensoral is compatible with existing languages. Tensoral tensor 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. Tensoral is very-high-level. Tensor operations in Tensoral typically act on entire databases (i.e., arrays) at one time and may, therefore, correspond to many lines of code in a conventional language. Tensoral is efficient. Tensoral is a compiled language. Database manipulations are simplified optimized and scheduled by the compiler eventually resulting in efficient machine code to implement them.

  18. Hawking radiation from a spherical loop quantum gravity black hole

    NASA Astrophysics Data System (ADS)

    Gambini, Rodolfo; Pullin, Jorge

    2014-06-01

    We introduce quantum field theory on quantum space-times techniques to characterize the quantum vacua as a first step toward studying black hole evaporation in spherical symmetry in loop quantum gravity and compute the Hawking radiation. We use as quantum space-time the recently introduced exact solution of the quantum Einstein equations in vacuum with spherical symmetry and consider a spherically symmetric test scalar field propagating on it. The use of loop quantum gravity techniques in the background space-time naturally regularizes the matter content, solving one of the main obstacles to back-reaction calculations in more traditional treatments. The discreteness of area leads to modifications of the quantum vacua, eliminating the trans-Planckian modes close to the horizon, which in turn eliminates all singularities from physical quantities, like the expectation value of the stress-energy tensor. Apart from this, the Boulware, Hartle-Hawking and Unruh vacua differ little from the treatment on a classical space-time. The asymptotic modes near scri are reproduced very well. We show that the Hawking radiation can be computed, leading to an expression similar to the conventional one but with a high frequency cutoff. Since many of the conclusions concern asymptotic behavior, where the spherical mode of the field behaves in a similar way as higher multipole modes do, the results can be readily generalized to non spherically symmetric fields.

  19. Tensorially consistent microleveling of high resolution full tensor gradiometry data

    NASA Astrophysics Data System (ADS)

    Schiffler, M.; Queitsch, M.; Schneider, M.; Stolz, R.; Krech, W.; Meyer, H.; Kukowski, N.

    2013-12-01

    Full Tensor Magnetic Gradiometry (FTMG) data obtained with Superconductive Quantum Interference Device (SQUID) sensors offer high resolution and a low signal-to-noise ratio. In airborne operation, processing steps for leveling of flight lines using tie-lines and subsequent micro-leveling become important. Airborne SQUID-FTMG surveys show that in magnetically calm regions the overall measurement system noise level of ≈10pT/m RMS is the main contribution to the magnetograms and line-dependent artifacts become visible. Both tie-line and micro-leveling are used to remove these artifacts (corrugations). But, in the application of these standard leveling routines - originally designed for total magnetic intensity measurements - to the tensor components independently, the tracelessness and the symmetry of the resulting corrected tensor is not preserved. We show that tie-line leveling for airborne SQUID-FTMG data can be surpassed using the presented micro-leveling algorithm and discuss how it is designed to preserve the tensor properties. The micro-leveling process is performed via a moving median filter using a geometric median which preserves the properties of the tensor either to the entire tensor at once or to its structural part (eigenvalues) and rotational part (eigenvectors or idempotences) independently. We discuss the impact on data quality for the different micro-leveling methods. At each observation point, the median along the distance of the flight line is subtracted and the median in a specific footprint radius is added. For application of this filter to the rotational states, we use quaternions and quaternion interpolation. Examples of the new processing methods on data acquired with the FTMG system will be presented in this work.

  20. Tensor Target Polarization at TRIUMF

    SciTech Connect

    Smith, G

    2014-10-27

    The first measurements of tensor 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 tensor 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 tensor polarization was also made independent of the usual NMR techniques by exploiting the (nearly) model-independent result for the tensor 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 tensor polarization by RF burning of the NMR spectrum. A brief description of the methods developed to measure and analyze these experiments is provided.

  1. Compressive sensing of sparse tensors.

    PubMed

    Friedland, Shmuel; Li, Qun; Schonfeld, Dan

    2014-10-01

    Compressive sensing (CS) has triggered an enormous research activity since its first appearance. CS exploits the signal's sparsity or compressibility in a particular domain and integrates data compression and acquisition, thus allowing exact reconstruction through relatively few nonadaptive linear measurements. While conventional CS theory relies on data representation in the form of vectors, many data types in various applications, such as color imaging, video sequences, and multisensor networks, are intrinsically represented by higher order tensors. Application of CS to higher order data representation is typically performed by conversion of the data to very long vectors that must be measured using very large sampling matrices, thus imposing a huge computational and memory burden. In this paper, we propose generalized tensor compressive sensing (GTCS)-a unified framework for CS of higher order tensors, which preserves the intrinsic structure of tensor data with reduced computational complexity at reconstruction. GTCS offers an efficient means for representation of multidimensional data by providing simultaneous acquisition and compression from all tensor modes. In addition, we propound two reconstruction procedures, a serial method and a parallelizable method. We then compare the performance of the proposed method with Kronecker compressive sensing (KCS) and multiway compressive sensing (MWCS). We demonstrate experimentally that GTCS outperforms KCS and MWCS in terms of both reconstruction accuracy (within a range of compression ratios) and processing speed. The major disadvantage of our methods (and of MWCS as well) is that the compression ratios may be worse than that offered by KCS.

  2. The Riegeom package: abstract tensor calculation

    NASA Astrophysics Data System (ADS)

    Portugal, R.

    2000-04-01

    This paper describes a new package for abstract tensor calculation. Riegeom can efficiently simplify generic tensor expressions written in the indicial format. It addresses the problem of the cyclic symmetry and the dimension dependent relations of Riemann tensor polynomials. There are tools to manipulate tensors such as substitution and symmetrization functions. The main tensors of the Riemannian geometry have been implemented. The underlying algorithms are based on a precise mathematical formulation of canonical form of tensor expressions described elsewhere. Riegeom is implemented over the Maple system.

  3. Face recognition based tensor structure

    NASA Astrophysics Data System (ADS)

    Yang, De-qiang; Ye, Zhi-xia; Zhao, Yang; Liu, Li-mei

    2012-01-01

    Face recognition has broad applications, and it is a difficult problem since face image can change with photographic conditions, such as different illumination conditions, pose changes and camera angles. How to obtain some invariable features for a face image is the key issue for a face recognition algorithm. In this paper, a novel tensor structure of face image is proposed to represent image features with eight directions for a pixel value. The invariable feature of the face image is then obtained from gradient decomposition to make up the tensor structure. Then the singular value decomposition (SVD) and principal component analysis (PCA) of this tensor structure are used for face recognition. The experimental results from this study show that many difficultly recognized samples can correctly be recognized, and the recognition rate is increased by 9%-11% in comparison with same type of algorithms.

  4. Scalar-tensor cosmological models

    NASA Astrophysics Data System (ADS)

    Serna, A.; Alimi, J. M.

    1996-03-01

    We analyze the qualitative behavior of scalar-tensor cosmologies with an arbitrary monotonic $\\omega(\\Phi)$ function. In particular, we are interested in scalar-tensor theories distinguishable at early epochs from general relativity (GR) but leading to predictions compatible with solar-system experiments. After extending the method developed by Lorentz-Petzold and Barrow, we establish the conditions required for convergence towards GR at $t \\rightarrow \\infty$. Then, we obtain all the asymptotic analytical solutions at early times which are possible in the framework of these theories. The subsequent qualitative evolution, from these asymptotic solutions until their later convergence towards GR, is analyzed by means of numerical computations. From this analysis, we are able to establish a classification of the different qualitative behaviors of scalar-tensor cosmological models with an arbitrary monotonic $\\omega(\\Phi)$ function

  5. O( N) Random Tensor Models

    NASA Astrophysics Data System (ADS)

    Carrozza, Sylvain; Tanasa, Adrian

    2016-11-01

    We define in this paper a class of three-index tensor models, endowed with {O(N)^{⊗ 3}} invariance ( N being the size of the tensor). This allows to generate, via the usual QFT perturbative expansion, a class of Feynman tensor 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.

  6. Wave transport and statistical properties of an open non-Hermitian quantum dot with parity-time symmetry

    NASA Astrophysics Data System (ADS)

    Wahlstrand, B.; Yakimenko, I. I.; Berggren, K.-F.

    2014-06-01

    A basic quantum-mechanical model for wave functions and current flow in open quantum dots or billiards is investigated. The model involves non-Hertmitian quantum mechanics, parity-time (PT) symmetry, and PT-symmetry breaking. Attached leads are represented by positive and negative imaginary potentials. Thus probability densities, currents flows, etc., for open quantum dots or billiards may be simulated in this way by solving the Schrödinger equation with a complex potential. Here we consider a nominally open ballistic quantum dot emulated by a planar microwave billiard. Results for probability distributions for densities, currents (Poynting vector), and stress tensor components are presented and compared with predictions based on Gaussian random wave theory. The results are also discussed in view of the corresponding measurements for the analogous microwave cavity. The model is of conceptual as well as of practical and educational interest.

  7. The current density in quantum electrodynamics in external potentials

    NASA Astrophysics Data System (ADS)

    Schlemmer, Jan; Zahn, Jochen

    2015-08-01

    We review different definitions of the current density for quantized fermions in the presence of an external electromagnetic field. Several deficiencies in the popular prescription due to Schwinger and the mode sum formula for static external potentials are pointed out. We argue that Dirac's method, which is the analog of the Hadamard point-splitting employed in quantum field theory in curved space-times, is conceptually the most satisfactory. As a concrete example, we discuss vacuum polarization and the stress-energy tensor for massless fermions in 1+1 dimension. Also a general formula for the vacuum polarization in static external potentials in 3+1 dimensions is derived.

  8. Spherical tensor analysis of nuclear magnetic resonance signals.

    PubMed

    van Beek, Jacco D; Carravetta, Marina; Antonioli, Gian Carlo; Levitt, Malcolm H

    2005-06-22

    In a nuclear magnetic-resonance (NMR) experiment, the spin density operator may be regarded as a superposition of irreducible spherical tensor operators. Each of these spin operators evolves during the NMR experiment and may give rise to an NMR signal at a later time. The NMR signal at the end of a pulse sequence may, therefore, be regarded as a superposition of spherical components, each derived from a different spherical tensor operator. We describe an experimental method, called spherical tensor analysis (STA), which allows the complete resolution of the NMR signal into its individual spherical components. The method is demonstrated on a powder of a (13)C-labeled amino acid, exposed to a pulse sequence generating a double-quantum effective Hamiltonian. The propagation of spin order through the space of spherical tensor operators is revealed by the STA procedure, both in static and rotating solids. Possible applications of STA to the NMR of liquids, liquid crystals, and solids are discussed. PMID:16035785

  9. Mixed symmetry tensors in the worldline formalism

    NASA Astrophysics Data System (ADS)

    Corradini, Olindo; Edwards, James P.

    2016-05-01

    We consider the first quantised approach to quantum field theory coupled to a non-Abelian gauge field. Representing the colour degrees of freedom with a single family of auxiliary variables the matter field transforms in a reducible representation of the gauge group which — by adding a suitable Chern-Simons term to the particle action — can be projected onto a chosen fully (anti-)symmetric representation. By considering F families of auxiliary variables, we describe how to extend the model to arbitrary tensor products of F reducible representations, which realises a U( F ) "flavour" symmetry on the world-line particle model. Gauging this symmetry allows the introduction of constraints on the Hilbert space of the colour fields which can be used to project onto an arbitrary irreducible representation, specified by a certain Young tableau. In particular the occupation numbers of the wavefunction — i.e. the lengths of the columns (rows) of the Young tableau — are fixed through the introduction of Chern-Simons terms. We verify this projection by calculating the number of colour degrees of freedom associated to the matter field. We suggest that, using the worldline approach to quantum field theory, this mechanism will allow the calculation of one-loop scattering amplitudes with the virtual particle in an arbitrary representation of the gauge group.

  10. The Invar tensor package: Differential invariants of Riemann

    NASA Astrophysics Data System (ADS)

    Martín-García, J. M.; Yllanes, D.; Portugal, R.

    2008-10-01

    the distribution. To obtain the Mathematica and Maple database files click on this link. Classification:1.5, 5 Does the new version supersede the previous version?:Yes. The previous version (1.0) only handled algebraic invariants. The current version (2.0) has been extended to cover differential invariants as well. Nature of problem:Manipulation and simplification of scalar polynomial expressions formed from the Riemann tensor and its covariant derivatives. Solution method:Algorithms of computational group theory to simplify expressions with tensors that obey permutation symmetries. Tables of syzygies of the scalar invariants of the Riemann tensor. Reasons for new version:With this new version, the user can manipulate differential invariants of the Riemann tensor. Differential invariants are required in many physical problems in classical and quantum gravity. Summary of revisions:The database of syzygies has been expanded by a factor of 30. New commands were added in order to deal with the enlarged database and to manipulate the covariant derivative. Restrictions:The present version only handles scalars, and not expressions with free indices. Additional comments:The distribution file for this program is over 53 Mbytes and therefore is not delivered directly when download or Email is requested. Instead a html file giving details of how the program can be obtained is sent. Running time:One second to fully reduce any monomial of the Riemann tensor up to degree 7 or order 10 in terms of independent invariants. The Mathematica notebook included in the distribution takes approximately 5 minutes to run.

  11. Darkening of interwell excitons in coupled quantum wells due to a stress-induced direct-to-indirect transition

    NASA Astrophysics Data System (ADS)

    Wuenschell, J. K.; Sinclair, N. W.; Vörös, Z.; Snoke, D. W.; Pfeiffer, L. N.; West, K. W.

    2015-12-01

    In previous studies, an inhomogeneous strain field was used as a trapping mechanism for interwell excitons in coupled GaAs/Al0.45Ga0.55As quantum wells. Photoluminescence measurements in this system demonstrated the presence of a dark population of excitons at trap center in the low-temperature, high-stress, high-density regime. The dramatic appearance of this effect at low temperature and high density initially suggested that it may be indicative of a Bose-Einstein condensation phase transition. Further experiments revealed that this effect appears more readily in wider quantum wells and occurs at strain values near the heavy-hole/light-hole crossover point. In this paper, it will be shown that this effect occurs in a regime where the heavy-hole valence band maximum shifts away from k||=0 , which is expected to strongly suppress the recombination rate at low temperatures. Simulations based on this assumption will be shown to match the experimentally observed behavior, without requiring the appearance of a Bose-Einstein condensate.

  12. Residual stress induced crystalline to amorphous phase transformation in Nb{sub 2}O{sub 5} quantum dots

    SciTech Connect

    Dhawan, Sahil; Vedeshwar, Agnikumar G.; Dhawan, Tanuj

    2014-07-28

    Nb{sub 2}O{sub 5} quantum 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 stress 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 stress with film thickness. The residual stress dependence of band gap of crystalline films yields stress 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.

  13. Databases post-processing in Tensoral

    NASA Technical Reports Server (NTRS)

    Dresselhaus, Eliot

    1994-01-01

    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 Tensoral language, introduced in this document and currently existing in prototype form, is the foundation of this effort. Tensoral 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 Tensoral and its prototype implementation in the form of a user's guide. This guide focuses on use of Tensoral for post-processing turbulence databases. The corresponding document - the Tensoral 'author's guide' - which focuses on how authors can make databases available to users via the Tensoral system - is currently unwritten. Section 1 of this user's guide defines Tensoral's basic notions: we explain the class of problems at hand and how Tensoral abstracts them. Section 2 defines Tensoral syntax for mathematical expressions. Section 3 shows how these expressions make up Tensoral statements. Section 4 shows how Tensoral statements and expressions are embedded into other computer languages (such as C or Vectoral) to make Tensoral programs. We conclude with a complete example program.

  14. Viability of vector-tensor theories of gravity

    SciTech Connect

    Jimenez, Jose Beltran; Maroto, Antonio L. E-mail: maroto@fis.ucm.es

    2009-02-15

    We present a detailed study of the viability of general vector-tensor 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 tensor 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 quantum 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.

  15. Quantum Max-flow/Min-cut

    NASA Astrophysics Data System (ADS)

    Cui, Shawn X.; Freedman, Michael H.; Sattath, Or; Stong, Richard; Minton, Greg

    2016-06-01

    The classical max-flow min-cut theorem describes transport through certain idealized classical networks. We consider the quantum analog for tensor networks. By associating an integral capacity to each edge and a tensor to each vertex in a flow network, we can also interpret it as a tensor network and, more specifically, as a linear map from the input space to the output space. The quantum max-flow is defined to be the maximal rank of this linear map over all choices of tensors. The quantum min-cut is defined to be the minimum product of the capacities of edges over all cuts of the tensor network. We show that unlike the classical case, the quantum 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 quantum max-flow is proved to equal the quantum min-cut. However, concrete examples are also provided where the equality does not hold. We also found connections of quantum max-flow/min-cut with entropy of entanglement and the quantum satisfiability problem. We speculate that the phenomena revealed may be of interest both in spin systems in condensed matter and in quantum gravity.

  16. An efficient tensor transpose algorithm for multicore CPU, Intel Xeon Phi, and NVidia Tesla GPU

    DOE PAGESBeta

    Lyakh, Dmitry I.

    2015-01-05

    An efficient parallel tensor transpose algorithm is suggested for shared-memory computing units, namely, multicore CPU, Intel Xeon Phi, and NVidia GPU. The algorithm operates on dense tensors (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 tensor contractions into matrix multiplications in computer implementations of advanced methods of quantum many-body theory (e.g., in electronic structure theory and nuclear physics). A particular accent is made on higher-dimensional tensors that typicallymore » appear in the so-called multireference correlated methods of electronic structure theory. Depending on tensor 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 tensor transpose routines developed in this work have been incorporated into a general-purpose tensor algebra library (TAL-SH).« less

  17. An efficient tensor transpose algorithm for multicore CPU, Intel Xeon Phi, and NVidia Tesla GPU

    SciTech Connect

    Lyakh, Dmitry I.

    2015-01-05

    An efficient parallel tensor transpose algorithm is suggested for shared-memory computing units, namely, multicore CPU, Intel Xeon Phi, and NVidia GPU. The algorithm operates on dense tensors (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 tensor contractions into matrix multiplications in computer implementations of advanced methods of quantum many-body theory (e.g., in electronic structure theory and nuclear physics). A particular accent is made on higher-dimensional tensors that typically appear in the so-called multireference correlated methods of electronic structure theory. Depending on tensor 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 tensor transpose routines developed in this work have been incorporated into a general-purpose tensor algebra library (TAL-SH).

  18. An efficient tensor transpose algorithm for multicore CPU, Intel Xeon Phi, and NVidia Tesla GPU

    NASA Astrophysics Data System (ADS)

    Lyakh, Dmitry I.

    2015-04-01

    An efficient parallel tensor transpose algorithm is suggested for shared-memory computing units, namely, multicore CPU, Intel Xeon Phi, and NVidia GPU. The algorithm operates on dense tensors (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 tensor contractions into matrix multiplications in computer implementations of advanced methods of quantum many-body theory (e.g., in electronic structure theory and nuclear physics). A particular accent is made on higher-dimensional tensors that typically appear in the so-called multireference correlated methods of electronic structure theory. Depending on tensor 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 tensor transpose routines developed in this work have been incorporated into a general-purpose tensor algebra library (TAL-SH).

  19. A practical introduction to tensor networks: Matrix product states and projected entangled pair states

    SciTech Connect

    Orús, Román

    2014-10-15

    This is a partly non-technical introduction to selected topics on tensor 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 tensor 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 quantum lattice systems are also discussed. - Highlights: • A practical introduction to selected aspects of tensor network methods is presented. • We provide analytical examples of MPS and 2d PEPS. • We provide basic aspects on several numerical methods for MPS and 2d PEPS. • We discuss a number of applications of tensor network methods from a broad perspective.

  20. Superactivation of quantum nonlocality.

    PubMed

    Palazuelos, Carlos

    2012-11-01

    In this Letter we show that quantum nonlocality can be superactivated. That is, one can obtain violations of Bell inequalities by tensorizing a local state with itself. In the second part of this work we study how large these violations can be. In particular, we show the existence of quantum states with very low Bell violation but such that five copies of them give very large violations. In fact, this gap can be made arbitrarily large by increasing the dimension of the states.

  1. Projectors and seed conformal blocks for traceless mixed-symmetry tensors

    NASA Astrophysics Data System (ADS)

    Costa, Miguel S.; Hansen, Tobias; Penedones, João; Trevisani, Emilio

    2016-07-01

    In this paper we derive the projectors to all irreducible SO( d) representations (traceless mixed-symmetry tensors) that appear in the partial wave decomposition of a conformal correlator of four stress-tensors 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 tensors and the general normalization constant of the shadow operator.

  2. Experimental evaluation of the tensor polynomial failure criterion for the design of composite structures

    NASA Technical Reports Server (NTRS)

    Tennyson, R. C.

    1975-01-01

    The experimental measures and techniques are described which are used to obtain the strength tensor 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 stress tensor 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 tensor strength terms, F sub 2 and F sub 22. Other laminate configurations yield corresponding variations for the remaining strength parameters.

  3. The classical model for moment tensors

    NASA Astrophysics Data System (ADS)

    Tape, W.; Tape, C.

    2013-12-01

    A seismic moment tensor is a description of an earthquake source, but the description is indirect. The moment tensor describes seismic radiation rather than the actual physical process that initiates the radiation. A moment tensor 'model' then ties the physical process to the moment tensor. The model is not unique, and the physical process is therefore not unique. In the classical moment tensor 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 tensor 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 tensors, 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 tensor is regarded as the sum of a crack tensor and a double couple. A compilation of full moment tensors 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 tensors have very large uncertainties. We question the common interpretation of the isotropic component as a volume change in the source region.

  4. A uniform parametrization of moment tensors

    NASA Astrophysics Data System (ADS)

    Tape, Walter; Tape, Carl

    2015-09-01

    A moment tensor is a 3 × 3 symmetric matrix that expresses an earthquake source. We construct a parametrization of the 5-D space of all moment tensors of unit norm. The coordinates associated with the parametrization are closely related to moment tensor orientations and source types. The parametrization is uniform, in the sense that equal volumes in the coordinate domain of the parametrization correspond to equal volumes of moment tensors. Uniformly distributed points in the coordinate domain therefore give uniformly distributed moment tensors. A cartesian grid in the coordinate domain can be used to search efficiently over moment tensors. We find that uniformly distributed moment tensors have uniformly distributed orientations (eigenframes), but that their source types (eigenvalue triples) are distributed so as to favour double couples.

  5. Killing(-Yano) tensors in string theory

    NASA Astrophysics Data System (ADS)

    Chervonyi, Yuri; Lunin, Oleg

    2015-09-01

    We construct the Killing(-Yano) tensors for a large class of charged black holes in higher dimensions and study general properties of such tensors, in particular, their behavior under string dualities. Killing(-Yano) tensors 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 tensor, we provide a prescription for constructing several conserved quantities starting from a single object, and we demonstrate that Killing tensors in higher dimensions are always associated with ellipsoidal coordinates. We also determine the transformations of the Killing(-Yano) tensors 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) tensors for the Myers-Perry black hole in arbitrary number of dimensions and for its charged version.

  6. The method of planes pressure tensor for a spherical subvolume

    SciTech Connect

    Heyes, D. M. Smith, E. R. Dini, D. Zaki, T. A.

    2014-02-07

    Various formulas for the local pressure tensor 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 tensor 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 tensor formulas for a plane are shown to be the large radius limits of those for spherical surfaces. The radial-dependence of the pressure tensor 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 stress 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.

  7. Local virial and tensor theorems.

    PubMed

    Cohen, Leon

    2011-11-17

    We show that for any wave function and potential the local virial theorem can always be satisfied 2K(r) = r·ΔV by choosing a particular expression for the local kinetic energy. In addition, we show that for each choice of local kinetic energy there are an infinite number of quasi-probability distributions which will generate the same expression. We also consider the local tensor virial theorem.

  8. Local virial and tensor theorems.

    PubMed

    Cohen, Leon

    2011-11-17

    We show that for any wave function and potential the local virial theorem can always be satisfied 2K(r) = r·ΔV by choosing a particular expression for the local kinetic energy. In addition, we show that for each choice of local kinetic energy there are an infinite number of quasi-probability distributions which will generate the same expression. We also consider the local tensor virial theorem. PMID:21863837

  9. Multiview face recognition: from TensorFace to V-TensorFace and K-TensorFace.

    PubMed

    Tian, Chunna; Fan, Guoliang; Gao, Xinbo; Tian, Qi

    2012-04-01

    Face images under uncontrolled environments suffer from the changes of multiple factors such as camera view, illumination, expression, etc. Tensor analysis provides a way of analyzing the influence of different factors on facial variation. However, the TensorFace model creates a difficulty in representing the nonlinearity of view subspace. In this paper, to break this limitation, we present a view-manifold-based TensorFace (V-TensorFace), in which the latent view manifold preserves the local distances in the multiview face space. Moreover, a kernelized TensorFace (K-TensorFace) for multiview face recognition is proposed to preserve the structure of the latent manifold in the image space. Both methods provide a generative model that involves a continuous view manifold for unseen view representation. Most importantly, we propose a unified framework to generalize TensorFace, V-TensorFace, and K-TensorFace. Finally, an expectation-maximization like algorithm is developed to estimate the identity and view parameters iteratively for a face image of an unknown/unseen view. The experiment on the PIE database shows the effectiveness of the manifold construction method. Extensive comparison experiments on Weizmann and Oriental Face databases for multiview face recognition demonstrate the superiority of the proposed V- and K-TensorFace methods over the view-based principal component analysis and other state-of-the-art approaches for such purpose. PMID:22318490

  10. Multireference Ab Initio Calculations of g tensors for Trinuclear Copper Clusters in Multicopper Oxidases

    PubMed Central

    Vancoillie, Steven; Chalupský, Jakub; Ryde, Ulf; Solomon, Edward I.; Pierloot, Kristine; Neese, Frank; Rulíšek, Lubomír

    2010-01-01

    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 quantum chemical packages. However, there have only been a few attempts to calculate EPR g tensors for exchange-coupled systems with more than two spins. In this work, we present a quantum 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 tensors as the current benchmark of quantum chemical methods. By decomposing the calculated g tensors 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 tensors 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 quantum chemical method that is applicable to systems of the size of our target systems. PMID:20469875

  11. Generalised tensor fluctuations and inflation

    SciTech Connect

    Cannone, Dario; Tasinato, Gianmassimo; Wands, David E-mail: g.tasinato@swansea.ac.uk

    2015-01-01

    Using an effective field theory approach to inflation, we examine novel properties of the spectrum of inflationary tensor 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 tensor 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 tensor fluctuations, and showing that they can mimic some of the interesting effects of symmetry breaking operators, even in scenarios that preserve spatial diffeomorphism invariance.

  12. Fundamental limitations in the purifications of tensor networks

    NASA Astrophysics Data System (ADS)

    De las Cuevas, G.; Cubitt, T. S.; Cirac, J. I.; Wolf, M. M.; Pérez-García, D.

    2016-07-01

    We show a fundamental limitation in the description of quantum many-body mixed states with tensor 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.

  13. Sparse alignment for robust tensor learning.

    PubMed

    Lai, Zhihui; Wong, Wai Keung; Xu, Yong; Zhao, Cairong; Sun, Mingming

    2014-10-01

    Multilinear/tensor 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 tensor alignment framework. From this framework, it is easy to show that the manifold learning based tensor learning methods are intrinsically different from the alignment techniques. Based on the alignment framework, a robust tensor learning method called sparse tensor alignment (STA) is then proposed for unsupervised tensor feature extraction. Different from the existing tensor 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 tensor 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 tensors demonstrate that the proposed STA algorithm gives the most competitive performance when compared with the tensor-based unsupervised learning methods. PMID:25291733

  14. Tensor Network Algorithms for Braiding Anyons

    NASA Astrophysics Data System (ADS)

    Ayeni, Babatunde; Singh, Sukhwinder; Pfeifer, Robert; Brennen, Gavin

    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 quantum 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 tensor 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.

  15. Calibration of SQUID vector magnetometers in full tensor gradiometry systems

    NASA Astrophysics Data System (ADS)

    Schiffler, M.; Queitsch, M.; Stolz, R.; Chwala, A.; Krech, W.; Meyer, H.-G.; Kukowski, N.

    2014-08-01

    Measurement of magnetic vector or tensor quantities, namely of field or field gradient, delivers more details of the underlying geological setting in geomagnetic prospection than a scalar measurement of a single component or of the scalar total magnetic intensity. Currently, highest measurement resolutions are achievable with superconducting quantum interference device (SQUID)-based systems. Due to technological limitations, it is necessary to suppress the parasitic magnetic field response from the SQUID gradiometer signals, which are a superposition of one tensor component and all three orthogonal magnetic field components. This in turn requires an accurate estimation of the local magnetic field. Such a measurement can itself be achieved via three additional orthogonal SQUID reference magnetometers. It is the calibration of such a SQUID reference vector magnetometer system that is the subject of this paper. A number of vector magnetometer calibration methods are described in the literature. We present two methods that we have implemented and compared, for their suitability of rapid data processing and integration into a full tensor magnetic gradiometry, SQUID-based, system. We conclude that the calibration routines must necessarily model fabrication misalignments, field offset and scale factors, and include comparison with a reference magnetic field. In order to enable fast processing on site, the software must be able to function as a stand-alone toolbox.

  16. Optimizing Tensor Contraction Expressions for Hybrid CPU-GPU Execution

    SciTech Connect

    Ma, Wenjing; Krishnamoorthy, Sriram; Villa, Oreste; Kowalski, Karol; Agrawal, Gagan

    2013-03-01

    Tensor contractions are generalized multidimensional matrix multiplication operations that widely occur in quantum chemistry. Efficient execution of tensor 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 tensor 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.

  17. Inflationary tensor perturbations after BICEP2.

    PubMed

    Caligiuri, Jerod; Kosowsky, Arthur

    2014-05-16

    The measurement of B-mode polarization of the cosmic microwave background at large angular scales by the BICEP experiment suggests a stochastic gravitational wave background from early-Universe inflation with a surprisingly large amplitude. The power spectrum of these tensor perturbations can be probed both with further measurements of the microwave background polarization at smaller scales and also directly via interferometry in space. We show that sufficiently sensitive high-resolution B-mode measurements will ultimately have the ability to test the inflationary consistency relation between the amplitude and spectrum of the tensor perturbations, confirming their inflationary origin. Additionally, a precise B-mode measurement of the tensor spectrum will predict the tensor amplitude on solar system scales to 20% accuracy for an exact power-law tensor spectrum, so a direct detection will then measure the running of the tensor spectral index to high precision.

  18. Gravitoelectromagnetic analogy based on tidal tensors

    SciTech Connect

    Costa, L. Filipe O.; Herdeiro, Carlos A. R.

    2008-07-15

    We propose a new approach to a physical analogy between general relativity and electromagnetism, based on tidal tensors 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 tensors to exact electromagnetic tidal tensors in Minkowski spacetime. The second one matches exact magnetic gravitational tidal tensors for ultrastationary metrics to exact magnetic tidal tensors 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 tensors of both theories are also discussed.

  19. Tensor coupling effect on relativistic symmetries

    NASA Astrophysics Data System (ADS)

    Chen, ShouWan; Li, DongPeng; Guo, JianYou

    2016-08-01

    The similarity renormalization group is used to transform the Dirac Hamiltonian with tensor coupling into a diagonal form. The upper (lower) diagonal element becomes a Schr¨odinger-like operator with the tensor component separated from the original Hamiltonian. Based on the operator, the tensor effect of the relativistic symmetries is explored with a focus on the single-particle energy contributed by the tensor coupling. The results show that the tensor coupling destroying (improving) the spin (pseudospin) symmetry is mainly attributed to the coupling of the spin-orbit and the tensor term, which plays an opposite role in the single-particle energy for the (pseudo-) spin-aligned and spin-unaligned states and has an important influence on the shell structure and its evolution.

  20. Inflationary tensor perturbations after BICEP2.

    PubMed

    Caligiuri, Jerod; Kosowsky, Arthur

    2014-05-16

    The measurement of B-mode polarization of the cosmic microwave background at large angular scales by the BICEP experiment suggests a stochastic gravitational wave background from early-Universe inflation with a surprisingly large amplitude. The power spectrum of these tensor perturbations can be probed both with further measurements of the microwave background polarization at smaller scales and also directly via interferometry in space. We show that sufficiently sensitive high-resolution B-mode measurements will ultimately have the ability to test the inflationary consistency relation between the amplitude and spectrum of the tensor perturbations, confirming their inflationary origin. Additionally, a precise B-mode measurement of the tensor spectrum will predict the tensor amplitude on solar system scales to 20% accuracy for an exact power-law tensor spectrum, so a direct detection will then measure the running of the tensor spectral index to high precision. PMID:24877926

  1. Distinct expression profiles of stress defense and DNA repair genes in Daphnia pulex exposed to cadmium, zinc, and quantum dots.

    PubMed

    Tang, Song; Wu, Yonggan; Ryan, Caitlin N; Yu, Shuangying; Qin, Guangqiu; Edwards, Donn S; Mayer, Gregory D

    2015-02-01

    The ever-increasing production and use of nanocrystaline semiconductors (Quantum dots; QDs) will inevitably result in increased appearance of these nanomaterials in the aquatic environment. However, the behavior and potential toxicity of heavy metal constituted nanoparticulates in aquatic invertebrates is largely unknown, especially with regard to molecular responses. The freshwater crustacean Daphnia pulex is a well-suited toxicological and ecological model to study molecular responses to environmental stressors. In this study, D. pulex were exposed for 48 h to sublethal doses of QDs (25% and 50% of LC50) with differing spectral properties (CdTe and CdSe/ZnS QDs) and Cd and Zn salts. Our data suggest that acute exposure to both CdSO4 and Cd-based QDs leads to Cd uptake in vivo, which was biologically supported by the observation of increased expression of metallothionein (MT-1). Furthermore, Cd, Zn, and CdSe/ZnS QDs induced different patterns of gene expression regarding stress defense and DNA repair, which furthers our knowledge regarding which response pathways are affected by nanoparticulate forms of metals versus ionic forms in aquatic crustaceans. PMID:25014899

  2. Liver Toxicity of Cadmium Telluride Quantum Dots (CdTe QDs) Due to Oxidative Stress in Vitro and in Vivo

    PubMed Central

    Zhang, Ting; Hu, Yuanyuan; Tang, Meng; Kong, Lu; Ying, Jiali; Wu, Tianshu; Xue, Yuying; Pu, Yuepu

    2015-01-01

    With the applications of quantum 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 stress 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

  3. Some classes of renormalizable tensor models

    NASA Astrophysics Data System (ADS)

    Geloun, Joseph Ben; Livine, Etera R.

    2013-08-01

    We identify new families of renormalizable tensor models from anterior renormalizable tensor 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 tensor model as defined by Ben Geloun and Samary [Ann. Henri Poincare 14, 1599 (2013); e-print arXiv:1201.0176 [hep-th

  4. Curvature tensors unified field equations on SEXn

    NASA Astrophysics Data System (ADS)

    Chung, Kyung Tae; Lee, Il Young

    1988-09-01

    We study the curvature tensors 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 tensor 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 tensor. Finally, a system of field equations is discussed in SEXn and one of its particular solutions is constructed and displayed.

  5. Wormholes, the weak energy condition, and scalar-tensor gravity

    NASA Astrophysics Data System (ADS)

    Shaikh, Rajibul; Kar, Sayan

    2016-07-01

    We obtain a large class of Lorentzian wormhole spacetimes in scalar-tensor gravity, for which the matter stress energy does satisfy the weak energy condition. Our constructions have zero Ricci scalar and an everywhere finite, nonzero scalar field profile. Interpreting the scalar-tensor 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.

  6. Cosmological footprints of loop quantum gravity.

    PubMed

    Grain, J; Barrau, A

    2009-02-27

    The primordial spectrum of cosmological tensor perturbations is considered as a possible probe of quantum gravity effects. Together with string theory, loop quantum gravity is one of the most promising frameworks to study quantum 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 quantum gravity. PMID:19257730

  7. Cosmological footprints of loop quantum gravity.

    PubMed

    Grain, J; Barrau, A

    2009-02-27

    The primordial spectrum of cosmological tensor perturbations is considered as a possible probe of quantum gravity effects. Together with string theory, loop quantum gravity is one of the most promising frameworks to study quantum 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 quantum gravity.

  8. Quantum modifications to gravity waves in de Sitter spacetime

    SciTech Connect

    Hsiang, Jen-Tsung; Lee, Da-Shin; Ford, L. H.; Yu, Hoi-Lai

    2011-04-15

    We treat a model in which tensor 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 stress tensor 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 quantum stress tensor. We find a correction term which is of the same form as the original wave, but displaced in phase by {pi}/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 tensor perturbations in inflationary cosmology. This enhancement of the power spectrum depends upon the initial time, and is greater for shorter wavelengths.

  9. The classical model for moment tensors

    NASA Astrophysics Data System (ADS)

    Tape, Walter; Tape, Carl

    2013-12-01

    A seismic moment tensor is a description of an earthquake source, but the description is indirect. The moment tensor describes seismic radiation rather than the actual physical process that initiates the radiation. A moment tensor `model' then ties the physical process to the moment tensor. The model is not unique, and the physical process is therefore not unique. In the classical moment tensor 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 tensor 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 tensors, 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 tensor is regarded as the sum of a crack tensor and a double couple.

  10. A uniform parameterization of moment tensors

    NASA Astrophysics Data System (ADS)

    Tape, C.; Tape, W.

    2015-12-01

    A moment tensor is a 3 x 3 symmetric matrix that expresses an earthquake source. We construct a parameterization of the five-dimensional space of all moment tensors of unit norm. The coordinates associated with the parameterization are closely related to moment tensor orientations and source types. The parameterization is uniform, in the sense that equal volumes in the coordinate domain of the parameterization correspond to equal volumes of moment tensors. Uniformly distributed points in the coordinate domain therefore give uniformly distributed moment tensors. A cartesian grid in the coordinate domain can be used to search efficiently over moment tensors. We find that uniformly distributed moment tensors have uniformly distributed orientations (eigenframes), but that their source types (eigenvalue triples) are distributed so as to favor double couples. An appropriate choice of a priori moment tensor probability is a prerequisite for parameter estimation. As a seemingly sensible choice, we consider the homogeneous probability, in which equal volumes of moment tensors are equally likely. We believe that it will lead to improved characterization of source processes.

  11. Diffusion Tensor Estimation by Maximizing Rician Likelihood

    PubMed Central

    Landman, Bennett; Bazin, Pierre-Louis; Prince, Jerry

    2012-01-01

    Diffusion tensor imaging (DTI) is widely used to characterize white matter in health and disease. Previous approaches to the estimation of diffusion tensors have either been statistically suboptimal or have used Gaussian approximations of the underlying noise structure, which is Rician in reality. This can cause quantities derived from these tensors — e.g., fractional anisotropy and apparent diffusion coefficient — to diverge from their true values, potentially leading to artifactual changes that confound clinically significant ones. This paper presents a novel maximum likelihood approach to tensor estimation, denoted Diffusion Tensor Estimation by Maximizing Rician Likelihood (DTEMRL). In contrast to previous approaches, DTEMRL considers the joint distribution of all observed data in the context of an augmented tensor model to account for variable levels of Rician noise. To improve numeric stability and prevent non-physical solutions, DTEMRL incorporates a robust characterization of positive definite tensors and a new estimator of underlying noise variance. In simulated and clinical data, mean squared error metrics show consistent and significant improvements from low clinical SNR to high SNR. DTEMRL may be readily supplemented with spatial regularization or a priori tensor distributions for Bayesian tensor estimation. PMID:23132746

  12. Fast stray field computation on tensor grids.

    PubMed

    Exl, L; Auzinger, W; Bance, S; Gusenbauer, M; Reichel, F; Schrefl, T

    2012-04-01

    A direct integration algorithm is described to compute the magnetostatic field and energy for given magnetization distributions on not necessarily uniform tensor grids. We use an analytically-based tensor approximation approach for function-related tensors, which reduces calculations to multilinear algebra operations. The algorithm scales with N(4/3) for N computational cells used and with N(2/3) (sublinear) when magnetization is given in canonical tensor format. In the final section we confirm our theoretical results concerning computing times and accuracy by means of numerical examples.

  13. Fast stray field computation on tensor grids

    PubMed Central

    Exl, L.; Auzinger, W.; Bance, S.; Gusenbauer, M.; Reichel, F.; Schrefl, T.

    2012-01-01

    A direct integration algorithm is described to compute the magnetostatic field and energy for given magnetization distributions on not necessarily uniform tensor grids. We use an analytically-based tensor approximation approach for function-related tensors, which reduces calculations to multilinear algebra operations. The algorithm scales with N4/3 for N computational cells used and with N2/3 (sublinear) when magnetization is given in canonical tensor format. In the final section we confirm our theoretical results concerning computing times and accuracy by means of numerical examples. PMID:24910469

  14. Spectral expansions of homogeneous and isotropic tensor-valued random fields

    NASA Astrophysics Data System (ADS)

    Malyarenko, Anatoliy; Ostoja-Starzewski, Martin

    2016-06-01

    We establish spectral expansions of tensor-valued homogeneous and isotropic random fields in terms of stochastic integrals with respect to orthogonal scattered random measures previously known only for the case of tensor rank 0. The fields under consideration take values in the 3-dimensional Euclidean space {E^3} and in the space {S^2(E^3)} of symmetric rank 2 tensors over {E^3}. We find a link between the theory of random fields and the theory of finite-dimensional convex compact sets. These random fields furnish stepping-stone for models of rank 1 and rank 2 tensor-valued fields in continuum physics, such as displacement, velocity, stress, strain, providing appropriate conditions (such as the governing equation or positive-definiteness) are imposed.

  15. A practical introduction to tensor networks: Matrix product states and projected entangled pair states

    NASA Astrophysics Data System (ADS)

    Orús, Román

    2014-10-01

    This is a partly non-technical introduction to selected topics on tensor 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 tensor 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 quantum lattice systems are also discussed.

  16. 3D reconstruction of tensors and vectors

    SciTech Connect

    Defrise, Michel; Gullberg, Grant T.

    2005-02-17

    Here we have developed formulations for the reconstruction of 3D tensor fields from planar (Radon) and line-integral (X-ray) projections of 3D vector and tensor fields. Much of the motivation for this work is the potential application of MRI to perform diffusion tensor 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 tensor tomography problem provides insight into the structure of the nonlinear MRI diffusion tensor inverse problem. A particular application of tensor imaging in MRI is the potential application of cardiac diffusion tensor 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 tensor 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 tensor 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 tensor fields and to other geometric acquisitions such as cone beam tomography of tensor fields.

  17. Stress

    MedlinePlus

    ... hurt or killed. Examples include a major accident, war, assault, or a natural disaster. This type of ... stress, so you can avoid more serious health effects. NIH: National Institute of Mental Health

  18. In Vivo Generalized Diffusion Tensor Imaging (GDTI) Using Higher-Order Tensors (HOT)

    PubMed Central

    Liu, Chunlei; Mang, Sarah C.; Moseley, Michael E.

    2009-01-01

    Generalized diffusion tensor imaging (GDTI) using higher order tensor statistics (HOT) generalizes the technique of diffusion tensor 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 tensor statistics (i.e. the cumulant tensors or the moment tensors) such as the covariance matrix (the second-order cumulant tensor), the skewness tensor (the third-order cumulant tensor) and the kurtosis tensor (the fourth-order cumulant tensor) 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

  19. Inflation and alternatives with blue tensor spectra

    SciTech Connect

    Wang, Yi; Xue, Wei E-mail: wei.xue@sissa.it

    2014-10-01

    We study the tilt of the primordial gravitational waves spectrum. A hint of blue tilt is shown from analyzing the BICEP2 and POLARBEAR data. Motivated by this, we explore the possibilities of blue tensor spectra from the very early universe cosmology models, including null energy condition violating inflation, inflation with general initial conditions, and string gas cosmology, etc. For the simplest G-inflation, blue tensor spectrum also implies blue scalar spectrum. In general, the inflation models with blue tensor spectra indicate large non-Gaussianities. On the other hand, string gas cosmology predicts blue tensor spectrum with highly Gaussian fluctuations. If further experiments do confirm the blue tensor spectrum, non-Gaussianity becomes a distinguishing test between inflation and alternatives.

  20. X-ray tensor tomography

    NASA Astrophysics Data System (ADS)

    Malecki, A.; Potdevin, G.; Biernath, T.; Eggl, E.; Willer, K.; Lasser, T.; Maisenbacher, J.; Gibmeier, J.; Wanner, A.; Pfeiffer, F.

    2014-02-01

    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 tensor 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.

  1. Dislocation Reduction and Stress Relaxation of GaN and InGaN Multiple Quantum Wells with Improved Performance via Serpentine Channel Patterned Mask.

    PubMed

    Ji, Qingbin; Li, Lei; Zhang, Wei; Wang, Jia; Liu, Peichi; Xie, Yahong; Yan, Tongxing; Yang, Wei; Chen, Weihua; Hu, Xiaodong

    2016-08-24

    The existence of high threading dislocation density (TDD) in GaN-based epilayers is a long unsolved problem, which hinders further applications of defect-sensitive GaN-based devices. Multiple-modulation of epitaxial lateral overgrowth (ELOG) is used to achieve high-quality GaN template on a novel serpentine channel patterned sapphire substrate (SCPSS). The dislocation blocking brought by the serpentine channel patterned mask, coupled with repeated dislocation bending, can reduce the dislocation density to a yet-to-be-optimized level of ∼2 × 10(5) to 2 × 10(6) cm(-2). About 80% area utilization rate of GaN with low TDD and stress relaxation is obtained. The periodical variations of dislocation density, optical properties and residual stress in GaN-based epilayers on SCPSS are analyzed. The quantum efficiency of InGaN/GaN multiple quantum wells (MQWs) on it can be increased by 52% compared with the conventional sapphire substrate. The reduced nonradiative recombination centers, the enhanced carrier localization, and the suppressed quantum confined Stark effect, are the main determinants of improved luminous performance in MQWs on SCPSS. This developed ELOG on serpentine shaped mask needs no interruption and regrowth, which can be a promising candidate for the heteroepitaxy of semipolar/nonpolar GaN and GaAs with high quality.

  2. Dislocation Reduction and Stress Relaxation of GaN and InGaN Multiple Quantum Wells with Improved Performance via Serpentine Channel Patterned Mask.

    PubMed

    Ji, Qingbin; Li, Lei; Zhang, Wei; Wang, Jia; Liu, Peichi; Xie, Yahong; Yan, Tongxing; Yang, Wei; Chen, Weihua; Hu, Xiaodong

    2016-08-24

    The existence of high threading dislocation density (TDD) in GaN-based epilayers is a long unsolved problem, which hinders further applications of defect-sensitive GaN-based devices. Multiple-modulation of epitaxial lateral overgrowth (ELOG) is used to achieve high-quality GaN template on a novel serpentine channel patterned sapphire substrate (SCPSS). The dislocation blocking brought by the serpentine channel patterned mask, coupled with repeated dislocation bending, can reduce the dislocation density to a yet-to-be-optimized level of ∼2 × 10(5) to 2 × 10(6) cm(-2). About 80% area utilization rate of GaN with low TDD and stress relaxation is obtained. The periodical variations of dislocation density, optical properties and residual stress in GaN-based epilayers on SCPSS are analyzed. The quantum efficiency of InGaN/GaN multiple quantum wells (MQWs) on it can be increased by 52% compared with the conventional sapphire substrate. The reduced nonradiative recombination centers, the enhanced carrier localization, and the suppressed quantum confined Stark effect, are the main determinants of improved luminous performance in MQWs on SCPSS. This developed ELOG on serpentine shaped mask needs no interruption and regrowth, which can be a promising candidate for the heteroepitaxy of semipolar/nonpolar GaN and GaAs with high quality. PMID:27484167

  3. Acceleration of Streamed Tensor Contraction Expressions on GPGPU-based Clusters

    SciTech Connect

    Ma, Wenjing; Krishnamoorthy, Sriram; Villa, Oreste; Kowalski, Karol

    2010-09-20

    Tensor contractions are generalized multidimensional matrix multiplication operations that widely occur in quantum chemistry. Efficient execution of tensor contractions on GPUs requires tackling several challenges to be addressed, including index permutation and small dimension-sizes reducing thread block utilization. In this paper, we present our approach to automatically generate CUDA code to execute tensor contractions on GPUs, including management of data movement between CPU and GPU. GPU-enabled code is generated for the most expensive contractions in CCSD(T) and incorporated into NWChem, a popular computational chemistry suite. We demonstrate speedup over a factor of 8.4 using one core per node and over 2.6 when utilizing the entire system using hybrid CPU+GPU solution with 2 GPUs and 5 cores. We finally analyze the behavior of the application on future GPU systems.

  4. Fundamentals in generalized elasticity and dislocation theory of quasicrystals: Green tensor, dislocation key-formulas and dislocation loops

    NASA Astrophysics Data System (ADS)

    Lazar, Markus; Agiasofitou, Eleni

    2014-12-01

    The present work provides fundamental quantities in generalized elasticity and dislocation theory of quasicrystals. In a clear and straightforward manner, the three-dimensional Green tensor 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 tensor 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 stress tensor, Peach-Koehler force, stress function tensor 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 tensor, all other dislocation key-formulas for loops, known from the theory of anisotropic elasticity, like the Peach-Koehler stress formula, Mura-Willis equation, Volterra equation, stress function tensor and the interaction energy are derived for quasicrystals.

  5. Evaluation of the Tensor Polynomial and Hoffman strength theories for composite materials

    NASA Technical Reports Server (NTRS)

    Narayanaswami, R.; Adelman, H. M.

    1977-01-01

    The Hoffman theory and the Tensor Polynomial (Tsai-Wu) theory with the stress interaction term set equal to zero have been found to be preferred alternatives to the general Tensor 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 Tensor Polynomial theory with the stress interaction term equal to zero can predict failure of practical filamentary composite materials under general biaxial loading with sufficient accuracy for engineering applications.

  6. Incremental Discriminant Analysis in Tensor Space

    PubMed Central

    Chang, Liu; Weidong, Zhao; Tao, Yan; Qiang, Pu; Xiaodan, Du

    2015-01-01

    To study incremental machine learning in tensor space, this paper proposes incremental tensor discriminant analysis. The algorithm employs tensor 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

  7. Low uncertainty method for inertia tensor identification

    NASA Astrophysics Data System (ADS)

    Barreto, J. P.; Muñoz, L. E.

    2016-02-01

    The uncertainty associated with the experimental identification of the inertia tensor 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 tensor 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 tensor 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).

  8. Tensor methods for large, sparse unconstrained optimization

    SciTech Connect

    Bouaricha, A.

    1996-11-01

    Tensor 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 tensor 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 tensor methods are significantly more efficient and more reliable than standard methods based on Newton`s method.

  9. Tensor network and a black hole

    NASA Astrophysics Data System (ADS)

    Matsueda, Hiroaki; Ishihara, Masafumi; Hashizume, Yoichiro

    2013-03-01

    A tensor-network variational formalism of thermofield dynamics is introduced. The formalism relates the original Hilbert space with its tilde space by a product of two copies of a tensor network. Then, their interface becomes an event horizon, and the logarithm of the tensor rank corresponds to the black hole entropy. Eventually, a multiscale entanglement renormalization ansatz reproduces an anti-de Sitter black hole at finite temperature. Our finding shows rich functionalities of multiscale entanglement renormalization ansatz as efficient graphical representation of AdS/CFT correspondence.

  10. Continuum tensor network field states, path integral representations and spatial symmetries

    NASA Astrophysics Data System (ADS)

    Jennings, David; Brockt, Christoph; Haegeman, Jutho; Osborne, Tobias J.; Verstraete, Frank

    2015-06-01

    A natural way to generalize tensor network variational classes to quantum field systems is via a continuous tensor contraction. This approach is first illustrated for the class of quantum 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 quantum 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 quantum 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, quantum field theory and quantum information theory, and facilitate future exchanges of ideas and insights between these disciplines.

  11. The energy-momentum tensor for a dissipative fluid in general relativity

    NASA Astrophysics Data System (ADS)

    Pimentel, Oscar M.; Lora-Clavijo, F. D.; González, Guillermo A.

    2016-10-01

    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 tensor of a viscous fluid with heat flux. We introduce the general form of this tensor and, using the approximation of small velocity gradients, we relate the stresses of the fluid with the viscosity coefficients, the shear tensor and the expansion factor. Exploiting these relations, we can write the stresses 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 tensor 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 tensor.

  12. ConnesFusionTensorProduct/Photon GluonFusion in Mitochondria

    NASA Astrophysics Data System (ADS)

    Wh-Maksoed, Prodi Of Physics Ui, Depok 16415-Indonesia; Ssi, Wh-Maksoed

    2016-05-01

    As in AJ Wassermann distinguished of classical invariant theory & quantum invariant theory subfactor, in S. Palcoux:``From Neveu-Schwarz Subfactors & Connes Fusion'' described the subfactor theory & Witt-algebra whereas Andreas Thom's explanation about ConnesFusionTensorProduct/CFTP related Connes fusion to composition of homomorphism (i). classical tensor product O-X adds the changes,(ii). Relative tensor 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 ``quantum field theory which are invariant under conformal transformation & in 2D there are infinite dimensional algebra. Alain Connes states theirselves Connes fusion as ``associative tensor 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.

  13. Vacuum for a massless quantum scalar field outside a collapsing shell in anti-de Sitter space-time

    NASA Astrophysics Data System (ADS)

    Abel, Paul G.; Winstanley, Elizabeth

    2016-08-01

    We consider a massless quantum 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 quantum 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 stress-energy tensor, we find that at late times the black hole is in thermal equilibrium with a heat bath at the Hawking temperature, so the quantum field is in a state analogous to the Hartle-Hawking vacuum on an eternal black hole space-time.

  14. Evolution of tensor perturbations in scalar-tensor theories of gravity

    SciTech Connect

    Carloni, Sante; Dunsby, Peter K. S.

    2007-03-15

    The evolution equations for tensor perturbations in a generic scalar-tensor 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 tensor models depends on the choice of parameters of the theory, no amplification is possible if the gravitational interaction is attractive.

  15. Adaptive Multilinear Tensor Product Wavelets.

    PubMed

    Weiss, Kenneth; Lindstrom, Peter

    2016-01-01

    Many foundational visualization techniques including isosurfacing, direct volume rendering and texture mapping rely on piecewise multilinear interpolation over the cells of a mesh. However, there has not been much focus within the visualization community on techniques that efficiently generate and encode globally continuous functions defined by the union of multilinear cells. Wavelets provide a rich context for analyzing and processing complicated datasets. In this paper, we exploit adaptive regular refinement as a means of representing and evaluating functions described by a subset of their nonzero wavelet coefficients. We analyze the dependencies involved in the wavelet transform and describe how to generate and represent the coarsest adaptive mesh with nodal function values such that the inverse wavelet transform is exactly reproduced via simple interpolation (subdivision) over the mesh elements. This allows for an adaptive, sparse representation of the function with on-demand evaluation at any point in the domain. We focus on the popular wavelets formed by tensor products of linear B-splines, resulting in an adaptive, nonconforming but crack-free quadtree (2D) or octree (3D) mesh that allows reproducing globally continuous functions via multilinear interpolation over its cells.

  16. Interpretation of the Weyl tensor

    NASA Astrophysics Data System (ADS)

    Hofmann, Stefan; Niedermann, Florian; Schneider, Robert

    2013-09-01

    According to folklore in general relativity, the Weyl tensor can be decomposed into parts corresponding to Newton-like, incoming and outgoing wavelike field components. It is shown here that this one-to-one correspondence does not hold for space-time geometries with cylindrical isometries. This is done by investigating some well-known exact solutions of Einstein’s field equations with whole-cylindrical symmetry, for which the physical interpretation is very clear, but for which the standard Weyl interpretation would give contradictory results. For planar or spherical geometries, however, the standard interpretation works for both static and dynamical space-times. It is argued that one reason for the failure in the cylindrical case is that for waves spreading in two spatial dimensions there is no local criterion to distinguish incoming and outgoing waves already at the linear level. It turns out that Thorne’s local energy notion, subject to certain qualifications, provides an efficient diagnostic tool to extract the proper physical interpretation of the space-time geometry in the case of cylindrical configurations.

  17. Unsupervised Tensor Mining for Big Data Practitioners.

    PubMed

    Papalexakis, Evangelos E; Faloutsos, Christos

    2016-09-01

    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? Tensors, 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 tensors and tensor 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 tensor mining tool that can be easily and broadly adopted by practitioners in academia and industry.

  18. The Weyl tensor correlator in cosmological spacetimes

    SciTech Connect

    Fröb, Markus B.

    2014-12-05

    We give a general expression for the Weyl tensor 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 tensor 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 tensor power spectrum from the Weyl tensor correlation function.

  19. Shifted power method for computing tensor eigenpairs.

    SciTech Connect

    Mayo, Jackson R.; Kolda, Tamara Gibson

    2010-10-01

    Recent work on eigenvalues and eigenvectors for tensors 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-tensor 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 tensor. Our contribution is a novel shifted symmetric higher-order power method (SS-HOPM), which we showis guaranteed to converge to a tensor 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.

  20. Shifted power method for computing tensor eigenvalues.

    SciTech Connect

    Mayo, Jackson R.; Kolda, Tamara Gibson

    2010-07-01

    Recent work on eigenvalues and eigenvectors for tensors 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-tensor eigenpairs of the form Ax{sup m-1} = lambda x subject to ||x||=1, which is closely related to optimal rank-1 approximation of a symmetric tensor. Our contribution is a shifted symmetric higher-order power method (SS-HOPM), which we show is guaranteed to converge to a tensor 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 finding complex eigenpairs.

  1. Unsupervised Tensor Mining for Big Data Practitioners.

    PubMed

    Papalexakis, Evangelos E; Faloutsos, Christos

    2016-09-01

    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? Tensors, 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 tensors and tensor 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 tensor mining tool that can be easily and broadly adopted by practitioners in academia and industry. PMID:27642720

  2. The energy-momentum tensor(s) in classical gauge theories

    DOE PAGESBeta

    Gieres, Francois; Blaschke, Daniel N.; Reboud, Meril; Schweda, Manfred

    2016-07-01

    We give an introduction to, and review of, the energy–momentum tensors in classical gauge field theories in Minkowski space, and to some extent also in curved space–time. For the canonical energy–momentum tensor 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 tensor. Here, the relationship with the Einstein–Hilbert tensor following from the coupling to a gravitational field is also discussed.

  3. Temperature-polarization correlations from tensor fluctuations

    SciTech Connect

    Crittenden, R.G.; Coulson, D.; Turok, N.G. |

    1995-11-15

    We study the polarization-temperature correlations on the cosmic microwave sky resulting from an initial scale-invariant spectrum of tensor (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 tensor component. We briefly discuss the important problem of estimating the expected foreground contamination.

  4. Novel Physics with Tensor Polarized Deuteron Targets

    SciTech Connect

    Slifer, Karl J.; Long, Elena A.

    2013-09-01

    Development of solid spin-1 polarized targets will open the study of tensor 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 tensor structure function b1, along with prospects for future experiments with a solid tensor polarized target. The recently approved JLab experiment E12-13-011 will measure the lead- ing twist tensor 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 tensor 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 tensor quark polarization, and allow a test of the Close-Kumano sum rule, which vanishes in the absence of tensor polarization in the quark sea. Until now, tensor 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.

  5. Tensor network studies of the two-dimensional t-J and Hubbard models

    NASA Astrophysics Data System (ADS)

    Corboz, Philippe

    Tensor networks are a class of variational wave functions enabling an efficient representation of quantum many-body states, where the accuracy can be systematically controlled by the bond dimension of the tensors. A well-known example are matrix product states, the underlying ansatz of the density matrix renormalization group (DMRG) method, which has become the state-of-the-art tool to study (quasi-) 1D systems. Progress in quantum information theory, in particular a better understanding of entanglement in quantum many-body systems, has led to the development of 2D tensor networks, including projected entangled-pair states (PEPS) or the 2D multi-scale entanglement renormalization ansatz (MERA). These methods provide one of the most promising routes for the simulation of strongly correlated systems in 2D, in particular models where Quantum Monte Carlo fails due to the negative sign problem. In this talk I report on recent progress in simulating the 2D t-J and Hubbard models with infinite PEPS (iPEPS) which is a tensor network ansatz for a 2D wave function in the thermodynamic limit. Our results reveal an extremely close competition between a uniform d-wave superconducting state and different types of stripe states, where iPEPS yields better variational energies than other state-of-the-art variational methods for large 2D systems. The stripes are site-centered with coexisting charge-, spin-, and superconducting order, where stripes with in-phase d-wave order have an equal or only slightly lower energy than stripes with anti-phase d-wave order. Finally, a nematic anisotropy reduces the pairing amplitude and the energies of stripe states are lowered relative to the uniform state with increasing nematicity.

  6. C%2B%2B tensor toolbox user manual.

    SciTech Connect

    Plantenga, Todd D.; Kolda, Tamara Gibson

    2012-04-01

    The C++ Tensor Toolbox is a software package for computing tensor decompositions. It is based on the Matlab Tensor Toolbox, and is particularly optimized for sparse data sets. This user manual briefly overviews tensor decomposition mathematics, software capabilities, and installation of the package. Tensors (also known as multidimensional arrays or N-way arrays) are used in a variety of applications ranging from chemometrics to network analysis. The Tensor Toolbox provides classes for manipulating dense, sparse, and structured tensors in C++. The Toolbox compiles into libraries and is intended for use with custom applications written by users.

  7. Non-standard symmetries and quantum anomalies

    SciTech Connect

    Visinescu, Anca; Visinescu, Mihai

    2008-08-31

    Quantum anomalies are investigated on curved spacetimes. The intimate relation between Killing-Yano tensors and non-standard symmetries is pointed out. The gravitational anomalies are absent if the hidden symmetry is associated to a Killing-Yano tensor. 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 tensors generate Dirac-type operators involved in interesting algebraic structures. The general results are applied to the 4-dimensional Euclidean Taub-NUT space.

  8. Time Evolution of Modeled Reynolds Stresses in Planar Homogeneous Flows

    NASA Technical Reports Server (NTRS)

    Jongen, T.; Gatski, T. B.

    1997-01-01

    The analytic expression of the time evolution of the Reynolds stress anisotropy tensor in all planar homogeneous flows is obtained by exact integration of the modeled differential Reynolds stress equations. The procedure is based on results of tensor representation theory, is applicable for general pressure-strain correlation tensors, 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 tensor. The properties of this solution are discussed, and the dynamic behavior of the Reynolds stresses is studied, including limit cycles and sensitivity to initial anisotropies.

  9. Smooth PARAFAC Decomposition for Tensor Completion

    NASA Astrophysics Data System (ADS)

    Yokota, Tatsuya; Zhao, Qibin; Cichocki, Andrzej

    2016-10-01

    In recent years, low-rank based tensor completion, which is a higher-order extension of matrix completion, has received considerable attention. However, the low-rank assumption is not sufficient for the recovery of visual data, such as color and 3D images, where the ratio of missing data is extremely high. In this paper, we consider "smoothness" constraints as well as low-rank approximations, and propose an efficient algorithm for performing tensor completion that is particularly powerful regarding visual data. The proposed method admits significant advantages, owing to the integration of smooth PARAFAC decomposition for incomplete tensors and the efficient selection of models in order to minimize the tensor rank. Thus, our proposed method is termed as "smooth PARAFAC tensor completion (SPC)." In order to impose the smoothness constraints, we employ two strategies, total variation (SPC-TV) and quadratic variation (SPC-QV), and invoke the corresponding algorithms for model learning. Extensive experimental evaluations on both synthetic and real-world visual data illustrate the significant improvements of our method, in terms of both prediction performance and efficiency, compared with many state-of-the-art tensor completion methods.

  10. Visualization of Tensor Fields Using Superquadric Glyphs

    PubMed Central

    Ennis, Daniel B.; Kindlman, Gordon; Rodriguez, Ignacio; Helm, Patrick A.; McVeigh, Elliot R.

    2007-01-01

    The spatially varying tensor fields that arise in magnetic resonance imaging are difficult to visualize due to the multivariate nature of the data. To improve the understanding of myocardial structure and function a family of objects called glyphs, derived from superquadric parametric functions, are used to create informative and intuitive visualizations of the tensor fields. The superquadric glyphs are used to visualize both diffusion and strain tensors obtained in canine myocardium. The eigensystem of each tensor defines the glyph shape and orientation. Superquadric functions provide a continuum of shapes across four distinct eigensystems (λi, sorted eigenvalues), λ1 = λ2 = λ3 (spherical), λ1 < λ2 = λ3 (oblate), λ1 > λ2 = λ3 (prolate), and λ1 > λ2 > λ3 (cuboid). The superquadric glyphs are especially useful for identifying regions of anisotropic structure and function. Diffusion tensor renderings exhibit fiber angle trends and orthotropy (three distinct eigenvalues). Visualization of strain tensors with superquadric glyphs compactly exhibits radial thickening gradients, circumferential and longitudinal shortening, and torsion combined. The orthotropic nature of many biologic tissues and their DTMRI and strain data require visualization strategies that clearly exhibit the anisotropy of the data if it is to be interpreted properly. Superquadric glyphs improve the ability to distinguish fiber orientation and tissue orthotropy compared to ellipsoids. PMID:15690516

  11. Measuring Nematic Susceptibilities from the Elastoresistivity Tensor

    NASA Astrophysics Data System (ADS)

    Hristov, A. T.; Shapiro, M. C.; Hlobil, Patrick; Maharaj, Akash; Chu, Jiun-Haw; Fisher, Ian

    The elastoresistivity tensor mijkl relates changes in resistivity to the strain on a material. As a fourth-rank tensor, it contains considerably more information about the material than the simpler (second-rank) resistivity tensor; in particular, certain elastoresistivity coefficients can be related to thermodynamic susceptibilities and serve as a direct probe of symmetry breaking at a phase transition. The aim of this talk is twofold. First, we enumerate how symmetry both constrains the structure of the elastoresistivity tensor into an easy-to-understand form and connects tensor elements to thermodynamic susceptibilities. In the process, we generalize previous studies of elastoresistivity to include the effects of magnetic field. Second, we describe an approach to measuring quantities in the elastoresistivity tensor with a novel transverse measurement, which is immune to relative strain offsets. These techniques are then applied to BaFe2As2 in a proof of principle measurement. This work is supported by the Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division, under Contract DE-AC02-76SF00515.

  12. Visualization of 3-D tensor fields

    NASA Technical Reports Server (NTRS)

    Hesselink, L.

    1996-01-01

    Second-order tensor fields have applications in many different areas of physics, such as general relativity and fluid mechanics. The wealth of multivariate information in tensor 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 tensor field is equivalent to simultaneously visualizing its three eigenvector fields. In the past, research has been conducted in the area of two-dimensional tensor 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 tensor 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 tensor fields, and interpret topological patterns in terms of physical properties.

  13. Tensor network states and algorithms in the presence of a global SU(2) symmetry

    NASA Astrophysics Data System (ADS)

    Singh, Sukhwinder; Vidal, Guifre

    2012-11-01

    The benefits of exploiting the presence of symmetries in tensor network algorithms have been extensively demonstrated in the context of matrix product states (MPSs). These include the ability to select a specific symmetry sector (e.g., with a given particle number or spin), to ensure the exact preservation of total charge, and to significantly reduce computational costs. Compared to the case of a generic tensor network, the practical implementation of symmetries in the MPS is simplified by the fact that tensors only have three indices (they are trivalent, just as the Clebsch-Gordan coefficients of the symmetry group) and are organized as a one-dimensional array of tensors, without closed loops. Instead, a more complex tensor network, one where tensors have a larger number of indices and/or a more elaborate network structure, requires a more general treatment. In two recent papers, namely, (i) [Singh, Pfeifer, and Vidal, Phys. Rev. APLRAAN1050-294710.1103/PhysRevA.82.050301 82, 050301 (2010)] and (ii) [Singh, Pfeifer, and Vidal, Phys. Rev. BPRBMDO1098-012110.1103/PhysRevB.83.115125 83, 115125 (2011)], we described how to incorporate a global internal symmetry into a generic tensor network algorithm based on decomposing and manipulating tensors that are invariant under the symmetry. In (i) we considered a generic symmetry group G that is compact, completely reducible, and multiplicity free, acting as a global internal symmetry. Then, in (ii) we described the implementation of Abelian group symmetries in much more detail, considering a U(1) symmetry (e.g., conservation of global particle number) as a concrete example. In this paper, we describe the implementation of non-Abelian group symmetries in great detail. For concreteness, we consider an SU(2) symmetry (e.g., conservation of global quantum spin). Our formalism can be readily extended to more exotic symmetries associated with conservation of total fermionic or anyonic charge. As a practical demonstration, we

  14. Classification of trivial spin-1 tensor network states on a square lattice

    NASA Astrophysics Data System (ADS)

    Lee, Hyunyong; Han, Jung Hoon

    2016-09-01

    Classification of possible quantum 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 quantum 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 tensor 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 quantum 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 tensors 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 tensors, 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.

  15. Additivity of the classical capacity of entanglement-breaking quantum channels

    NASA Astrophysics Data System (ADS)

    Shor, Peter W.

    2002-09-01

    We show that for the tensor product of an entanglement-breaking quantum channel with an arbitrary quantum channel, both the minimum entropy of an output of the channel and the Holevo-Schumacher-Westmoreland capacity are additive. In addition, for the tensor product of two arbitrary quantum channels, we give a bound involving entanglement of formation for the amount of subadditivity (for minimum entropy output) or superadditivity (for classical capacity) that can occur.

  16. Dark energy, scalar-tensor gravity, and large extra dimensions

    SciTech Connect

    Kainulainen, Kimmo; Sunhede, Daniel

    2006-04-15

    We explore in detail a dilatonic scalar-tensor theory of gravity inspired by large extra dimensions, where a radion field from compact extra dimensions gives rise to quintessence in our 4-dimensional world. We show that the model can give rise to other types of cosmologies as well, some more akin to k-essence and possibly variants of phantom dark energy. In our model the field (or radius) stabilization arises from quantum corrections to the effective 4D Ricci scalar. We then show that various constraints nearly determine the model parameters, and give an example of a quintessence-type cosmology consistent with observations. We show that the upcoming SNAP-experiment would easily distinguish the present model from a constant {lambda} model with an equal amount of dark energy, but that the SNAP-data alone will not be able distinguish it from a {lambda} model with about 5% less dark energy.

  17. Symmetry-enriched topological invariants from tensor network representations

    NASA Astrophysics Data System (ADS)

    Ware, Brayden; Cheng, Meng; Bauer, Bela

    We examine topologically ordered quantum 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 tensor 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.

  18. Local Scale Transformations on the Lattice with Tensor Network Renormalization.

    PubMed

    Evenbly, G; Vidal, G

    2016-01-29

    Consider the partition function of a classical system in two spatial dimensions, or the Euclidean path integral of a quantum system in two space-time dimensions, both on a lattice. We show that the tensor 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.

  19. Local Scale Transformations on the Lattice with Tensor Network Renormalization

    NASA Astrophysics Data System (ADS)

    Evenbly, G.; Vidal, G.

    2016-01-01

    Consider the partition function of a classical system in two spatial dimensions, or the Euclidean path integral of a quantum system in two space-time dimensions, both on a lattice. We show that the tensor 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.

  20. Possible observational windows for quantum effects from black holes

    NASA Astrophysics Data System (ADS)

    Giddings, Steven B.

    2014-12-01

    Quantum information transfer necessary to reconcile black hole evaporation with quantum mechanics, while approximately preserving regular near-horizon geometry, can be simply parametrized in terms of couplings of the black hole internal state to quantum fields of the black hole atmosphere. The necessity of transferring sufficient information for unitarization sets the strengths of these couplings. Such couplings via the stress tensor offer apparently significant advantages, and behave like quantum fluctuations of the effective metric near the horizon. At the requisite strength, these fluctuations, while soft (low energy/momentum), have significant magnitude, and so can deflect near-horizon geodesics that span distances of order the black hole radius. Thus, the presence of such couplings can result in effects that could be detected or constrained by observation: disruption of near-horizon accretion flows, scintillation of light passing close to the black hole, and alteration of gravitational wave emission from inspirals. These effects could in particular distort features of Sgr A* expected to be observed, e.g., by the Event Horizon Telescope, such as the black hole shadow and photon ring.

  1. Moment tensors of a dislocation in a porous medium

    NASA Astrophysics Data System (ADS)

    Wang, Zhi; Hu, Hengshan

    2016-06-01

    A dislocation can be represented by a moment tensor for calculating seismic waves. However, the moment tensor expression was derived in an elastic medium and cannot completely describe a dislocation in a porous medium. In this paper, effective moment tensors of a dislocation in a porous medium are derived. It is found that the dislocation is equivalent to two independent moment tensors, i.e., the bulk moment tensor acting on the bulk of the porous medium and the isotropic fluid moment tensor acting on the pore fluid. Both of them are caused by the solid dislocation as well as the fluid-solid relative motion corresponding to fluid injection towards the surrounding rocks (or fluid outflow) through the fault plane. For a shear dislocation, the fluid moment tensor is zero, and the dislocation is equivalent to a double couple acting on the bulk; for an opening dislocation or fluid injection, the two moment tensors are needed to describe the source. The fluid moment tensor only affects the radiated compressional waves. By calculating the ratio of the radiation fields generated by unit fluid moment tensor and bulk moment tensor, it is found that the fast compressional wave radiated by the bulk moment tensor is much stronger than that radiated by the fluid moment tensor, while the slow compressional wave radiated by the fluid moment tensor is several times stronger than that radiated by the bulk moment tensor.

  2. Diffusion tensor smoothing through weighted Karcher means.

    PubMed

    Carmichael, Owen; Chen, Jun; Paul, Debashis; Peng, Jie

    2013-01-01

    Diffusion tensor 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 tensors within spatial neighborhoods, under various metrics imposed on the space of tensors. 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 tensor 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 tensor field geometric structure when assessing Diffusion tensor 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

  3. An Adaptive Spectrally Weighted Structure Tensor Applied to Tensor Anisotropic Nonlinear Diffusion for Hyperspectral Images

    ERIC Educational Resources Information Center

    Marin Quintero, Maider J.

    2013-01-01

    The structure tensor for vector valued images is most often defined as the average of the scalar structure tensors 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…

  4. Tensor network algorithm by coarse-graining tensor renormalization on finite periodic lattices

    NASA Astrophysics Data System (ADS)

    Zhao, Hui-Hai; Xie, Zhi-Yuan; Xiang, Tao; Imada, Masatoshi

    2016-03-01

    We develop coarse-graining tensor renormalization group algorithms to compute physical properties of two-dimensional lattice models on finite periodic lattices. Two different coarse-graining strategies, one based on the tensor renormalization group and the other based on the higher-order tensor renormalization group, are introduced. In order to optimize the tensor network model globally, a sweeping scheme is proposed to account for the renormalization effect from the environment tensors under the framework of second renormalization group. We demonstrate the algorithms by the classical Ising model on the square lattice and the Kitaev model on the honeycomb lattice, and show that the finite-size algorithms achieve substantially more accurate results than the corresponding infinite-size ones.

  5. Efficient compression of quantum information

    SciTech Connect

    Plesch, Martin; Buzek, Vladimir

    2010-03-15

    We propose a scheme for an exact efficient transformation of a tensor product state of many identically prepared qubits into a state of a logarithmically small number of qubits. Using a quadratic number of elementary quantum gates we transform N identically prepared qubits into a state, which is nontrivial only on the first [log{sub 2}(N+1)] qubits. This procedure might be useful for quantum memories, as only a small portion of the original qubits has to be stored. Another possible application is in communicating a direction encoded in a set of quantum states, as the compressed state provides a high-effective method for such an encoding.

  6. Assessing the Uncertainties on Seismic Source Parameters: Towards Realistic Estimates of Moment Tensor Determinations

    NASA Astrophysics Data System (ADS)

    Magnoni, F.; Scognamiglio, L.; Tinti, E.; Casarotti, E.

    2014-12-01

    Seismic moment tensor is one of the most important source parameters defining the earthquake dimension and style of the activated fault. Moment tensor 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 stress transfer determination and other analyses where self-consistency is important. In this work, we focus on the variability of the moment tensor 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 tensor solutions depending on the number, the epicentral distance and the azimuth of used stations. We endorse that the estimate of seismic moment from moment tensor 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.

  7. Tensor scale-based image registration

    NASA Astrophysics Data System (ADS)

    Saha, Punam K.; Zhang, Hui; Udupa, Jayaram K.; Gee, James C.

    2003-05-01

    Tangible solutions to image registration are paramount in longitudinal as well as multi-modal medical imaging studies. In this paper, we introduce tensor scale - a recently developed local morphometric parameter - in rigid image registration. A tensor scale-based registration method incorporates local structure size, orientation and anisotropy into the matching criterion, and therefore, allows efficient multi-modal image registration and holds potential to overcome the effects of intensity inhomogeneity in MRI. Two classes of two-dimensional image registration methods are proposed - (1) that computes angular shift between two images by correlating their tensor scale orientation histogram, and (2) that registers two images by maximizing the similarity of tensor scale features. Results of applications of the proposed methods on proton density and T2-weighted MR brain images of (1) the same slice of the same subject, and (2) different slices of the same subject are presented. The basic superiority of tensor scale-based registration over intensity-based registration is that it may allow the use of local Gestalts formed by the intensity patterns over the image instead of simply considering intensities as isolated events at the pixel level. This would be helpful in dealing with the effects of intensity inhomogeneity and noise in MRI.

  8. Robust Face Clustering Via Tensor Decomposition.

    PubMed

    Cao, Xiaochun; Wei, Xingxing; Han, Yahong; Lin, Dongdai

    2015-11-01

    Face clustering is a key component either in image managements or video analysis. Wild human faces vary with the poses, expressions, and illumination changes. All kinds of noises, like block occlusions, random pixel corruptions, and various disguises may also destroy the consistency of faces referring to the same person. This motivates us to develop a robust face clustering algorithm that is less sensitive to these noises. To retain the underlying structured information within facial images, we use tensors to represent faces, and then accomplish the clustering task based on the tensor data. The proposed algorithm is called robust tensor clustering (RTC), which firstly finds a lower-rank approximation of the original tensor data using a L1 norm optimization function. Because L1 norm does not exaggerate the effect of noises compared with L2 norm, the minimization of the L1 norm approximation function makes RTC robust. Then, we compute high-order singular value decomposition of this approximate tensor to obtain the final clustering results. Different from traditional algorithms solving the approximation function with a greedy strategy, we utilize a nongreedy strategy to obtain a better solution. Experiments conducted on the benchmark facial datasets and gait sequences demonstrate that RTC has better performance than the state-of-the-art clustering algorithms and is more robust to noises. PMID:25546869

  9. MULTILINEAR TENSOR REGRESSION FOR LONGITUDINAL RELATIONAL DATA

    PubMed Central

    Hoff, Peter D.

    2016-01-01

    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 tensor. The model is based on a general multilinear tensor regression model, a special case of which is a tensor autoregression model in which the tensor 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 tensor regression model can represent patterns that often appear in relational and network data, such as reciprocity and transitivity. PMID:27458495

  10. Non-standard symmetries and Killing tensors

    NASA Astrophysics Data System (ADS)

    Visinescu, Mihai

    2009-10-01

    Higher order symmetries corresponding to Killing tensors are investigated. The intimate relation between Killing-Yano tensors and non-standard supersymmetries is pointed out. The gravitational anomalies are absent if the hidden symmetry is associated with a Killing-Yano tensor. In the Dirac theory on curved spaces, Killing-Yano tensors generate Dirac type operators involved in interesting algebraic structures as dynamical algebras or even infinite dimensional algebras or superalgebras. The general results are applied to space-times which appear in modern studies. The 4-dimensional Euclidean Taub-NUT space and its generalizations introduced by Iwai and Katayama are analyzed from the point of view of hidden symmetries. One presents the infinite dimensional superalgebra of Dirac type operators on Taub-NUT space that can be seen as a twisted loop algebra. The axial anomaly, interpreted as the index of the Dirac operator, is computed for the generalized Taub-NUT metrics. The existence of the conformal Killing-Yano tensors is investigated for some spaces with mixed Sasakian structures.

  11. Physics and numerics of the tensor code (incomplete preliminary documentation)

    SciTech Connect

    Burton, D.E.; Lettis, L.A. Jr.; Bryan, J.B.; Frary, N.R.

    1982-07-15

    The present TENSOR 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 stress 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. TENSOR 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 TENSOR 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.

  12. Possibilities and limitations of rod-beam theories. [nonlinear distortion tensor and nonlinear stress tensors

    NASA Technical Reports Server (NTRS)

    Peterson, D.

    1979-01-01

    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.

  13. Quantum corrected spherical collapse: A phenomenological framework

    SciTech Connect

    Ziprick, Jonathan; Kunstatter, Gabor

    2010-08-15

    A phenomenological framework is presented for incorporating quantum 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 stress energy tensor violates only the dominant energy condition. The violations are maximum near the inner horizon and die off rapidly. A numerical study of the quantum 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.

  14. TensorPack: a Maple-based software package for the manipulation of algebraic expressions of tensors in general relativity

    NASA Astrophysics Data System (ADS)

    Huf, P. A.; Carminati, J.

    2015-09-01

    In this paper we: (1) introduce TensorPack, a software package for the algebraic manipulation of tensors in covariant index format in Maple; (2) briefly demonstrate the use of the package with an orthonormal tensor proof of the shearfree conjecture for dust. TensorPack is based on the Riemann and Canon tensor software packages and uses their functions to express tensors in an indexed covariant format. TensorPack uses a string representation as input and provides functions for output in index form. It extends the functionality to basic algebra of tensors, substitution, covariant differentiation, contraction, raising/lowering indices, symmetry functions and other accessory functions. The output can be merged with text in the Maple environment to create a full working document with embedded dynamic functionality. The package offers potential for manipulation of indexed algebraic tensor expressions in a flexible software environment.

  15. Geodesic-loxodromes for diffusion tensor interpolation and difference measurement.

    PubMed

    Kindlmann, Gordon; Estépar, Raúl San José; Niethammer, Marc; Haker, Steven; Westin, Carl-Fredrik

    2007-01-01

    In algorithms for processing diffusion tensor images, two common ingredients are interpolating tensors, and measuring the distance between them. We propose a new class of interpolation paths for tensors, termed geodesic-loxodromes, which explicitly preserve clinically important tensor attributes, such as mean diffusivity or fractional anisotropy, while using basic differential geometry to interpolate tensor 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 tensors, and of difference in shape and in orientation. PMID:18051037

  16. O(N) Random Tensor Models

    NASA Astrophysics Data System (ADS)

    Carrozza, Sylvain; Tanasa, Adrian

    2016-08-01

    We define in this paper a class of three-index tensor models, endowed with {O(N)^{⊗ 3}} invariance (N being the size of the tensor). This allows to generate, via the usual QFT perturbative expansion, a class of Feynman tensor 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.

  17. Spectral analysis of the full gravity tensor

    NASA Astrophysics Data System (ADS)

    Rummel, R.; van Gelderen, M.

    1992-10-01

    It is shown that, when the five independent components of the gravity tensor 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 tensors, 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 tensor 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.

  18. Role of the tensor interaction in He isotopes with a tensor-optimized shell model

    SciTech Connect

    Myo, Takayuki; Umeya, Atsushi; Toki, Hiroshi; Ikeda, Kiyomi

    2011-09-15

    We studied the role of the tensor interaction in He isotopes systematically on the basis of the tensor-optimized shell model (TOSM). We use a bare nucleon-nucleon interaction AV8{sup '} obtained from nucleon-nucleon scattering data. The short-range correlation is treated in the unitary correlation operator method (UCOM). Using the TOSM + UCOM approach, we investigate the role of tensor interaction on each spectrum in He isotopes. It is found that the tensor interaction enhances the LS splitting energy observed in {sup 5}He, in which the p{sub 1/2} and p{sub 3/2} orbits play different roles on the tensor correlation. In {sup 6,7,8}He, the low-lying states containing extra neutrons in the p{sub 3/2} orbit gain the tensor contribution. On the other hand, the excited states containing extra neutrons in the p{sub 1/2} orbit lose the tensor contribution due to the Pauli-blocking effect with the 2p2h states in the {sup 4}He core configuration.

  19. Blue running of the primordial tensor spectrum

    SciTech Connect

    Gong, Jinn-Ouk

    2014-07-01

    We examine the possibility of positive spectral index of the power spectrum of the primordial tensor 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 tensor power spectrum can be obtained. We also briefly discuss other consistency tests for further studies on inflationary dynamics.

  20. Energy-momentum tensor of the electromagnetic field in dispersive media

    NASA Astrophysics Data System (ADS)

    Toptygin, I. N.; Levina, K.

    2016-02-01

    We study the relation between the energy-momentum tensor 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 tensor turns out to be symmetric, and the Maxwell stress tensor 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 stress tensor 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.

  1. Second order tensor finite element

    NASA Technical Reports Server (NTRS)

    Oden, J. Tinsley; Fly, J.; Berry, C.; Tworzydlo, W.; Vadaketh, S.; Bass, J.

    1990-01-01

    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 stresses from strain measurements were considered. For both cases, numerical procedures and software for the optimization of strain gauge and material axes orientation were developed.

  2. Spacetime encodings. III. Second order Killing tensors

    SciTech Connect

    Brink, Jeandrew

    2010-01-15

    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 tensor. 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 tensors. 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 tensor 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 tensors.

  3. An integral relation for tensor polynomials

    NASA Astrophysics Data System (ADS)

    Vshivtseva, P. A.; Denisov, V. I.; Denisova, I. P.

    2011-02-01

    We prove two lemmas and one theorem that allow integrating the product of an arbitrary number of unit vectors and the Legendre polynomials over a sphere of arbitrary radius. Such integral tensor products appear in solving inhomogeneous Helmholtz equations whose right-hand side is proportional to the product of a nonfixed number of unit vectors.

  4. Tensor squeezed limits and the Higuchi bound

    NASA Astrophysics Data System (ADS)

    Bordin, Lorenzo; Creminelli, Paolo; Mirbabayi, Mehrdad; Noreña, Jorge

    2016-09-01

    We point out that tensor consistency relations—i.e. the behavior of primordial correlation functions in the limit a tensor 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 tensor 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 tensor modes. This anisotropy has a well-defined statistics which can be distinguished from cases in which the background has a privileged direction.

  5. Black holes in scalar-tensor gravity.

    PubMed

    Sotiriou, Thomas P; Faraoni, Valerio

    2012-02-24

    Hawking has proven that black holes which are stationary as the end point of gravitational collapse in Brans-Dicke theory (without a potential) are no different than in general relativity. We extend this proof to the much more general class of scalar-tensor and f(R) gravity theories, without assuming any symmetries apart from stationarity.

  6. Cosmic Ray Diffusion Tensor Throughout the Heliosphere

    NASA Astrophysics Data System (ADS)

    Pei, C.; Bieber, J. W.; Breech, B.; Burger, R. A.; Clem, J.; Matthaeus, W. H.

    2008-12-01

    We calculate the cosmic ray diffusion tensor based on a recently developed model of magnetohydrodynamic (MHD) turbulence in the expanding solar wind [Breech et al., 2008.]. Parameters of this MHD model are tuned by using published observations from Helios, Voyager 2, and Ulysses. We present solutions of two turbulence parameter sets and derive the characteristics of the cosmic ray diffusion tensor for each. We determine the parallel diffusion coefficient of the cosmic ray following the method presented in Bieber et al. [1995]. We use the nonlinear guiding center (NLGC) theory to obtain the perpendicular diffusion coefficient of the cosmic ray [Matthaeus et al. 2003]. We find that (1) the radial mean free path decreases from 1 AU to 20 AU for both turbulence scenarios; (2) after 40 AU the radial mean free path is nearly constant; (3) the radial mean free path is dominated by the parallel component before 20 AU, after which the perpendicular component becomes important; (4) the rigidity P dependence of the parallel component of the diffusion tensor is proportional to P.404 for one turbulence scenario and P.374 for the other at 1 AU from 0.1 GVto 10 GV, but in the outer heliosphere its dependence becomes stronger above 4 GV; (5) the rigidity P dependence of the perpendicular component of the diffusion tensor is very weak. Supported by NASA Heliophysics Guest Investigator grant NNX07AH73G and by NASA Heliophysics Theory grant NNX08AI47G.

  7. Nonlinear symmetries on spaces admitting Killing tensors

    NASA Astrophysics Data System (ADS)

    Visinescu, Mihai

    2010-04-01

    Nonlinear symmetries corresponding to Killing tensors are investigated. The intimate relation between Killing-Yano tensors and non-standard supersymmetries is pointed out. The gravitational anomalies are absent if the hidden symmetry is associated with a Killing-Yano tensor. 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 tensors is investigated for some spaces with mixed Sasakian structures.

  8. Closure of the cubic tensor polynomial failure surface

    NASA Technical Reports Server (NTRS)

    Jiang, Zhiqing; Tennyson, R. C.

    1989-01-01

    An analytical method has been developed to ensure closure of the cubic form of the tensor polynomial strength criterion. The intrinsic complexity of the cubic function is such that special conditions must be met to close the failure surface in three-dimensional stress space. These requirements are derived in terms of non-intersecting conditions for asymptotes and an asymptotic plane. To demonstrate the validity of this approach, closed failure surfaces were derived for two graphite/epoxy material systems (3M SP288-T300 and IM7 8551-7). The agreement of test data with this model clearly shows that it is possible to use a higher order cubic failure theory with confidence.

  9. Adding stress plot function to NASTRAN

    NASA Technical Reports Server (NTRS)

    Katoh, S.

    1978-01-01

    Stress plot function was developed and added to the NASTRAN level 15.5. Computed stress distribution can be displayed by this function, with vectors showing the principal stresses of the finite elements over the specified portions of the structure. NASTRAN is reviewed in the aspect of plotting capabilities. Stress tensor field is examined in preparation of stress display. Then the stress plot function as added to the NASTRAN is described. A sample plotout by this function is shown.

  10. Role of Tensor Force in Light Nuclei Based on the Tensor Optimized Shell Model

    SciTech Connect

    Myo, Takayuki; Umeya, Atsushi; Ikeda, Kiyomi; Valverde, Manuel; Toki, Hiroshi

    2011-10-21

    We propose a new theoretical approach to describe nucleus using bare nuclear interaction, in which the tensor and short-range correlations are described with the tensor optimized shell model (TOSM) and the unitary correlation operator method (UCOM), respectively. We show the obtained results of He isotopes using TOSM+UCOM, such as the importance of the pn-pair correlated by the tensor force, and the structure differences in the LS partners of 3/2{sup -} and 1/2{sup -} states of {sup 5}He. We also apply TOSM to the analysis of two-neutron halo nucleus {sup 11}Li, on the basis of the ''core described in TOSM''+n+n model. The halo formation of {sup 11}Li is naturally explained, in which the tensor correlation in the {sup 9}Li core is Pauli-blocked on the p-wave neutrons in {sup 11}Li and the s-wave component of halo structure is enhanced.

  11. Efficient MATLAB computations with sparse and factored tensors.

    SciTech Connect

    Bader, Brett William; Kolda, Tamara Gibson (Sandia National Lab, Livermore, CA)

    2006-12-01

    In this paper, the term tensor refers simply to a multidimensional or N-way array, and we consider how specially structured tensors allow for efficient storage and computation. First, we study sparse tensors, which have the property that the vast majority of the elements are zero. We propose storing sparse tensors using coordinate format and describe the computational efficiency of this scheme for various mathematical operations, including those typical to tensor decomposition algorithms. Second, we study factored tensors, which have the property that they can be assembled from more basic components. We consider two specific types: a Tucker tensor can be expressed as the product of a core tensor (which itself may be dense, sparse, or factored) and a matrix along each mode, and a Kruskal tensor can be expressed as the sum of rank-1 tensors. We are interested in the case where the storage of the components is less than the storage of the full tensor, 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 Tensor Toolbox for MATLAB.

  12. Skyrme tensor force in heavy ion collisions

    NASA Astrophysics Data System (ADS)

    Stevenson, P. D.; Suckling, E. B.; Fracasso, S.; Barton, M. C.; Umar, A. S.

    2016-05-01

    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 tensor 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 tensor force. Method: The full version of the Skyrme force, including terms arising only from the Skyrme tensor 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 tensor 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 tensor force can play a non

  13. Generalization of the Bollobás-Riordan polynomial for tensor graphs

    NASA Astrophysics Data System (ADS)

    Tanasa, Adrian

    2011-07-01

    Tensor models are used nowadays for implementing a fundamental theory of quantum 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 tensor 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.

  14. Vector and tensor contributions to the curvature perturbation at second order

    NASA Astrophysics Data System (ADS)

    Carrilho, Pedro; Malik, Karim A.

    2016-02-01

    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 tensor perturbations, as well as anisotropic stress, 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 stress tensor 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.

  15. A preliminary report on the development of MATLAB tensor classes for fast algorithm prototyping.

    SciTech Connect

    Bader, Brett William; Kolda, Tamara Gibson

    2004-07-01

    We describe three MATLAB classes for manipulating tensors in order to allow fast algorithm prototyping. A tensor is a multidimensional or N-way array. We present a tensor class for manipulating tensors which allows for tensor multiplication and 'matricization.' We have further added two classes for representing tensors in decomposed format: cp{_}tensor and tucker{_}tensor. We demonstrate the use of these classes by implementing several algorithms that have appeared in the literature.

  16. Geometrodynamics of quantum fields in black hole anti-de Sitter spacetimes

    NASA Astrophysics Data System (ADS)

    Debenedictis, Andrew

    In the context of semi-classical general relativity, an in depth study of quantum effects on classical singularity structure is performed. The system studied is that of an asymptotically anti-de Sitter (AdS) cylindrical black hole spacetime with conformally coupled scalars as the matter field. This fact requires special care with boundary conditions which is discussed in detail. Thermodynamic properties of torroidal versions of these black holes are first studied. The free energy and entropy are obtained using simple thermodynamic arguments and the stability of the black holes is discussed. The renormalized expectation value =lim x→x' is calculated using a mode sum decomposition. It is found that the field is divergence free throughout the spacetime and attains its maximum value near the horizon. The gravitational back-reaction which this field introduces is also calculated. By first calculating the expectation value of the field's stress-energy-tensor, , the Einstein field equations are solved (to first order in h) and the perturbation on the Kretschmann scalar is obtained. It is found that near the horizon, the perturbation initially strengthens the singularity. Near spatial infinity, however, curvature is weakened . Finally, a method of adding successive boundary counter-terms is utilized to renormalize the bulk gravitational action in asymptotically AdS solutions. It is shown that the correct conserved quantities of the spacetime are produced and therefore this renormalized quantity may be viewed as a "gravitational stress-energy tensor". The resulting stress-energy tensor yields both the correct black hole energies as well as terms interpreted as vacuum Casimir energies of the dual field theory (including a negative energy contribution). This calculation is done up to d = 8 (d being the boundary dimension). In light of the anti-de Sitter/conformal field theory (AdS/CFT) correspondence, the trace of this quantity yields the Weyl anomaly

  17. Coherent states in noncommutative quantum mechanics

    SciTech Connect

    Ben Geloun, J.; Scholtz, F. G.

    2009-04-15

    Gazeau-Klauder coherent states in noncommutative quantum 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 quantum Hilbert space of Hilbert-Schmidt operators and the tensor product of the classical configuration space and its dual, we reveal the inherent vector feature of these states.

  18. Seismic moment tensors of acoustic emissions recorded during laboratory rock deformation experiments: sensitivity to attenuation and anisotropy

    NASA Astrophysics Data System (ADS)

    Stierle, Eva; Vavryčuk, Václav; Kwiatek, Grzegorz; Charalampidou, Elli-Maria; Bohnhoff, Marco

    2016-04-01

    Seismic moment tensors can provide information on the size and orientation of fractures producing acoustic emissions (AEs) and on the stress conditions in the sample. The moment tensor inversion of AEs is, however, a demanding procedure requiring carefully calibrated sensors and accurate knowledge of the velocity model. In field observations, the velocity model is usually isotropic and time independent. In laboratory experiments, the velocity is often anisotropic and time dependent and attenuation might be significant due to opening or closure of microcracks in the sample during loading. In this paper, we study the sensitivity of the moment tensor inversion to anisotropy of P-wave velocities and attenuation. We show that retrieved moment tensors critically depend on anisotropy and attenuation and their neglect can lead to misinterpretations of the source mechanisms. The accuracy of the inversion also depends on the fracturing mode of AEs: tensile events are more sensitive to P-wave anisotropy and attenuation than shear events. We show that geometry of faulting in anisotropic rocks should be studied using the source tensors, since the P- and T-axes of the moment tensors are affected by velocity anisotropy and deviate from the true orientation of faulting. The stronger the anisotropy is, the larger the deviations are. Finally, we prove that the moment tensor inversion applied to a large dataset of AEs can be utilized to provide information on the attenuation parameters of the rock sample. The method is capable of measuring anisotropic attenuation in the sample and allows for detection of dilatant cracking according to the stress regime.

  19. Analytic electrical-conductivity tensor of a nondegenerate Lorentz plasma

    NASA Astrophysics Data System (ADS)

    Stygar, W. A.; Gerdin, G. A.; Fehl, D. L.

    2002-10-01

    We have developed explicit quantum-mechanical expressions for the conductivity and resistivity tensors 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 quantum-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 tensor (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

  20. Exploiting Quantum Resonance to Solve Combinatorial Problems

    NASA Technical Reports Server (NTRS)

    Zak, Michail; Fijany, Amir

    2006-01-01

    Quantum resonance would be exploited in a proposed quantum-computing approach to the solution of combinatorial optimization problems. In quantum 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 quantum computing have involved exploitation of only a subset of known quantum physical effects, notably including parallelism and entanglement, but not including resonance. In the proposed approach, one would utilize the combinatorial properties of tensor-product decomposability of unitary evolution of many-particle quantum 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 quantum 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.

  1. Tensoral for post-processing users and simulation authors

    NASA Technical Reports Server (NTRS)

    Dresselhaus, Eliot

    1993-01-01

    The CTR post-processing effort aims to make turbulence simulations and data more readily and usefully available to the research and industrial communities. The Tensoral language, which provides the foundation for this effort, is introduced here in the form of a user's guide. The Tensoral 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 Tensoral database back ends. The two-part structure of this document conforms to the two-level design structure of the Tensoral language. Tensoral has been designed to be a general computer language for performing tensor calculus and statistics on numerical data. Tensoral'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, Tensoral's specialization to a minute task (namely, to numerical tensor calculus and statistics) allows it to be easily embedded into applications written partly in Tensoral and partly in other computer languages (here, C and Vectoral). Embedded Tensoral, 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.

  2. Quantum inflaton, primordial perturbations, and CMB fluctuations

    SciTech Connect

    Cao, F.J.; Vega, H.J. de; Sanchez, N.G.

    2004-10-15

    We compute the primordial scalar, vector and tensor metric perturbations arising from quantum field inflation. Quantum field inflation takes into account the nonperturbative quantum dynamics of the inflaton consistently coupled to the dynamics of the (classical) cosmological metric. For chaotic inflation, the quantum 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. Quantum field inflation (under conditions that are the quantum 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 quantum effects into account. The results for the scalar, vector and tensor 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 quantum field treatment of inflation provides the foundations to the classical inflation and permits to compute quantum corrections to it.

  3. Gravity induced from quantum spacetime

    NASA Astrophysics Data System (ADS)

    Beggs, Edwin J.; Majid, Shahn

    2014-02-01

    We show that tensoriality constraints in noncommutative Riemannian geometry in the two-dimensional bicrossproduct model quantum 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 tensor 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 quantum case as a new description of the quantum spacetime model as a quadratic algebra. The noncommutative Riemannian geometry is fully solved for n = 2 and includes the quantum Levi-Civita connection and a second, nonperturbative, Levi-Civita connection which blows up as λ → 0. We also propose a ‘quantum Einstein tensor’ which is identically zero for the main part of the moduli space of connections (as classically in 2D). However, when the quantum Ricci tensor and metric are viewed as deformations of their classical counterparts there would be an O(λ2) correction to the classical Einstein tensor and an O(λ) correction to the classical metric.

  4. FAST TRACK COMMUNICATION Algebraic classification of the Weyl tensor in higher dimensions based on its 'superenergy' tensor

    NASA Astrophysics Data System (ADS)

    Senovilla, José M. M.

    2010-11-01

    The algebraic classification of the Weyl tensor in the arbitrary dimension n is recovered by means of the principal directions of its 'superenergy' tensor. This point of view can be helpful in order to compute the Weyl aligned null directions explicitly, and permits one to obtain the algebraic type of the Weyl tensor by computing the principal eigenvalue of rank-2 symmetric future tensors. The algebraic types compatible with states of intrinsic gravitational radiation can then be explored. The underlying ideas are general, so that a classification of arbitrary tensors in the general dimension can be achieved.

  5. Tensors: A guide for undergraduate students

    NASA Astrophysics Data System (ADS)

    Battaglia, Franco; George, Thomas F.

    2013-07-01

    A guide on tensors 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 tensors of any rank in any coordinate system, without index-manipulation obstacles standing in the way.

  6. Extended scalar-tensor theories of gravity

    NASA Astrophysics Data System (ADS)

    Crisostomi, Marco; Koyama, Kazuya; Tasinato, Gianmassimo

    2016-04-01

    We study new consistent scalar-tensor 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-tensor 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.

  7. Lifted tensors and Hamilton-Jacobi separability

    NASA Astrophysics Data System (ADS)

    Waeyaert, G.; Sarlet, W.

    2014-12-01

    Starting from a bundle τ : E → R, the bundle π :J1τ∗ → E, which is the dual of the first jet bundle J1 τ and a sub-bundle of T∗ E, is the appropriate manifold for the geometric description of time-dependent Hamiltonian systems. Based on previous work, we recall properties of the complete lifts of a type (1 , 1) tensor R on E to both T∗ E and J1τ∗. We discuss how an interplay between both lifted tensors leads to the identification of related distributions on both manifolds. The integrability of these distributions, a coordinate free condition, is shown to produce exactly Forbat's conditions for separability of the time-dependent Hamilton-Jacobi equation in appropriate coordinates.

  8. Saliency Mapping Enhanced by Structure Tensor

    PubMed Central

    He, Zhiyong; Chen, Xin; Sun, Lining

    2015-01-01

    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 tensor. 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 tensor 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

  9. Oscillating chiral tensor spectrum from axionic inflation

    NASA Astrophysics Data System (ADS)

    Obata, Ippei; Soda, Jiro

    2016-08-01

    We study axionic inflation with a modulated potential and examine if the primordial tensor power spectrum exhibits oscillatory feature, which is testable with future space-based gravitational-wave experiments such as DECIGO and BBO. In the case of single-field axion monodromy inflation, it turns out that it is difficult to detect an oscillation in the spectrum due to the suppression of the sub-Planckian decay constant of the axion. On the other hand, in the case of aligned chromo-natural inflation where the axion is coupled to a SU(2) gauge field, it turns out that a sizable oscillation in the tensor spectrum can occur due to the enhancement of chiral gravitational waves sourced by the gauge field. We expect that this feature will be a new probe for axion phenomenologies in the early Universe through chiral gravitational waves.

  10. Arbuscular mycorrhizal symbiosis ameliorates the optimum quantum yield of photosystem II and reduces non-photochemical quenching in rice plants subjected to salt stress.

    PubMed

    Porcel, Rosa; Redondo-Gómez, Susana; Mateos-Naranjo, Enrique; Aroca, Ricardo; Garcia, Rosalva; Ruiz-Lozano, Juan Manuel

    2015-08-01

    Rice is the most important food crop in the world and is a primary source of food for more than half of the world population. However, salinity is considered the most common abiotic stress reducing its productivity. Soil salinity inhibits photosynthetic processes, which can induce an over-reduction of the reaction centres in photosystem II (PSII), damaging the photosynthetic machinery. The arbuscular mycorrhizal (AM) symbiosis may improve host plant tolerance to salinity, but it is not clear how the AM symbiosis affects the plant photosynthetic capacity, particularly the efficiency of PSII. This study aimed at determining the influence of the AM symbiosis on the performance of PSII in rice plants subjected to salinity. Photosynthetic activity, plant gas-exchange parameters, accumulation of photosynthetic pigments and rubisco activity and gene expression were also measured in order to analyse comprehensively the response of the photosynthetic processes to AM symbiosis and salinity. Results showed that the AM symbiosis enhanced the actual quantum yield of PSII photochemistry and reduced the quantum yield of non-photochemical quenching in rice plants subjected to salinity. AM rice plants maintained higher net photosynthetic rate, stomatal conductance and transpiration rate than nonAM plants. Thus, we propose that AM rice plants had a higher photochemical efficiency for CO2 fixation and solar energy utilization and this increases plant salt tolerance by preventing the injury to the photosystems reaction centres and by allowing a better utilization of light energy in photochemical processes. All these processes translated into higher photosynthetic and rubisco activities in AM rice plants and improved plant biomass production under salinity.

  11. Arbuscular mycorrhizal symbiosis ameliorates the optimum quantum yield of photosystem II and reduces non-photochemical quenching in rice plants subjected to salt stress.

    PubMed

    Porcel, Rosa; Redondo-Gómez, Susana; Mateos-Naranjo, Enrique; Aroca, Ricardo; Garcia, Rosalva; Ruiz-Lozano, Juan Manuel

    2015-08-01

    Rice is the most important food crop in the world and is a primary source of food for more than half of the world population. However, salinity is considered the most common abiotic stress reducing its productivity. Soil salinity inhibits photosynthetic processes, which can induce an over-reduction of the reaction centres in photosystem II (PSII), damaging the photosynthetic machinery. The arbuscular mycorrhizal (AM) symbiosis may improve host plant tolerance to salinity, but it is not clear how the AM symbiosis affects the plant photosynthetic capacity, particularly the efficiency of PSII. This study aimed at determining the influence of the AM symbiosis on the performance of PSII in rice plants subjected to salinity. Photosynthetic activity, plant gas-exchange parameters, accumulation of photosynthetic pigments and rubisco activity and gene expression were also measured in order to analyse comprehensively the response of the photosynthetic processes to AM symbiosis and salinity. Results showed that the AM symbiosis enhanced the actual quantum yield of PSII photochemistry and reduced the quantum yield of non-photochemical quenching in rice plants subjected to salinity. AM rice plants maintained higher net photosynthetic rate, stomatal conductance and transpiration rate than nonAM plants. Thus, we propose that AM rice plants had a higher photochemical efficiency for CO2 fixation and solar energy utilization and this increases plant salt tolerance by preventing the injury to the photosystems reaction centres and by allowing a better utilization of light energy in photochemical processes. All these processes translated into higher photosynthetic and rubisco activities in AM rice plants and improved plant biomass production under salinity. PMID:26291919

  12. Inflation in anisotropic scalar-tensor theories

    NASA Technical Reports Server (NTRS)

    Pimentel, Luis O.; Stein-Schabes, Jaime

    1988-01-01

    The existence of an inflationary phase in anisotropic Scalar-Tensor 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.

  13. Monte Carlo Volcano Seismic Moment Tensors

    NASA Astrophysics Data System (ADS)

    Waite, G. P.; Brill, K. A.; Lanza, F.

    2015-12-01

    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-tensor 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 tensor eigenvectors. Point sources densely sample the summit area and moment tensors are constrained to a randomly chosen geometry within the inversion; Green's functions for the random moment tensors 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.

  14. Effect of Multi-Axial Loading on Residual Strain Tensor for 12L14 Steel Alloy

    SciTech Connect

    Bunn, J. R.; Penumadu, Dayakar; Lou, Xin; Hubbard, Camden R

    2014-01-01

    Evaluating the state of residual strain or stress is critically important for structural materials and for reliable design of complex shape components that need to function in extreme environment subjected to large thermo-mechanical loading. When residual stress state is superposed to external loads, it can lead to reduction or increase in failure strength. Past diffraction studies for evaluating the residual strain state involved measuring lattice spacings in three orthogonal directions and do not often correspond to principal directions. To completely resolve the state of strain at a given location, a full strain tensor must be determined. This is especially important when characterizing materials or metallic components exposed to biaxial or complex loading. Neutron diffraction at the second Generation Neutron Residual Stress Facility (NRSF2) at Oak Ridge National Laboratory is used in this study to measure strain tensors associated with different modes of stress path. Hollow cylinder steel samples with 2 mm wall thickness are subjected to either pure axial extension or pure torsion to simulate multi-axial loading conditions. A virgin sample that is not subjected to any deformation, but subjected to identical manufacturing conditions and machining steps involved to obtain hollow cylinder geometry is used for obtaining reference d-spacing for given hkl planes at target spatial location(s). The two samples which are subjected to either pure tension or torsion are loaded to a deformation state that corresponded to equal amount of octahedral shear strain which is an invariant. This procedure is used so that a basis for comparison between the two samples can be made to isolate the stress path effects. A 2-circle Huber orienter is used to obtain strain measurements on identical gauge volume at a series of chi and psi values. The residual state of stress tensor corresponding to ex situ (upon unloading) conditions is presented for three lattice planes (211, 110, 200) for

  15. Minkowski Space and Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    O'Hara, Paul

    A paradigm shift distinguishes general relativity from classical mechanics. In general relativity the energy-momentum tensor 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 quantum mechanics, which is usually developed by changing classical (including special relativity) Hamiltonians into quantum wave equations.

  16. Tensor integrand reduction via Laurent expansion

    NASA Astrophysics Data System (ADS)

    Hirschi, Valentin; Peraro, Tiziano

    2016-06-01

    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 tensor 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 tensor. 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 tensor 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.

  17. Diffusion tensor image registration using polynomial expansion

    NASA Astrophysics Data System (ADS)

    Wang, Yuanjun; Chen, Zengai; Nie, Shengdong; Westin, Carl-Fredrik

    2013-09-01

    In this paper, we present a deformable registration framework for the diffusion tensor image (DTI) using polynomial expansion. The use of polynomial expansion in image registration has previously been shown to be beneficial due to fast convergence and high accuracy. However, earlier work was developed only for 3D scalar medical image registration. In this work, it is shown how polynomial expansion can be applied to DTI registration. A new measurement is proposed for DTI registration evaluation, which seems to be robust and sensitive in evaluating the result of DTI registration. We present the algorithms for DTI registration using polynomial expansion by the fractional anisotropy image, and an explicit tensor reorientation strategy is inherent to the registration process. Analytic transforms with high accuracy are derived from polynomial expansion and used for transforming the tensor's orientation. Three measurements for DTI registration evaluation are presented and compared in experimental results. The experiments for algorithm validation are designed from simple affine deformation to nonlinear deformation cases, and the algorithms using polynomial expansion give a good performance in both cases. Inter-subject DTI registration results are presented showing the utility of the proposed method.

  18. Tensor integrand reduction via Laurent expansion

    DOE PAGESBeta

    Hirschi, Valentin; Peraro, Tiziano

    2016-06-09

    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 tensor with cut-dependent projectors, making it possible to interface Ninja to any one-loop matrix element generator that can provide the components of this tensor. 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 tensor 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

  19. Integrated calibration of magnetic gradient tensor system

    NASA Astrophysics Data System (ADS)

    Gang, Yin; Yingtang, Zhang; Hongbo, Fan; GuoQuan, Ren; Zhining, Li

    2015-01-01

    Measurement precision of a magnetic gradient tensor system is not only connected with the imperfect performance of magnetometers such as bias, scale factor, non-orthogonality and misalignment errors, but also connected with the external soft-iron and hard-iron magnetic distortion fields when the system is used as a strapdown device. So an integrated scalar calibration method is proposed in this paper. In the first step, a mathematical model for scalar calibration of a single three-axis magnetometer is established, and a least squares ellipsoid fitting algorithm is proposed to estimate the detailed error parameters. For the misalignment errors existing at different magnetometers caused by the installation process and misalignment errors aroused by ellipsoid fitting estimation, a calibration method for combined misalignment errors is proposed in the second step to switch outputs of different magnetometers into the ideal reference orthogonal coordinate system. In order to verify effectiveness of the proposed method, simulation and experiment with a cross-magnetic gradient tensor system are performed, and the results show that the proposed method estimates error parameters and improves the measurement accuracy of magnetic gradient tensor greatly.

  20. Cytotoxicity of CdTe quantum dots in human umbilical vein endothelial cells: the involvement of cellular uptake and induction of pro-apoptotic endoplasmic reticulum stress

    PubMed Central

    Yan, Ming; Zhang, Yun; Qin, Haiyan; Liu, Kezhou; Guo, Miao; Ge, Yakun; Xu, Mingen; Sun, Yonghong; Zheng, Xiaoxiang

    2016-01-01

    Cadmium telluride quantum dots (CdTe QDs) have been proposed to induce oxidative stress, which plays a crucial role in CdTe QDs-mediated mitochondrial-dependent apoptosis in human umbilical vein endothelial cells (HUVECs). However, the direct interactions of CdTe QDs with HUVECs and their potential impairment of other organelles like endoplasmic reticulum (ER) in HUVECs are poorly understood. In this study, we reported that the negatively charged CdTe QDs (−21.63±0.91 mV), with good dispersity and fluorescence stability, were rapidly internalized via endocytosis by HUVECs, as the notable internalization could be inhibited up to 95.52% by energy depletion (NaN3/deoxyglucose or low temperature). The endocytosis inhibitors (methyl-β-cyclodextrin, genistein, sucrose, chlorpromazine, and colchicine) dramatically decreased the uptake of CdTe QDs by HUVECs, suggesting that both caveolae/raft- and clathrin-mediated endocytosis were involved in the endothelial uptake of CdTe QDs. Using immunocytochemistry, a striking overlap of the internalized CdTe QDs and ER marker was observed, which indicates that QDs may be transported to ER. The CdTe QDs also caused remarkable ER stress responses in HUVECs, confirmed by significant dilatation of ER cisternae, upregulation of ER stress markers GRP78/GRP94, and activation of protein kinase RNA-like ER kinase-eIF2α-activating transcription factor 4 pathway (including phosphorylation of both protein kinase RNA-like ER kinase and eIF2α and elevated level of activating transcription factor 4). CdTe QDs further promoted an increased C/EBP homologous protein expression, phosphorylation of c-JUN NH2-terminal kinase, and cleavage of ER-resident caspase-4, while the specific inhibitor (SP600125, Z-LEVD-fmk, or salubrinal) significantly attenuated QDs-triggered apoptosis, indicating that all three ER stress-mediated apoptosis pathways were activated and the direct participation of ER in the CdTe QDs-caused apoptotic cell death in HUVECs

  1. Cytotoxicity of CdTe quantum dots in human umbilical vein endothelial cells: the involvement of cellular uptake and induction of pro-apoptotic endoplasmic reticulum stress.

    PubMed

    Yan, Ming; Zhang, Yun; Qin, Haiyan; Liu, Kezhou; Guo, Miao; Ge, Yakun; Xu, Mingen; Sun, Yonghong; Zheng, Xiaoxiang

    2016-01-01

    Cadmium telluride quantum dots (CdTe QDs) have been proposed to induce oxidative stress, which plays a crucial role in CdTe QDs-mediated mitochondrial-dependent apoptosis in human umbilical vein endothelial cells (HUVECs). However, the direct interactions of CdTe QDs with HUVECs and their potential impairment of other organelles like endoplasmic reticulum (ER) in HUVECs are poorly understood. In this study, we reported that the negatively charged CdTe QDs (-21.63±0.91 mV), with good dispersity and fluorescence stability, were rapidly internalized via endocytosis by HUVECs, as the notable internalization could be inhibited up to 95.52% by energy depletion (NaN3/deoxyglucose or low temperature). The endocytosis inhibitors (methyl-β-cyclodextrin, genistein, sucrose, chlorpromazine, and colchicine) dramatically decreased the uptake of CdTe QDs by HUVECs, suggesting that both caveolae/raft- and clathrin-mediated endocytosis were involved in the endothelial uptake of CdTe QDs. Using immunocytochemistry, a striking overlap of the internalized CdTe QDs and ER marker was observed, which indicates that QDs may be transported to ER. The CdTe QDs also caused remarkable ER stress responses in HUVECs, confirmed by significant dilatation of ER cisternae, upregulation of ER stress markers GRP78/GRP94, and activation of protein kinase RNA-like ER kinase-eIF2α-activating transcription factor 4 pathway (including phosphorylation of both protein kinase RNA-like ER kinase and eIF2α and elevated level of activating transcription factor 4). CdTe QDs further promoted an increased C/EBP homologous protein expression, phosphorylation of c-JUN NH2-terminal kinase, and cleavage of ER-resident caspase-4, while the specific inhibitor (SP600125, Z-LEVD-fmk, or salubrinal) significantly attenuated QDs-triggered apoptosis, indicating that all three ER stress-mediated apoptosis pathways were activated and the direct participation of ER in the CdTe QDs-caused apoptotic cell death in HUVECs. Our

  2. Strain balanced quantum posts

    SciTech Connect

    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.

    2011-04-25

    Quantum posts are assembled by epitaxial growth of closely spaced quantum dot layers, modulating the composition of a semiconductor alloy, typically InGaAs. In contrast with most self-assembled nanostructures, the height of quantum posts can be controlled with nanometer precision, up to a maximum value limited by the accumulated stress 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 quantum post height. The luminescence from the resulting nanostructures presents giant linear polarization anisotropy.

  3. Auxiliary Field Diffusion Monte Carlo Calculation of Nuclei with A{<=}40 with Tensor Interactions

    SciTech Connect

    Gandolfi, S.; Pederiva, F.

    2007-07-13

    We calculate the ground-state energy of {sup 4}He, {sup 8}He, {sup 16}O, and {sup 40}Ca using the auxiliary field diffusion Monte Carlo method in the fixed-phase approximation and the Argonne v{sub 6}{sup '} interaction which includes a tensor force. Comparison of our light nuclei results to those of Green's function Monte Carlo calculations shows the accuracy of our method for both open and closed-shell nuclei. We also apply it to {sup 16}O and {sup 40}Ca to show that quantum Monte Carlo methods are now applicable to larger nuclei.

  4. Extremal spacings between eigenphases of random unitary matrices and their tensor products.

    PubMed

    Smaczyński, Marek; Tkocz, Tomasz; Kuś, Marek; Życzkowski, Karol

    2013-11-01

    Extremal spacings between eigenphases of random unitary matrices of size N pertaining to circular ensembles are investigated. Explicit probability distributions for the minimal spacing for various ensembles are derived for N=4. We study ensembles of tensor product of k random unitary matrices of size n which describe independent evolution of a composite quantum system consisting of k subsystems. In the asymptotic case, as the total dimension N=n(k) becomes large, the nearest neighbor distribution P(s) becomes Poissonian, but statistics of extreme spacings P(s(min)) and P(s(max)) reveal certain deviations from the Poissonian behavior.

  5. Extremal spacings between eigenphases of random unitary matrices and their tensor products

    NASA Astrophysics Data System (ADS)

    Smaczyński, Marek; Tkocz, Tomasz; Kuś, Marek; Życzkowski, Karol

    2013-11-01

    Extremal spacings between eigenphases of random unitary matrices of size N pertaining to circular ensembles are investigated. Explicit probability distributions for the minimal spacing for various ensembles are derived for N=4. We study ensembles of tensor product of k random unitary matrices of size n which describe independent evolution of a composite quantum system consisting of k subsystems. In the asymptotic case, as the total dimension N=nk becomes large, the nearest neighbor distribution P(s) becomes Poissonian, but statistics of extreme spacings P(smin) and P(smax) reveal certain deviations from the Poissonian behavior.

  6. Continuous states for a relativistic problem plus tensor coupling in D-dimensional space

    NASA Astrophysics Data System (ADS)

    Eshghi, Mahdi; Mehraban, Hosein

    2015-10-01

    In this research, a relativistic particle scattering was investigated for particles with spin 1/2 in a hyperbolic potential including Coulomb-like tensor interaction in D-dimensional space. By using the Greene and Aldrich approximately, we presented solutions of the Dirac equation with this potential for any spin-orbit quantum number κ under spin symmetry. The normalized wave functions are expressed in terms of the hyper geometric series of continuous states on the k/ 2π scale. Also, the formula for the phase shifts is calculated. Some of the thermodynamics properties of a system Dirac electrons are also discussed.

  7. Quantum mechanics from invariance principles

    NASA Astrophysics Data System (ADS)

    Moldoveanu, Florin

    2015-07-01

    Quantum mechanics is an extremely successful theory of nature and yet it lacks an intuitive axiomatization. In contrast, the special theory of relativity is well understood and is rooted into natural or experimentally justified postulates. Here we introduce an axiomatization approach to quantum mechanics which is very similar to special theory of relativity derivation. The core idea is that a composed system obeys the same laws of nature as its components. This leads to a Jordan-Lie algebraic formulation of quantum mechanics. The starting assumptions are minimal: the laws of nature are invariant under time evolution, the laws of nature are invariant under tensor composition, the laws of nature are relational, together with the ability to define a physical state (positivity). Quantum mechanics is singled out by a fifth experimentally justified postulate: nature violates Bell's inequalities.

  8. Quantum gravity and renormalization

    NASA Astrophysics Data System (ADS)

    Anselmi, Damiano

    2015-01-01

    The properties of quantum gravity are reviewed from the point of view of renormalization. Various attempts to overcome the problem of non-renormalizability are presented, and the reasons why most of them fail for quantum gravity are discussed. Interesting possibilities come from relaxing the locality assumption, which also can inspire the investigation of a largely unexplored sector of quantum field theory. Another possibility is to work with infinitely many independent couplings, and search for physical quantities that only depend on a finite subset of them. In this spirit, it is useful to organize the classical action of quantum gravity, determined by renormalization, in a convenient way. Taking advantage of perturbative local field redefinitions, we write the action as the sum of the Hilbert term, the cosmological term, a peculiar scalar that is important only in higher dimensions, plus invariants constructed with at least three Weyl tensors. We show that the FRLW configurations, and many other locally conformally flat metrics, are exact solutions of the field equations in arbitrary dimensions d>3. If the metric is expanded around such configurations the quadratic part of the action is free of higher-time derivatives. Other well-known metrics, such as those of black holes, are instead affected in nontrivial ways by the classical corrections of quantum origin.

  9. High Tg photorefractive polymers: Influence of the chromophores' β tensor

    NASA Astrophysics Data System (ADS)

    Acebal, P.; Blaya, S.; Carretero, L.

    2004-11-01

    In this paper we study the effect of the chromophores' β tensor active components on the diffraction efficiency of a high Tg photorefractive polymer. In particular, we study the two simplest structures with nonvanishing dipole moment, the one-dimension push-pull systems, and the Λ-shaped chromophores. We have developed a model that relate the diffraction efficiency expression with experimental conditions and microscopic properties of the molecules used. Using this model we determine the optimum experimental conditions for both kinds of chromophores and the criteria for the design of chromophores with improved microscopic properties. The model was also used to evaluate the diffraction efficiency of the chromophore Disperse Red 1 (DR1) with a good agreement with experimental data present in bibliography, and of other chromophores selected with the criteria derived from the model, using quantum mechanical calculations to obtain the microscopic properties. Using the designed chromophores diffraction efficiencies more than one order of magnitude higher than that calculated for DR1 with the experimental conditions has been obtained in simulations. These chromophores also exhibit a low dependency of η on the electric field polarization in contrast to the DR1 or the low Tg photoreactive materials.

  10. Tensor-polarized structure functions: Tensor structure of deuteron in 2020's

    NASA Astrophysics Data System (ADS)

    Kumano, S.

    2014-10-01

    We explain spin structure for a spin-one hadron, in which there are new structure functions, in addition to the ones (F1, F2, g1, g2) which exist for the spin-1/2 nucleon, associated with its tensor structure. The new structure functions are b1, b2, b3, and b4 in deep inelastic scattering of a charged-lepton from a spin-one hadron such as the deuteron. Among them, twist- two functions are related by the Callan-Gross type relation b2 = 2xb1 in the Bjorken scaling limit. First, these new structure functions are introduced, and useful formulae are derived for projection operators of b1-4 from a hadron tensor Wμν. Second, a sum rule is explained for b1, and possible tensor-polarized distributions are discussed by using HERMES data in order to propose future experimental measurements and to compare them with theoretical models. A proposal was approved to measure b1 at the Thomas Jefferson National Accelerator Facility (JLab), so that much progress is expected for b1 in the near future. Third, formalisms of polarized proton-deuteron Drell-Yan processes are explained for probing especially tensor- polarized antiquark distributions, which were suggested by the HERMES data. The studies of the tensor-polarized structure functions will open a new era in 2020's for tensor-structure studies in terms of quark and gluon degrees of freedom, which are very different from ordinary descriptions in terms of nucleons and mesons.

  11. Chaos in quantum channels

    NASA Astrophysics Data System (ADS)

    Hosur, Pavan; Qi, Xiao-Liang; Roberts, Daniel A.; Yoshida, Beni

    2016-02-01

    We study chaos and scrambling in unitary channels by considering their entanglement properties as states. Using out-of-time-order correlation functions to diagnose chaos, we characterize the ability of a channel to process quantum information. We show that the generic decay of such correlators implies that any input subsystem must have near vanishing mutual information with almost all partitions of the output. Additionally, we propose the negativity of the tripartite information of the channel as a general diagnostic of scrambling. This measures the delocalization of information and is closely related to the decay of out-of-time-order correlators. We back up our results with numerics in two non-integrable models and analytic results in a perfect tensor network model of chaotic time evolution. These results show that the butterfly effect in quantum systems implies the information-theoretic definition of scrambling.

  12. Quantum Critical Elasticity.

    PubMed

    Zacharias, Mario; Paul, Indranil; Garst, Markus

    2015-07-10

    We discuss elastic instabilities of the atomic crystal lattice at zero temperature. Because of long-range shear forces of the solid, at such transitions the phonon velocities vanish, if at all, only along certain crystallographic directions, and, consequently, the critical phonon fluctuations are suppressed to a lower dimensional manifold and governed by a Gaussian fixed point. In the case of symmetry-breaking elastic transitions, a characteristic critical phonon thermodynamics arises that is found, e.g., to violate Debye's T(3) law for the specific heat. We point out that quantum critical elasticity is triggered whenever a critical soft mode couples linearly to the strain tensor. In particular, this is relevant for the electronic Ising-nematic quantum phase transition in a tetragonal crystal as discussed in the context of certain cuprates, ruthenates, and iron-based superconductors. PMID:26207483

  13. Chaos in quantum channels

    DOE PAGESBeta

    Hosur, Pavan; Qi, Xiao-Liang; Roberts, Daniel A.; Yoshida, Beni

    2016-02-01

    For this research, we study chaos and scrambling in unitary channels by considering their entanglement properties as states. Using out-of-time-order correlation functions to diagnose chaos, we characterize the ability of a channel to process quantum information. We show that the generic decay of such correlators implies that any input subsystem must have near vanishing mutual information with almost all partitions of the output. Additionally, we propose the negativity of the tripartite information of the channel as a general diagnostic of scrambling. This measures the delocalization of information and is closely related to the decay of out-of-time-order correlators. We back upmore » our results with numerics in two non-integrable models and analytic results in a perfect tensor network model of chaotic time evolution. In conclusion, these results show that the butterfly effect in quantum systems implies the information-theoretic definition of scrambling.« less

  14. Temperature effects in first-principles solid state calculations of the chemical shielding tensor made simple

    SciTech Connect

    Monserrat, Bartomeu Needs, Richard J.; Pickard, Chris J.

    2014-10-07

    We study the effects of atomic vibrations on the solid-state chemical shielding tensor using first principles density functional theory calculations. At the harmonic level, we use a Monte Carlo method and a perturbative expansion. The Monte Carlo method is accurate but computationally expensive, while the perturbative method is computationally more efficient, but approximate. We find excellent agreement between the two methods for both the isotropic shift and the shielding anisotropy. The effects of zero-point quantum mechanical nuclear motion are important up to relatively high temperatures: at 500 K they still represent about half of the overall vibrational contribution. We also investigate the effects of anharmonic vibrations, finding that their contribution to the zero-point correction to the chemical shielding tensor is small. We exemplify these ideas using magnesium oxide and the molecular crystals L-alanine and β-aspartyl-L-alanine. We therefore propose as the method of choice to incorporate the effects of temperature in solid state chemical shielding tensor calculations using the perturbative expansion within the harmonic approximation. This approach is accurate and requires a computational effort that is about an order of magnitude smaller than that of dynamical or Monte Carlo approaches, so these effects might be routinely accounted for.

  15. Temperature effects in first-principles solid state calculations of the chemical shielding tensor made simple

    NASA Astrophysics Data System (ADS)

    Monserrat, Bartomeu; Needs, Richard J.; Pickard, Chris J.

    2014-10-01

    We study the effects of atomic vibrations on the solid-state chemical shielding tensor using first principles density functional theory calculations. At the harmonic level, we use a Monte Carlo method and a perturbative expansion. The Monte Carlo method is accurate but computationally expensive, while the perturbative method is computationally more efficient, but approximate. We find excellent agreement between the two methods for both the isotropic shift and the shielding anisotropy. The effects of zero-point quantum mechanical nuclear motion are important up to relatively high temperatures: at 500 K they still represent about half of the overall vibrational contribution. We also investigate the effects of anharmonic vibrations, finding that their contribution to the zero-point correction to the chemical shielding tensor is small. We exemplify these ideas using magnesium oxide and the molecular crystals L-alanine and β-aspartyl-L-alanine. We therefore propose as the method of choice to incorporate the effects of temperature in solid state chemical shielding tensor calculations using the perturbative expansion within the harmonic approximation. This approach is accurate and requires a computational effort that is about an order of magnitude smaller than that of dynamical or Monte Carlo approaches, so these effects might be routinely accounted for.

  16. More on loops in reheating: non-gaussianities and tensor power spectrum

    SciTech Connect

    Katırcı, Nihan; Kaya, Ali; Tarman, Merve

    2014-06-11

    We consider the single field chaotic m{sup 2}ϕ{sup 2} inflationary model with a period of preheating, where the inflaton decays to another scalar field χ in the parametric resonance regime. In a recent work, one of us has shown that the χ modes circulating in the loops during preheating notably modify the <ζζ> correlation function. We first rederive this result using a different gauge condition hence reconfirm that superhorizon ζ modes are affected by the loops in preheating. Further, we examine how χ loops give rise to non-gaussianity and affect the tensor perturbations. For that, all cubic and some higher order interactions involving two χ fields are determined and their contribution to the non-gaussianity parameter f{sub NL} and the tensor power spectrum are calculated at one loop. Our estimates for these corrections show that while a large amount of non-gaussianity can be produced during reheating, the tensor power spectrum receive moderate corrections. We observe that the loop quantum effects increase with more χ fields circulating in the loops indicating that the perturbation theory might be broken down. These findings demonstrate that the loop corrections during reheating are significant and they must be taken into account for precision inflationary cosmology.

  17. More on loops in reheating: non-gaussianities and tensor power spectrum

    SciTech Connect

    Katirci, Nihan; Kaya, Ali; Tarman, Merve E-mail: ali.kaya@boun.edu.tr

    2014-06-01

    We consider the single field chaotic m{sup 2}φ{sup 2} inflationary model with a period of preheating, where the inflaton decays to another scalar field χ in the parametric resonance regime. In a recent work, one of us has shown that the χ modes circulating in the loops during preheating notably modify the (ζζ) correlation function. We first rederive this result using a different gauge condition hence reconfirm that superhorizon ζ modes are affected by the loops in preheating. Further, we examine how χ loops give rise to non-gaussianity and affect the tensor perturbations. For that, all cubic and some higher order interactions involving two χ fields are determined and their contribution to the non-gaussianity parameter f{sub NL} and the tensor power spectrum are calculated at one loop. Our estimates for these corrections show that while a large amount of non-gaussianity can be produced during reheating, the tensor power spectrum receive moderate corrections. We observe that the loop quantum effects increase with more χ fields circulating in the loops indicating that the perturbation theory might be broken down. These findings demonstrate that the loop corrections during reheating are significant and they must be taken into account for precision inflationary cosmology.

  18. Reduction of noise in diffusion tensor images using anisotropic smoothing.

    PubMed

    Ding, Zhaohua; Gore, John C; Anderson, Adam W

    2005-02-01

    To improve the accuracy of tissue structural and architectural characterization with diffusion tensor imaging, a novel smoothing technique is developed for reducing noise in diffusion tensor images. The technique extends the traditional anisotropic diffusion filtering method by allowing isotropic smoothing within homogeneous regions and anisotropic smoothing along structure boundaries. This is particularly useful for smoothing diffusion tensor images in which direction information contained in the tensor needs to be restored following noise corruption and preserved around tissue boundaries. The effectiveness of this technique is quantitatively studied with experiments on simulated and human in vivo diffusion tensor data. Illustrative results demonstrate that the anisotropic smoothing technique developed can significantly reduce the impact of noise on the direction as well as anisotropy measures of the diffusion tensor images.

  19. Estimating missing tensor data by face synthesis for expression recognition

    NASA Astrophysics Data System (ADS)

    Tan, Huachun; Chen, Hao; Zhang, Jie

    2009-01-01

    In this paper, a new method of facial expression recognition is proposed for missing tensor data. In this method, the missing tensor data is estimated by facial expression synthesis in order to construct the full tensor, which is used for multi-factorization face analysis. The full tensor data allows for the full use of the information of a given database, and hence improves the performance of face analysis. Compared with EM algorithm for missing data estimation, the proposed method avoids iteration process and reduces the estimation complexity. The proposed missing tensor data estimation is applied for expression recognition. The experimental results show that the proposed method is performing better than only utilize the original smaller tensor.

  20. Emergent classical geometries on boundaries of randomly connected tensor networks

    NASA Astrophysics Data System (ADS)

    Chen, Hua; Sasakura, Naoki; Sato, Yuki

    2016-03-01

    It is shown that classical spaces with geometries emerge on boundaries of randomly connected tensor networks with appropriately chosen tensors in the thermodynamic limit. With variation of the tensors the dimensions of the spaces can be freely chosen, and the geometries—which are curved in general—can be varied. We give the explicit solvable examples of emergent flat tori in arbitrary dimensions, and the correspondence from the tensors to the geometries for general curved cases. The perturbative dynamics in the emergent space is shown to be described by an effective action which is invariant under the spatial diffeomorphism due to the underlying orthogonal group symmetry of the randomly connected tensor network. It is also shown that there are various phase transitions among spaces, including extended and point-like ones, under continuous change of the tensors.

  1. Using the quantum yields of photosystem II and the rate of net photosynthesis to monitor high irradiance and temperature stress in chrysanthemum (Dendranthema grandiflora).

    PubMed

    Janka, Eshetu; Körner, Oliver; Rosenqvist, Eva; Ottosen, Carl-Otto

    2015-05-01

    Under a dynamic greenhouse climate control regime, temperature is adjusted to optimise plant physiological responses to prevailing irradiance levels; thus, both temperature and irradiance are used by the plant to maximise the rate of photosynthesis, assuming other factors are not limiting. The control regime may be optimised by monitoring plant responses, and may be promptly adjusted when plant performance is affected by extreme microclimatic conditions, such as high irradiance or temperature. To determine the stress indicators of plants based on their physiological responses, net photosynthesis (Pn) and four chlorophyll-a fluorescence parameters: maximum photochemical efficiency of PSII [Fv/Fm], electron transport rate [ETR], PSII operating efficiency [F'q/F'm], and non-photochemical quenching [NPQ] were assessed for potted chrysanthemum (Dendranthema grandiflora Tzvelev) 'Coral Charm' under different temperature (20, 24, 28, 32, 36 °C) and daily light integrals (DLI; 11, 20, 31, and 43 mol m(-2) created by a PAR of 171, 311, 485 and 667 μmol m(-2) s(-1) for 16 h). High irradiance (667 μmol m(-2) s(-1)) combined with high temperature (>32 °C) significantly (p < 0.05) decreased Fv/Fm. Under high irradiance, the maximum Pn and ETR were reached at 24 °C. Increased irradiance decreased the PSII operating efficiency and increased NPQ, while both high irradiance and temperature had a significant effect on the PSII operating efficiency at temperatures >28 °C. Under high irradiance and temperature, changes in the NPQ determined the PSII operating efficiency, with no major change in the fraction of open PSII centres (qL) (indicating a QA redox state). We conclude that 1) chrysanthemum plants cope with excess irradiance by non-radiative dissipation or a reversible stress response, with the effect on the Pn and quantum yield of PSII remaining low until the temperature reaches 28 °C and 2) the integration of online measurements to monitor photosynthesis and PSII

  2. Cauchy's stress theorem for stresses represented by measures

    NASA Astrophysics Data System (ADS)

    Šilhavý, M.

    2008-05-01

    A version of Cauchy’s stress theorem is given in which the stress describing the system of forces in a continuous body is represented by a tensor valued measure with weak divergence a vector valued measure. The system of forces is formalized in the notion of an unbounded Cauchy flux generalizing the bounded Cauchy flux by Gurtin and Martins (Arch Ration Mech Anal 60:305-324, 1976). The main result of the paper says that unbounded Cauchy fluxes are in one-to-one correspondence with tensor valued measures with weak divergence a vector valued measure. Unavoidably, the force transmitted by a surface generally cannot be defined for all surfaces but only for almost every translation of the surface. Also conditions are given guaranteeing that the transmitted force is represented by a measure. These results are proved by using a new homotopy formula for tensor valued measure with weak divergence a vector valued measure.

  3. The Heisenberg representation of quantum computers

    SciTech Connect

    Gottesman, D.

    1998-06-24

    Since Shor`s discovery of an algorithm to factor numbers on a quantum computer in polynomial time, quantum computation has become a subject of immense interest. Unfortunately, one of the key features of quantum computers--the difficulty of describing them on classical computers--also makes it difficult to describe and understand precisely what can be done with them. A formalism describing the evolution of operators rather than states has proven extremely fruitful in understanding an important class of quantum operations. States used in error correction and certain communication protocols can be described by their stabilizer, a group of tensor products of Pauli matrices. Even this simple group structure is sufficient to allow a rich range of quantum effects, although it falls short of the full power of quantum computation.

  4. Irreducible Cartesian tensors of highest weight, for arbitrary order

    NASA Astrophysics Data System (ADS)

    Mane, S. R.

    2016-03-01

    A closed form expression is presented for the irreducible Cartesian tensor of highest weight, for arbitrary order. Two proofs are offered, one employing bookkeeping of indices and, after establishing the connection with the so-called natural tensors and their projection operators, the other one employing purely coordinate-free tensor manipulations. Some theorems and formulas in the published literature are generalized from SO(3) to SO(n), for dimensions n ≥ 3.

  5. Construction of energy-momentum tensor of gravitation

    NASA Astrophysics Data System (ADS)

    Bamba, Kazuharu; Shimizu, Katsutaro

    2016-10-01

    We construct the gravitational energy-momentum tensor in general relativity through the Noether theorem. In particular, we explicitly demonstrate that the constructed quantity can vary as a tensor under the general coordinate transformation. Furthermore, we verify that the energy-momentum conservation is satisfied because one of the two indices of the energy-momentum tensor should be in the local Lorentz frame. It is also shown that the gravitational energy and the matter one cancel out in certain space-times.

  6. Scalable tensor factorizations with missing data.

    SciTech Connect

    Morup, Morten; Dunlavy, Daniel M.; Acar, Evrim; Kolda, Tamara Gibson

    2010-04-01

    The problem of missing data is ubiquitous in domains such as biomedical signal processing, network traffic analysis, bibliometrics, social network analysis, chemometrics, computer vision, and communication networks|all domains in which data collection is subject to occasional errors. Moreover, these data sets can be quite large and have more than two axes of variation, e.g., sender, receiver, time. Many applications in those domains aim to capture the underlying latent structure of the data; in other words, they need to factorize data sets with missing entries. If we cannot address the problem of missing data, many important data sets will be discarded or improperly analyzed. Therefore, we need a robust and scalable approach for factorizing multi-way arrays (i.e., tensors) in the presence of missing data. We focus on one of the most well-known tensor factorizations, CANDECOMP/PARAFAC (CP), and formulate the CP model as a weighted least squares problem that models only the known entries. We develop an algorithm called CP-WOPT (CP Weighted OPTimization) using a first-order optimization approach to solve the weighted least squares problem. Based on extensive numerical experiments, our algorithm is shown to successfully factor tensors with noise and up to 70% missing data. Moreover, our approach is significantly faster than the leading alternative and scales to larger problems. To show the real-world usefulness of CP-WOPT, we illustrate its applicability on a novel EEG (electroencephalogram) application where missing data is frequently encountered due to disconnections of electrodes.

  7. Minimal tensors and purely electric or magnetic spacetimes of arbitrary dimension

    NASA Astrophysics Data System (ADS)

    Hervik, Sigbjørn; Ortaggio, Marcello; Wylleman, Lode

    2013-08-01

    We consider time reversal transformations to obtain twofold orthogonal splittings of any tensor on a Lorentzian space of arbitrary dimension n. Applied to the Weyl tensor of a spacetime, this leads to a definition of its electric and magnetic parts relative to an observer (defined by a unit timelike vector field u), in any dimension. We study the cases where one of these parts vanishes in detail, i.e., purely electric (PE) or magnetic (PM) spacetimes. We generalize several results from four to higher dimensions and discuss new features of higher dimensions. For instance, we prove that the only permitted Weyl types are G, Ii and D, and discuss the possible relation of u with the Weyl aligned null directions (WANDs); we provide invariant conditions that characterize PE/PM spacetimes, such as Bel-Debever-like criteria, or constraints on scalar invariants, and connect the PE/PM parts to the kinematic quantities of u; we present conditions under which direct product spacetimes (and certain warps) are PE/PM, which enables us to construct explicit examples. In particular, it is also shown that all static spacetimes are necessarily PE, while stationary spacetimes (such as spinning black holes) are in general neither PE nor PM. Whereas ample classes of PE spacetimes exist, PM solutions are elusive; specifically, we prove that PM Einstein spacetimes of type D do not exist, in any dimension. Finally, we derive corresponding results for the electric/magnetic parts of the Riemann tensor, which is useful when considering spacetimes with matter fields, and moreover leads to first examples of PM spacetimes in higher dimensions. We also note in passing that PE/PM Weyl (or Riemann) tensors provide examples of minimal tensors, and we make the connection hereof with the recently proved alignment theorem (Hervik 2011 Class. Quantum Grav. 28 215009). This in turn sheds new light on the classification of the Weyl tensors based on null alignment, providing a further invariant

  8. On the dynamic viscous permeability tensor symmetry.

    PubMed

    Perrot, Camille; Chevillotte, Fabien; Panneton, Raymond; Allard, Jean-François; Lafarge, Denis

    2008-10-01

    Based on a direct generalization of a proof given by Torquato for symmetry property in static regime, this express letter clarifies the reasons why the dynamic permeability tensor is symmetric for spatially periodic structures having symmetrical axes which do not coincide with orthogonal pairs being perpendicular to the axis of three-, four-, and sixfold symmetry. This somewhat nonintuitive property is illustrated by providing detailed numerical examples for a hexagonal lattice of solid cylinders in the asymptotic and frequency dependent regimes. It may be practically useful for numerical implementation validation and/or convergence assessment.

  9. Beam-plasma dielectric tensor with Mathematica

    NASA Astrophysics Data System (ADS)

    Bret, A.

    2007-03-01

    We present a Mathematica notebook allowing for the symbolic calculation of the 3×3 dielectric tensor of an electron-beam plasma system in the fluid approximation. Calculation is detailed for a cold relativistic electron beam entering a cold magnetized plasma, and for arbitrarily oriented wave vectors. We show how one can elaborate on this example to account for temperatures, arbitrarily oriented magnetic field or a different kind of plasma. Program summaryTitle of program: Tensor Catalog identifier: ADYT_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADYT_v1_0 Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Computer for which the program is designed and others on which it has been tested: Computers: Any computer running Mathematica 4.1. Tested on DELL Dimension 5100 and IBM ThinkPad T42. Installations: ETSI Industriales, Universidad Castilla la Mancha, Ciudad Real, Spain Operating system under which the program has been tested: Windows XP Pro Programming language used: Mathematica 4.1 Memory required to execute with typical data: 7.17 Mbytes No. of bytes in distributed program, including test data, etc.: 33 439 No. of lines in distributed program, including test data, etc.: 3169 Distribution format: tar.gz Nature of the physical problem: The dielectric tensor of a relativistic beam plasma system may be quite involved to calculate symbolically when considering a magnetized plasma, kinetic pressure, collisions between species, and so on. The present Mathematica notebook performs the symbolic computation in terms of some usual dimensionless variables. Method of solution: The linearized relativistic fluid equations are directly entered and solved by Mathematica to express the first-order expression of the current. This expression is then introduced into a combination of Faraday and Ampère-Maxwell's equations to give the dielectric tensor. Some additional manipulations are needed to express the result in terms of the

  10. A Tensor Hyperviscosity Model in Kull

    SciTech Connect

    Ulitsky, M

    2005-06-28

    A tensor artificial hyper-viscosity model has recently been added to the available list of artificial viscosities that one can chose from when running KULL. This model is based on the theoretical work of A. Cook and B. Cabot, and the numerical results of running the model in the high-order spectral/compact finite difference framework of the Eulerian MIRANDA code. The viscosity model is based on filtering a Laplacian or bi-Laplacian of the strain rate magnitude, and it was desired to investigate whether the formalism that worked so well for the MIRANDA research code could be carried over to an unstructured ALE code like KULL.

  11. 3D extension of Tensorial Polar Decomposition. Application to (photo-)elasticity tensors

    NASA Astrophysics Data System (ADS)

    Desmorat, Rodrigue; Desmorat, Boris

    2016-06-01

    The orthogonalized harmonic decomposition of symmetric fourth-order tensors (i.e. having major and minor indicial symmetries, such as elasticity tensors) is completed by a representation of harmonic fourth-order tensors H by means of two second-order harmonic (symmetric deviatoric) tensors only. A similar decomposition is obtained for non-symmetric tensors (i.e. having minor indicial symmetry only, such as photo-elasticity tensors or elasto-plasticity tangent operators) introducing a fourth-order major antisymmetric traceless tensor Z. The tensor Z is represented by means of one harmonic second-order tensor and one antisymmetric second-order tensor only. Representations of totally symmetric (rari-constant), symmetric and major antisymmetric fourth-order tensors are simple particular cases of the proposed general representation. Closed-form expressions for tensor decomposition are given in the monoclinic case. Practical applications to elasticity and photo-elasticity monoclinic tensors are finally presented. xml:lang="fr"

  12. Tensor Modeling Based for Airborne LiDAR Data Classification

    NASA Astrophysics Data System (ADS)

    Li, N.; Liu, C.; Pfeifer, N.; Yin, J. F.; Liao, Z. Y.; Zhou, Y.

    2016-06-01

    Feature selection and description is a key factor in classification of Earth observation data. In this paper a classification method based on tensor decomposition is proposed. First, multiple features are extracted from raw LiDAR point cloud, and raster LiDAR images are derived by accumulating features or the "raw" data attributes. Then, the feature rasters of LiDAR data are stored as a tensor, and tensor decomposition is used to select component features. This tensor representation could keep the initial spatial structure and insure the consideration of the neighborhood. Based on a small number of component features a k nearest neighborhood classification is applied.

  13. The Topology of Three-Dimensional Symmetric Tensor Fields

    NASA Technical Reports Server (NTRS)

    Lavin, Yingmei; Levy, Yuval; Hesselink, Lambertus

    1994-01-01

    We study the topology of 3-D symmetric tensor fields. The goal is to represent their complex structure by a simple set of carefully chosen points and lines analogous to vector field topology. The basic constituents of tensor topology are the degenerate points, or points where eigenvalues are equal to each other. First, we introduce a new method for locating 3-D degenerate points. We then extract the topological skeletons of the eigenvector fields and use them for a compact, comprehensive description of the tensor field. Finally, we demonstrate the use of tensor field topology for the interpretation of the two-force Boussinesq problem.

  14. Joint Tensor Feature Analysis For Visual Object Recognition.

    PubMed

    Wong, Wai Keung; Lai, Zhihui; Xu, Yong; Wen, Jiajun; Ho, Chu Po

    2015-11-01

    Tensor-based object recognition has been widely studied in the past several years. This paper focuses on the issue of joint feature selection from the tensor data and proposes a novel method called joint tensor feature analysis (JTFA) for tensor feature extraction and recognition. In order to obtain a set of jointly sparse projections for tensor feature extraction, we define the modified within-class tensor scatter value and the modified between-class tensor scatter value for regression. The k-mode optimization technique and the L(2,1)-norm jointly sparse regression are combined together to compute the optimal solutions. The convergent analysis, computational complexity analysis and the essence of the proposed method/model are also presented. It is interesting to show that the proposed method is very similar to singular value decomposition on the scatter matrix but with sparsity constraint on the right singular value matrix or eigen-decomposition on the scatter matrix with sparse manner. Experimental results on some tensor datasets indicate that JTFA outperforms some well-known tensor feature extraction and selection algorithms. PMID:26470058

  15. Low-tubal-rank tensor completion using alternating minimization

    NASA Astrophysics Data System (ADS)

    Liu, Xiao-Yang; Aeron, Shuchin; Aggarwal, Vaneet; Wang, Xiaodong

    2016-05-01

    The low-tubal-rank tensors have been recently proposed to model real-world multidimensional data. In this paper, we study the low-tubal-rank tensor completion problem, i.e., to recover a third-order tensor by observing a subset of elements selected uniform at random. We propose a fast iterative algorithm, called Tubal-Alt-Min, that is inspired by similar approach for low rank matrix completion. The unknown low-tubal-rank tensor is parameterized as the product of two much smaller tensors with the low-tubal-rank property being automatically incorporated, and Tubal-Alt-Min alternates between estimating those two tensors using tensor least squares minimization. We note that the tensor least squares minimization is different from its counterpart and nontrivial, and this paper gives a routine to carry out this operation. Further, on both synthetic data and real-world video data, evaluation results show that compared with the tensor nuclear norm minimization, the proposed algorithm improves the recovery error by orders of magnitude with smaller running time for higher sampling rates.

  16. On the geometry of mixed states and the Fisher information tensor

    NASA Astrophysics Data System (ADS)

    Contreras, I.; Ercolessi, E.; Schiavina, M.

    2016-06-01

    In this paper, we will review the co-adjoint orbit formulation of finite dimensional quantum mechanics, and in this framework, we will interpret the notion of quantum Fisher information index (and metric). Following previous work of part of the authors, who introduced the definition of Fisher information tensor, we will show how its antisymmetric part is the pullback of the natural Kostant-Kirillov-Souriau symplectic form along some natural diffeomorphism. In order to do this, we will need to understand the symmetric logarithmic derivative as a proper 1-form, settling the issues about its very definition and explicit computation. Moreover, the fibration of co-adjoint orbits, seen as spaces of mixed states, is also discussed.

  17. A general theory of linear cosmological perturbations: scalar-tensor and vector-tensor theories

    NASA Astrophysics Data System (ADS)

    Lagos, Macarena; Baker, Tessa; Ferreira, Pedro G.; Noller, Johannes

    2016-08-01

    We present a method for parametrizing linear cosmological perturbations of theories of gravity, around homogeneous and isotropic backgrounds. The method is sufficiently general and systematic that it can be applied to theories with any degrees of freedom (DoFs) and arbitrary gauge symmetries. In this paper, we focus on scalar-tensor and vector-tensor theories, invariant under linear coordinate transformations. In the case of scalar-tensor theories, we use our framework to recover the simple parametrizations of linearized Horndeski and ``Beyond Horndeski'' theories, and also find higher-derivative corrections. In the case of vector-tensor theories, we first construct the most general quadratic action for perturbations that leads to second-order equations of motion, which propagates two scalar DoFs. Then we specialize to the case in which the vector field is time-like (à la Einstein-Aether gravity), where the theory only propagates one scalar DoF. As a result, we identify the complete forms of the quadratic actions for perturbations, and the number of free parameters that need to be defined, to cosmologically characterize these two broad classes of theories.

  18. Application of modern tensor calculus to engineered domain structures. 2. Tensor distinction of domain states.

    PubMed

    Kopský, Vojtech

    2006-03-01

    The theory of domain states is reviewed as a prerequisite for consideration of tensorial distinction of domain states. It is then shown that the parameters of the first domain in a ferroic phase transition from a set of isomorphic groups of the same oriented Laue class can be systematically and suitably represented in terms of typical variables. On replacing these variables by actual tensor components according to the previous paper, we can reveal the tensorial parameters associated with each particular symmetry descent. Parameters are distinguished by the ireps to which they belong and this can be used to determine which of them are the principal parameters that distinguish all domain states, in contrast to secondary parameters which are common to several domain states. In general, the parameters are expressed as the covariant components of the tensors. A general procedure is described which is designed to transform the results to Cartesian components. It consists of two parts: the first, called the labelling of covariants, and its inverse, called the conversion equations. Transformation of parameters from the first domain state to other states is now reduced to irreducible subspaces whose maximal dimension is three in contrast with higher dimensions of tensor spaces. With this method, we can explicitly calculate tensor parameters for all domain states. To find the distinction of pairs of domain states, it is suitable to use the concept of the twinning group which is briefly described. PMID:16489243

  19. Geometry of Quantum States

    NASA Astrophysics Data System (ADS)

    Bengtsson, Ingemar; Zyczkowski, Karol

    2006-05-01

    Quantum information theory is at the frontiers of physics, mathematics and information science, offering a variety of solutions that are impossible using classical theory. This book provides an introduction to the key concepts used in processing quantum information and reveals that quantum mechanics is a generalisation of classical probability theory. After a gentle introduction to the necessary mathematics the authors describe the geometry of quantum state spaces. Focusing on finite dimensional Hilbert spaces, they discuss the statistical distance measures and entropies used in quantum theory. The final part of the book is devoted to quantum entanglement - a non-intuitive phenomenon discovered by Schrödinger, which has become a key resource for quantum computation. This richly-illustrated book is useful to a broad audience of graduates and researchers interested in quantum information theory. Exercises follow each chapter, with hints and answers supplied. The first book to focus on the geometry of quantum states Stresses the similarities and differences between classical and quantum theory Uses a non-technical style and numerous figures to make the book accessible to non-specialists

  20. Direct solution of the Chemical Master Equation using quantized tensor trains.

    PubMed

    Kazeev, Vladimir; Khammash, Mustafa; Nip, Michael; Schwab, Christoph

    2014-03-01

    The Chemical Master Equation (CME) is a cornerstone of stochastic analysis and simulation of models of biochemical reaction networks. Yet direct solutions of the CME have remained elusive. Although several approaches overcome the infinite dimensional nature of the CME through projections or other means, a common feature of proposed approaches is their susceptibility to the curse of dimensionality, i.e. the exponential growth in memory and computational requirements in the number of problem dimensions. We present a novel approach that has the potential to "lift" this curse of dimensionality. The approach is based on the use of the recently proposed Quantized Tensor Train (QTT) formatted numerical linear algebra for the low parametric, numerical representation of tensors. The QTT decomposition admits both, algorithms for basic tensor arithmetics with complexity scaling linearly in the dimension (number of species) and sub-linearly in the mode size (maximum copy number), and a numerical tensor rounding procedure which is stable and quasi-optimal. We show how the CME can be represented in QTT format, then use the exponentially-converging hp-discontinuous Galerkin discretization in time to reduce the CME evolution problem to a set of QTT-structured linear equations to be solved at each time step using an algorithm based on Density Matrix Renormalization Group (DMRG) methods from quantum chemistry. Our method automatically adapts the "basis" of the solution at every time step guaranteeing that it is large enough to capture the dynamics of interest but no larger than necessary, as this would increase the computational complexity. Our approach is demonstrated by applying it to three different examples from systems biology: independent birth-death process, an example of enzymatic futile cycle, and a stochastic switch model. The numerical results on these examples demonstrate that the proposed QTT method achieves dramatic speedups and several orders of magnitude storage

  1. Direct solution of the Chemical Master Equation using quantized tensor trains.

    PubMed

    Kazeev, Vladimir; Khammash, Mustafa; Nip, Michael; Schwab, Christoph

    2014-03-01

    The Chemical Master Equation (CME) is a cornerstone of stochastic analysis and simulation of models of biochemical reaction networks. Yet direct solutions of the CME have remained elusive. Although several approaches overcome the infinite dimensional nature of the CME through projections or other means, a common feature of proposed approaches is their susceptibility to the curse of dimensionality, i.e. the exponential growth in memory and computational requirements in the number of problem dimensions. We present a novel approach that has the potential to "lift" this curse of dimensionality. The approach is based on the use of the recently proposed Quantized Tensor Train (QTT) formatted numerical linear algebra for the low parametric, numerical representation of tensors. The QTT decomposition admits both, algorithms for basic tensor arithmetics with complexity scaling linearly in the dimension (number of species) and sub-linearly in the mode size (maximum copy number), and a numerical tensor rounding procedure which is stable and quasi-optimal. We show how the CME can be represented in QTT format, then use the exponentially-converging hp-discontinuous Galerkin discretization in time to reduce the CME evolution problem to a set of QTT-structured linear equations to be solved at each time step using an algorithm based on Density Matrix Renormalization Group (DMRG) methods from quantum chemistry. Our method automatically adapts the "basis" of the solution at every time step guaranteeing that it is large enough to capture the dynamics of interest but no larger than necessary, as this would increase the computational complexity. Our approach is demonstrated by applying it to three different examples from systems biology: independent birth-death process, an example of enzymatic futile cycle, and a stochastic switch model. The numerical results on these examples demonstrate that the proposed QTT method achieves dramatic speedups and several orders of magnitude storage

  2. Phase space quantum mechanics

    NASA Astrophysics Data System (ADS)

    Błaszak, Maciej; Domański, Ziemowit

    2012-02-01

    This paper develops an alternative formulation of quantum mechanics known as the phase space quantum mechanics or deformation quantization. It is shown that the quantization naturally arises as an appropriate deformation of the classical Hamiltonian mechanics. More precisely, the deformation of the point-wise product of observables to an appropriate noncommutative ⋆-product and the deformation of the Poisson bracket to an appropriate Lie bracket are the key elements in introducing the quantization of classical Hamiltonian systems. The formalism of the phase space quantum mechanics is presented in a very systematic way for the case of any smooth Hamiltonian function and for a very wide class of deformations. The considered class of deformations and the corresponding ⋆-products contains as a special case all deformations which can be found in the literature devoted to the subject of the phase space quantum mechanics. Fundamental properties of ⋆-products of observables, associated with the considered deformations are presented as well. Moreover, a space of states containing all admissible states is introduced, where the admissible states are appropriate pseudo-probability distributions defined on the phase space. It is proved that the space of states is endowed with a structure of a Hilbert algebra with respect to the ⋆-multiplication. The most important result of the paper shows that developed formalism is more fundamental than the axiomatic ordinary quantum mechanics which appears in the presented approach as the intrinsic element of the general formalism. The equivalence of two formulations of quantum mechanics is proved by observing that the Wigner-Moyal transform has all properties of the tensor product. This observation allows writing many previous results found in the literature in a transparent way, from which the equivalence of the two formulations of quantum mechanics follows naturally. In addition, examples of a free particle and a simple harmonic

  3. Quantum computing

    PubMed Central

    Li, Shu-Shen; Long, Gui-Lu; Bai, Feng-Shan; Feng, Song-Lin; Zheng, Hou-Zhi

    2001-01-01

    Quantum computing is a quickly growing research field. This article introduces the basic concepts of quantum computing, recent developments in quantum searching, and decoherence in a possible quantum dot realization. PMID:11562459

  4. Consistent cosmic microwave background spectra from quantum depletion

    SciTech Connect

    Casadio, Roberto; Orlandi, Alessio; Kühnel, Florian E-mail: florian.kuhnel@fysik.su.se

    2015-09-01

    Following a new quantum cosmological model proposed by Dvali and Gomez, we quantitatively investigate possible modifications to the Hubble parameter and following corrections to the cosmic microwave background spectrum. In this model, scalar and tensor perturbations are generated by the quantum depletion of the background inflaton and graviton condensate respectively. We show how the inflaton mass affects the power spectra and the tensor-to-scalar ratio. Masses approaching the Planck scale would lead to strong deviations, while standard spectra are recovered for an inflaton mass much smaller than the Planck mass.

  5. Moment tensor inversion of ground motion from mining-induced earthquakes, Trail Mountain, Utah

    USGS Publications Warehouse

    Fletcher, Joe B.; McGarr, A.

    2005-01-01

    A seismic network was operated in the vicinity of the Trail Mountain mine, central Utah, from the summer of 2000 to the spring of 2001 to investigate the seismic hazard to a local dam from mining-induced events that we expect to be triggered by future coal mining in this area. In support of efforts to develop groundmotion prediction relations for this situation, we inverted ground-motion recordings for six mining-induced events to determine seismic moment tensors and then to estimate moment magnitudes M for comparison with the network coda magnitudes Mc. Six components of the tensor were determined, for an assumed point source, following the inversion method of McGarr (1992a), which uses key measurements of amplitude from obvious features of the displacement waveforms. When the resulting moment tensors were decomposed into implosive and deviatoric components, we found that four of the six events showed a substantial volume reduction, presumably due to coseismic closure of the adjacent mine openings. For these four events, the volume reduction ranges from 27% to 55% of the shear component (fault area times average slip). Radiated seismic energy, computed from attenuation-corrected body-wave spectra, ranged from 2.4 ?? 105 to 2.4 ?? 106 J for events with M from 1.3 to 1.8, yielding apparent stresses from 0.02 to 0.06 MPa. The energy released for each event, approximated as the product of volume reduction and overburden stress, when compared with the corresponding seismic energies, revealed seismic efficiencies ranging from 0.5% to 7%. The low apparent stresses are consistent with the shallow focal depths of 0.2 to 0.6 km and rupture in a low stress/low strength regime compared with typical earthquake source regions at midcrustal depths.

  6. Topological transitions from multipartite entanglement with tensor networks: a procedure for sharper and faster characterization.

    PubMed

    Orús, Román; Wei, Tzu-Chieh; Buerschaper, Oliver; García-Saez, Artur

    2014-12-19

    Topological order in two-dimensional (2D) quantum matter can be determined by the topological contribution to the entanglement Rényi entropies. However, when close to a quantum phase transition, its calculation becomes cumbersome. Here, we show how topological phase transitions in 2D systems can be much better assessed by multipartite entanglement, as measured by the topological geometric entanglement of blocks. Specifically, we present an efficient tensor network algorithm based on projected entangled pair states to compute this quantity for a torus partitioned into cylinders and then use this method to find sharp evidence of topological phase transitions in 2D systems with a string-tension perturbation. When compared to tensor network methods for Rényi entropies, our approach produces almost perfect accuracies close to criticality and, additionally, is orders of magnitude faster. The method can be adapted to deal with any topological state of the system, including minimally entangled ground states. It also allows us to extract the critical exponent of the correlation length and shows that there is no continuous entanglement loss along renormalization group flows in topological phases.

  7. Tensor networks and the numerical renormalization group

    NASA Astrophysics Data System (ADS)

    Weichselbaum, Andreas

    2012-12-01

    The full-density-matrix numerical renormalization group has evolved as a systematic and transparent setting for the calculation of thermodynamical quantities at arbitrary temperatures within the numerical renormalization group (NRG) framework. It directly evaluates the relevant Lehmann representations based on the complete basis sets introduced by Anders and Schiller [Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.95.196801 95, 196801 (2005)]. In addition, specific attention is given to the possible feedback from low-energy physics to high energies by the explicit and careful construction of the full thermal density matrix, naturally generated over a distribution of energy shells. Specific examples are given in terms of spectral functions (fdmNRG), time-dependent NRG (tdmNRG), Fermi-golden-rule calculations (fgrNRG) as well as the calculation of plain thermodynamic expectation values. Furthermore, based on the very fact that, by its iterative nature, the NRG eigenstates are naturally described in terms of matrix product states, the language of tensor networks has proven enormously convenient in the description of the underlying algorithmic procedures. This paper therefore also provides a detailed introduction and discussion of the prototypical NRG calculations in terms of their corresponding tensor networks.

  8. Energy-momentum tensor of bouncing gravitons

    SciTech Connect

    Iofa, Mikhail Z.

    2015-07-01

    In models of the Universe with extra dimensions gravity propagates in the whole space-time. Graviton production by matter on the brane is significant in the early hot Universe. In a model of 3-brane with matter embedded in 5D space-time conditions for gravitons emitted from the brane to the bulk to return back to the brane are found. For a given 5-momentum of graviton falling back to the brane the interval between the times of emission and return to the brane is calculated. A method to calculate contribution to the energy-momentum tensor from multiple graviton bouncings is developed. Explicit expressions for contributions to the energy-momentum tensor of gravitons which have made one, two and three bounces are obtained and their magnitudes are numerically calculated. These expressions are used to solve the evolution equation for dark radiation. A relation connecting reheating temperature and the scale of extra dimension is obtained. For the reheating temperature T{sub R}∼ 10{sup 6} GeV we estimate the scale of extra dimension μ to be of order 10{sup −9} GeV (μ{sup −1}∼ 10{sup −5} cm)

  9. Energy-momentum tensor of bouncing gravitons

    SciTech Connect

    Iofa, Mikhail Z.

    2015-07-14

    In models of the Universe with extra dimensions gravity propagates in the whole space-time. Graviton production by matter on the brane is significant in the early hot Universe. In a model of 3-brane with matter embedded in 5D space-time conditions for gravitons emitted from the brane to the bulk to return back to the brane are found. For a given 5-momentum of graviton falling back to the brane the interval between the times of emission and return to the brane is calculated. A method to calculate contribution to the energy-momentum tensor from multiple graviton bouncings is developed. Explicit expressions for contributions to the energy-momentum tensor of gravitons which have made one, two and three bounces are obtained and their magnitudes are numerically calculated. These expressions are used to solve the evolution equation for dark radiation. A relation connecting reheating temperature and the scale of extra dimension is obtained. For the reheating temperature T{sub R}∼10{sup 6} GeV we estimate the scale of extra dimension μ to be of order 10{sup −9} GeV (μ{sup −1}∼10{sup −5} cm)

  10. Interactive Volume Rendering of Diffusion Tensor Data

    SciTech Connect

    Hlawitschka, Mario; Weber, Gunther; Anwander, Alfred; Carmichael, Owen; Hamann, Bernd; Scheuermann, Gerik

    2007-03-30

    As 3D volumetric images of the human body become an increasingly crucial source of information for the diagnosis and treatment of a broad variety of medical conditions, advanced techniques that allow clinicians to efficiently and clearly visualize volumetric images become increasingly important. Interaction has proven to be a key concept in analysis of medical images because static images of 3D data are prone to artifacts and misunderstanding of depth. Furthermore, fading out clinically irrelevant aspects of the image while preserving contextual anatomical landmarks helps medical doctors to focus on important parts of the images without becoming disoriented. Our goal was to develop a tool that unifies interactive manipulation and context preserving visualization of medical images with a special focus on diffusion tensor imaging (DTI) data. At each image voxel, DTI provides a 3 x 3 tensor whose entries represent the 3D statistical properties of water diffusion locally. Water motion that is preferential to specific spatial directions suggests structural organization of the underlying biological tissue; in particular, in the human brain, the naturally occuring diffusion of water in the axon portion of neurons is predominantly anisotropic along the longitudinal direction of the elongated, fiber-like axons [MMM+02]. This property has made DTI an emerging source of information about the structural integrity of axons and axonal connectivity between brain regions, both of which are thought to be disrupted in a broad range of medical disorders including multiple sclerosis, cerebrovascular disease, and autism [Mos02, FCI+01, JLH+99, BGKM+04, BJB+03].

  11. Stability of Horndeski vector-tensor interactions

    SciTech Connect

    Jiménez, Jose Beltrán; Durrer, Ruth; Heisenberg, Lavinia; Thorsrud, Mikjel E-mail: ruth.durrer@unige.ch E-mail: mikjel.thorsrud@astro.uio.no

    2013-10-01

    We study the Horndeski vector-tensor theory that leads to second order equations of motion and contains a non-minimally coupled abelian gauge vector field. This theory is remarkably simple and consists of only 2 terms for the vector field, namely: the standard Maxwell kinetic term and a coupling to the dual Riemann tensor. Furthermore, the vector sector respects the U(1) gauge symmetry and the theory contains only one free parameter, M{sup 2}, that controls the strength of the non-minimal coupling. We explore the theory in a de Sitter spacetime and study the presence of instabilities and show that it corresponds to an attractor solution in the presence of the vector field. We also investigate the cosmological evolution and stability of perturbations in a general FLRW spacetime. We find that a sufficient condition for the absence of ghosts is M{sup 2} > 0. Moreover, we study further constraints coming from imposing the absence of Laplacian instabilities. Finally, we study the stability of the theory in static and spherically symmetric backgrounds (in particular, Schwarzschild and Reissner-Nordström-de Sitter). We find that the theory, quite generally, do have ghosts or Laplacian instabilities in regions of spacetime where the non-minimal interaction dominates over the Maxwell term. We also calculate the propagation speed in these spacetimes and show that superluminality is a quite generic phenomenon in this theory.

  12. Tensor discriminant color space for face recognition.

    PubMed

    Wang, Su-Jing; Yang, Jian; Zhang, Na; Zhou, Chun-Guang

    2011-09-01

    Recent research efforts reveal that color may provide useful information for face recognition. For different visual tasks, the choice of a color space is generally different. How can a color space be sought for the specific face recognition problem? To address this problem, this paper represents a color image as a third-order tensor and presents the tensor discriminant color space (TDCS) model. The model can keep the underlying spatial structure of color images. With the definition of n-mode between-class scatter matrices and within-class scatter matrices, TDCS constructs an iterative procedure to obtain one color space transformation matrix and two discriminant projection matrices by maximizing the ratio of these two scatter matrices. The experiments are conducted on two color face databases, AR and Georgia Tech face databases, and the results show that both the performance and the efficiency of the proposed method are better than those of the state-of-the-art color image discriminant model, which involve one color space transformation matrix and one discriminant projection matrix, specifically in a complicated face database with various pose variations.

  13. Local thermodynamical equilibrium and the frame for a quantum relativistic fluid

    NASA Astrophysics Data System (ADS)

    Becattini, Francesco; Bucciantini, Leda; Grossi, Eduardo; Tinti, Leonardo

    2015-05-01

    We discuss the concept of local thermodynamical equilibrium in relativistic hydrodynamics in flat spacetime in a quantum statistical framework without an underlying kinetic description, suitable for strongly interacting fluids. We show that the appropriate definition of local equilibrium naturally leads to the introduction of a relativistic hydrodynamical frame in which the four-velocity vector is the one of a relativistic thermometer at equilibrium with the fluid, parallel to the inverse temperature four-vector , which then becomes a primary quantity. We show that this frame is the most appropriate for the expansion of the stress-energy tensor from local thermodynamical equilibrium and that therein the local laws of thermodynamics take on their simplest form. We discuss the difference between the frame and Landau frame and present an instance where they differ.

  14. Relativistic geometric quantum phases from the Lorentz symmetry violation effects in the CPT-even gauge sector of Standard Model Extension

    NASA Astrophysics Data System (ADS)

    Bakke, K.; Belich, H.

    2015-11-01

    We discuss the appearance of geometric quantum phases for a Dirac neutral particle in the context of relativistic quantum mechanics based on possible scenarios of the Lorentz symmetry violation tensor background in the CPT-even gauge sector of Standard Model Extension. We assume that the Lorentz symmetry breaking is determined by a tensor background given by (KF)μναβ, then, relativistic analogues of the Anandan quantum phase [J. Anandan, Phys. Lett. A 138, 347 (1989)] are obtained based on the parity-even and parity-odd sectors of the tensor (KF)μναβ.

  15. Maxwell stress on a small dielectric sphere in a dielectric

    NASA Astrophysics Data System (ADS)

    Datsyuk, Vitaly V.; Pavlyniuk, Oleg R.

    2015-02-01

    Electrically induced normal pressure and tangential stress at the surface of a small dielectric sphere (or cavity) in a dielectric are calculated using the Minkowski, Einstein-Laub, Abraham, and Lorentz forms of the Maxwell stress tensor. Only the Lorentz tensor is in agreement with the following observations: (1) A spherical cavity in a dielectric transforms into a sharp-edge plate perpendicular to the electric field; (2) a liquid drop placed in a medium with a slightly lower refractive index is stretched along the electric field; and (3) there is a torque on a small birefringent sphere. These phenomena cannot be explained by the conventional theory using the Minkowski stress tensor. For example, the Minkowski stress tensor predicts lateral compression of a spherical cavity in a dielectric.

  16. Self-consistency conditions for elementary Reynolds stress closures

    NASA Astrophysics Data System (ADS)

    Rubinstein, Robert

    2016-02-01

    This paper summarizes the analytical representation of the correlation tensor in homogeneous anisotropic turbulence and sketches an application to Reynolds stress transport turbulence models. It is shown that the analytical approach can address some of the limitations of conventional modeling.

  17. Tensor3D: A computer graphics program to simulate 3D real-time deformation and visualization of geometric bodies

    NASA Astrophysics Data System (ADS)

    Pallozzi Lavorante, Luca; Dirk Ebert, Hans

    2008-07-01

    Tensor3D is a geometric modeling program with the capacity to simulate and visualize in real-time the deformation, specified through a tensor matrix and applied to triangulated models representing geological bodies. 3D visualization allows the study of deformational processes that are traditionally conducted in 2D, such as simple and pure shears. Besides geometric objects that are immediately available in the program window, the program can read other models from disk, thus being able to import objects created with different open-source or proprietary programs. A strain ellipsoid and a bounding box are simultaneously shown and instantly deformed with the main object. The principal axes of strain are visualized as well to provide graphical information about the orientation of the tensor's normal components. The deformed models can also be saved, retrieved later and deformed again, in order to study different steps of progressive strain, or to make this data available to other programs. The shape of stress ellipsoids and the corresponding Mohr circles defined by any stress tensor can also be represented. The application was written using the Visualization ToolKit, a powerful scientific visualization library in the public domain. This development choice, allied to the use of the Tcl/Tk programming language, which is independent on the host computational platform, makes the program a useful tool for the study of geometric deformations directly in three dimensions in teaching as well as research activities.

  18. Quantum information-geometry of dissipative quantum phase transitions.

    PubMed

    Banchi, Leonardo; Giorda, Paolo; Zanardi, Paolo

    2014-02-01

    A general framework for analyzing the recently discovered phase transitions in the steady state of dissipation-driven open quantum systems is still lacking. To fill this gap, we extend the so-called fidelity approach to quantum phase transitions to open systems whose steady state is a Gaussian fermionic state. We endow the manifold of correlation matrices of steady states with a metric tensor g measuring the distinguishability distance between solutions corresponding to a different set of control parameters. The phase diagram can then be mapped out in terms of the scaling behavior of g and connections with the Liouvillean gap and the model correlation functions unveiled. We argue that the fidelity approach, thanks to its differential-geometric and information-theoretic nature, provides insights into dissipative quantum critical phenomena as well as a general and powerful strategy to explore them. PMID:25353417

  19. Quantum information-geometry of dissipative quantum phase transitions.

    PubMed

    Banchi, Leonardo; Giorda, Paolo; Zanardi, Paolo

    2014-02-01

    A general framework for analyzing the recently discovered phase transitions in the steady state of dissipation-driven open quantum systems is still lacking. To fill this gap, we extend the so-called fidelity approach to quantum phase transitions to open systems whose steady state is a Gaussian fermionic state. We endow the manifold of correlation matrices of steady states with a metric tensor g measuring the distinguishability distance between solutions corresponding to a different set of control parameters. The phase diagram can then be mapped out in terms of the scaling behavior of g and connections with the Liouvillean gap and the model correlation functions unveiled. We argue that the fidelity approach, thanks to its differential-geometric and information-theoretic nature, provides insights into dissipative quantum critical phenomena as well as a general and powerful strategy to explore them.

  20. Quantum Fluctuations and Thermodynamic Processes in the Presence of Closed Timelike Curves

    NASA Astrophysics Data System (ADS)

    Tanaka, Tsunefumi

    1997-10-01

    A closed timelike curve (CTC) is a closed loop in spacetime whose tangent vector is everywhere timelike. A spacetime which contains CTC's will allow time travel. One of these spacetimes is Grant space. It can be constructed from Minkowski space by imposing periodic boundary conditions in spatial directions and making the boundaries move toward each other. If Hawking's chronology protection conjecture is correct, there must be a physical mechanism preventing the formation of CTC's. Currently the most promising candidate for the chronology protection mechanism is the back reaction of the metric to quantum vacuum fluctuations. In this thesis the quantum fluctuations for a massive scalar field, a self-interacting field, and for a field at nonzero temperature are calculated in Grant space. The stress-energy tensor is found to remain finite everywhere in Grant space for the massive scalar field with sufficiently large field mass. Otherwise it diverges on chronology horizons like the stress-energy tensor for a massless scalar field. If CTC's exist they will have profound effects on physical processes. Causality can be protected even in the presence of CTC's if the self-consistency condition is imposed on all processes. Simple classical thermodynamic processes of a box filled with ideal gas in the presence of CTC's are studied. If a system of boxes is closed, its state does not change as it travels through a region of spacetime with CTC's. But if the system is open, the final state will depend on the interaction with the environment. The second law of thermodynamics is shown to hold for both closed and open systems. A similar problem is investigated at a statistical level for a gas consisting of multiple selves of a single particle in a spacetime with CTC's.

  1. Quantum Strategies and Local Operations

    NASA Astrophysics Data System (ADS)

    Gutoski, Gus

    2010-02-01

    This thesis is divided into two parts. In Part I we introduce a new formalism for quantum strategies, which specify the actions of one party in any multi-party interaction involving the exchange of multiple quantum messages among the parties. This formalism associates with each strategy a single positive semidefinite operator acting only upon the tensor product of the input and output message spaces for the strategy. We establish three fundamental properties of this new representation for quantum strategies and we list several applications, including a quantum version of von Neumann's celebrated 1928 Min-Max Theorem for zero-sum games and an efficient algorithm for computing the value of such a game. In Part II we establish several properties of a class of quantum operations that can be implemented locally with shared quantum entanglement or classical randomness. In particular, we establish the existence of a ball of local operations with shared randomness lying within the space spanned by the no-signaling operations and centred at the completely noisy channel. The existence of this ball is employed to prove that the weak membership problem for local operations with shared entanglement is strongly NP-hard. We also provide characterizations of local operations in terms of linear functionals that are positive and "completely" positive on a certain cone of Hermitian operators, under a natural notion of complete positivity appropriate to that cone. We end the thesis with a discussion of the properties of no-signaling quantum operations.

  2. Exploring the tensor networks/AdS correspondence

    NASA Astrophysics Data System (ADS)

    Bhattacharyya, Arpan; Gao, Zhe-Shen; Hung, Ling-Yan; Liu, Si-Nong

    2016-08-01

    In this paper we study the recently proposed tensor networks/AdS correspondence. We found that the Coxeter group is a useful tool to describe tensor networks in a negatively curved space. Studying generic tensor network populated by perfect tensors, we find that the physical wave function generically do not admit any connected correlation functions of local operators. To remedy the problem, we assume that wavefunctions admitting such semi-classical gravitational interpretation are composed of tensors close to, but not exactly perfect tensors. Computing corrections to the connected two point correlation functions, we find that the leading contribution is given by structures related to geodesics connecting the operators inserted at the boundary physical dofs. Such considerations admit generalizations at least to three point functions. This is highly suggestive of the emergence of the analogues of Witten diagrams in the tensor network. The perturbations alone however do not give the right entanglement spectrum. Using the Coxeter construction, we also constructed the tensor network counterpart of the BTZ black hole, by orbifolding the discrete lattice on which the network resides. We found that the construction naturally reproduces some of the salient features of the BTZ black hole, such as the appearance of RT surfaces that could wrap the horizon, depending on the size of the entanglement region A.

  3. Black holes with surrounding matter in scalar-tensor theories.

    PubMed

    Cardoso, Vitor; Carucci, Isabella P; Pani, Paolo; Sotiriou, Thomas P

    2013-09-13

    We uncover two mechanisms that can render Kerr black holes unstable in scalar-tensor gravity, both associated with the presence of matter in the vicinity of the black hole and the fact that this introduces an effective mass for the scalar. Our results highlight the importance of understanding the structure of spacetime in realistic, astrophysical black holes in scalar-tensor theories.

  4. PREFACE: 1st Tensor Polarized Solid Target Workshop

    NASA Astrophysics Data System (ADS)

    2014-10-01

    These are the proceedings of the first Tensor Spin Observables Workshop that was held in March 2014 at the Thomas Jefferson National Accelerator Facility in Newport News, Virginia. The conference was convened to study the physics that can be done with the recently approved E12-13-011 polarized target. A tensor polarized target holds the potential of initiating a new generation of tensor spin physics at Jefferson Lab. Experiments which utilize tensor polarized targets can help clarify how nuclear properties arise from partonic degrees of freedom, provide unique insight into short-range correlations and quark angular momentum, and also help pin down the polarization of the quark sea with a future Electron Ion Collider. This three day workshop was focused on tensor spin observables and the associated tensor target development. The workshop goals were to stimulate progress in the theoretical treatment of polarized spin-1 systems, foster the development of new proposals, and to reach a consensus on the optimal polarized target configuration for the tensor spin program. The workshop was sponsored by the University of New Hampshire, the Jefferson Science Associates, Florida International University, and Jefferson Lab. It was organized by Karl Slifer (chair), Patricia Solvignon, and Elena Long of the University of New Hampshire, Douglas Higinbotham and Christopher Keith of Jefferson Lab, and Misak Sargsian of the Florida International University. These proceedings represent the effort put forth by the community to begin exploring the possibilities that a high-luminosity, high-tensor polarized solid target can offer.

  5. MATLAB tensor classes for fast algorithm prototyping : source code.

    SciTech Connect

    Bader, Brett William; Kolda, Tamara Gibson

    2004-10-01

    We present the source code for three MATLAB classes for manipulating tensors in order to allow fast algorithm prototyping. A tensor is a multidimensional or Nway array. This is a supplementary report; details on using this code are provided separately in SAND-XXXX.

  6. The Kummer tensor density in electrodynamics and in gravity

    SciTech Connect

    Baekler, Peter; Favaro, Alberto; Itin, Yakov; Hehl, Friedrich W.

    2014-10-15

    Guided by results in the premetric electrodynamics of local and linear media, we introduce on 4-dimensional spacetime the new abstract notion of a Kummer tensor density of rank four, K{sup ijkl}. This tensor density is, by definition, a cubic algebraic functional of a tensor density of rank four T{sup ijkl}, which is antisymmetric in its first two and its last two indices: T{sup ijkl}=−T{sup jikl}=−T{sup ijlk}. Thus, K∼T{sup 3}, see Eq. (46). (i) If T is identified with the electromagnetic response tensor of local and linear media, the Kummer tensor density encompasses the generalized Fresnel wave surfaces for propagating light. In the reversible case, the wave surfaces turn out to be Kummer surfaces as defined in algebraic geometry (Bateman 1910). (ii) If T is identified with the curvature tensor R{sup ijkl} of a Riemann–Cartan spacetime, then K∼R{sup 3} and, in the special case of general relativity, K reduces to the Kummer tensor of Zund (1969). This K is related to the principal null directions of the curvature. We discuss the properties of the general Kummer tensor density. In particular, we decompose K irreducibly under the 4-dimensional linear group GL(4,R) and, subsequently, under the Lorentz group SO(1,3)

  7. Tensor spin observables and spin stucture at low Q2

    SciTech Connect

    Slifer, Karl J.

    2015-04-01

    We discuss recent spin structure results from Jefferson Lab, and outline an emerging program to study tensor spin observables using solid deuteron targets. These new experiments open the potential to study hidden color, the tensor nature of short range correlations, and to probe for exotic gluonic states.

  8. The Kummer tensor density in electrodynamics and in gravity

    NASA Astrophysics Data System (ADS)

    Baekler, Peter; Favaro, Alberto; Itin, Yakov; Hehl, Friedrich W.

    2014-10-01

    Guided by results in the premetric electrodynamics of local and linear media, we introduce on 4-dimensional spacetime the new abstract notion of a Kummer tensor density of rank four, K. This tensor density is, by definition, a cubic algebraic functional of a tensor density of rank four T, which is antisymmetric in its first two and its last two indices: T=-T=-T. Thus, K∼T3, see Eq. (46). (i) If T is identified with the electromagnetic response tensor of local and linear media, the Kummer tensor density encompasses the generalized Fresnel wave surfaces for propagating light. In the reversible case, the wave surfaces turn out to be Kummer surfaces as defined in algebraic geometry (Bateman 1910). (ii) If T is identified with the curvature tensor R of a Riemann-Cartan spacetime, then K∼R3 and, in the special case of general relativity, K reduces to the Kummer tensor of Zund (1969). This K is related to the principal null directions of the curvature. We discuss the properties of the general Kummer tensor density. In particular, we decompose K irreducibly under the 4-dimensional linear group GL(4,R) and, subsequently, under the Lorentz group SO(1,3).

  9. Quantum Mechanics

    NASA Astrophysics Data System (ADS)

    Auletta, Gennaro; Fortunato, Mauro; Parisi, Giorgio

    2014-01-01

    Introduction; Part I. Basic Features of Quantum Mechanics: 1. From classical mechanics to quantum mechanics; 2. Quantum observable and states; 3. Quantum dynamics; 4. Examples of quantum dynamics; 5. Density matrix; Part II. More Advanced Topics: 6. Angular momentum and spin; 7. Identical particles; 8. Symmetries and conservation laws; 9. The measurement problem; Part III. Matter and Light: 10. Perturbations and approximation methods; 11. Hydrogen and helium atoms; 12. Hydrogen molecular ion; 13. Quantum optics; Part IV. Quantum Information: State and Correlations: 14. Quantum theory of open systems; 15. State measurement in quantum mechanics; 16. Entanglement: non-separability; 17. Entanglement: quantum information; References; Index.

  10. Rotating quantum states

    NASA Astrophysics Data System (ADS)

    Ambruş, Victor E.; Winstanley, Elizabeth

    2014-06-01

    We revisit the definition of rotating thermal states for scalar and fermion fields in unbounded Minkowski space-time. For scalar fields such states are ill-defined everywhere, but for fermion fields an appropriate definition of the vacuum gives thermal states regular inside the speed-of-light surface. For a massless fermion field, we derive analytic expressions for the thermal expectation values of the fermion current and stress-energy tensor. These expressions may provide qualitative insights into the behaviour of thermal rotating states on more complex space-time geometries.

  11. Permeability tensor and representative elementary volume of fractured rock masses

    NASA Astrophysics Data System (ADS)

    Rong, Guan; Peng, Jun; Wang, Xiaojiang; Liu, Guang; Hou, Di

    2013-11-01

    Based on a simulation of three-dimensional fracture networks and a superposition principle of liquid dissipation energy for fractured rock masses, a model of the fracture permeability tensor is proposed. An elastic constitutive model of rock fractures, considering fracture closure and dilation during shearing, is also proposed, based on the dilation angle of the fracture. Algorithms of flow-path searching and calculation of the effective flow coefficients for fracture networks are presented, together with a discussion on the influence of geometric parameters of the fractures (trace length, spacing, aperture, orientation and the number of fracture sets) on magnitude, anisotropy of hydraulic permeability and the size of a representative elementary volume (REV). The anisotropy of hydraulic permeability of fractured rock masses is mainly affected by orientation and the number of fracture sets, and the REV size is mainly influenced by trace length, spacing and the number of fracture sets. The results of studies on REV size and the influence of in-situ stress on hydraulic conductivity of the rock mass on the slope of Jinping-I hydropower station, China, are presented using the developed models and methods. The simulation results agreed well with the results obtained from field water-pressure measurements, with an error of less than 10 %.

  12. Non-local mean denoising in diffusion tensor space

    PubMed Central

    SU, BAIHAI; LIU, QIANG; CHEN, JIE; WU, XI

    2014-01-01

    The aim of the present study was to present a novel non-local mean (NLM) method to denoise diffusion tensor imaging (DTI) data in the tensor space. Compared with the original NLM method, which uses intensity similarity to weigh the voxel, the proposed method weighs the voxel using tensor similarity measures in the diffusion tensor space. Euclidean distance with rotational invariance, and Riemannian distance and Log-Euclidean distance with affine invariance were implemented to compare the geometric and orientation features of the diffusion tensor comprehensively. The accuracy and efficacy of the proposed novel NLM method using these three similarity measures in DTI space, along with unbiased novel NLM in diffusion-weighted image space, were compared quantitatively and qualitatively in the present study. PMID:25009599

  13. On the energy-momentum tensor in Moyal space

    NASA Astrophysics Data System (ADS)

    Balasin, Herbert; Blaschke, Daniel N.; Gieres, François; Schweda, Manfred

    2015-06-01

    We study the properties of the energy-momentum tensor of gauge fields coupled to matter in non-commutative (Moyal) space. In general, the non-commutativity affects the usual conservation law of the tensor as well as its transformation properties (gauge covariance instead of gauge invariance). It is well known that the conservation of the energy-momentum tensor can be achieved by a redefinition involving another star-product. Furthermore, for a pure gauge theory it is always possible to define a gauge invariant energy-momentum tensor by means of a Wilson line. We show that the last two procedures are incompatible with each other if couplings of gauge fields to matter fields (scalars or fermions) are considered: The gauge invariant tensor (constructed via Wilson line) does not allow for a redefinition assuring its conservation, and vice versa the introduction of another star-product does not allow for gauge invariance by means of a Wilson line.

  14. On the energy-momentum tensor in Moyal space

    SciTech Connect

    Balasin, Herbert; Blaschke, Daniel N.; Gieres, François; Schweda, Manfred

    2015-06-26

    We study the properties of the energy-momentum tensor of gauge fields coupled to matter in non-commutative (Moyal) space. In general, the non-commutativity affects the usual conservation law of the tensor as well as its transformation properties (gauge covariance instead of gauge invariance). It is known that the conservation of the energy-momentum tensor can be achieved by a redefinition involving another starproduct. Furthermore, for a pure gauge theory it is always possible to define a gauge invariant energy-momentum tensor by means of a Wilson line. We show that the latter two procedures are incompatible with each other if couplings of gauge fields to matter fields (scalars or fermions) are considered: The gauge invariant tensor (constructed via Wilson line) does not allow for a redefinition assuring its conservation, and vice-versa the introduction of another star-product does not allow for gauge invariance by means of a Wilson line.

  15. An inflationary model with small scalar and large tensor nongaussianities

    SciTech Connect

    Cook, Jessica L.; Sorbo, Lorenzo E-mail: sorbo@physics.umass.edu

    2013-11-01

    We study a model of inflation where the scalar perturbations are almost gaussian while there is sizable (equilateral) nongaussianity in the tensor sector. In this model, a rolling pseudoscalar gravitationally coupled to the inflaton amplifies the vacuum fluctuations of a vector field. The vector sources both scalar and tensor metric perturbations. Both kinds of perturbations are nongaussian, but, due to helicity conservation, the tensors have a larger amplitude, so that nongaussianity in the scalar perturbations is negligible. Moreover, the tensors produced this way are chiral. We study, in the flat sky approximation, how constraints on tensor nongaussianities affect the detectability of parity violation in the Cosmic Microwave Background. We expect the model to feature interesting patterns on nongaussianities in the polarization spectra of the CMB.

  16. Tensor scale: An analytic approach with efficient computation and applications☆

    PubMed Central

    Xu, Ziyue; Saha, Punam K.; Dasgupta, Soura

    2015-01-01

    Scale is a widely used notion in computer vision and image understanding that evolved in the form of scale-space theory where the key idea is to represent and analyze an image at various resolutions. Recently, we introduced a notion of local morphometric scale referred to as “tensor scale” using an ellipsoidal model that yields a unified representation of structure size, orientation and anisotropy. In the previous work, tensor scale was described using a 2-D algorithmic approach and a precise analytic definition was missing. Also, the application of tensor scale in 3-D using the previous framework is not practical due to high computational complexity. In this paper, an analytic definition of tensor scale is formulated for n-dimensional (n-D) images that captures local structure size, orientation and anisotropy. Also, an efficient computational solution in 2- and 3-D using several novel differential geometric approaches is presented and the accuracy of results is experimentally examined. Also, a matrix representation of tensor scale is derived facilitating several operations including tensor field smoothing to capture larger contextual knowledge. Finally, the applications of tensor scale in image filtering and n-linear interpolation are presented and the performance of their results is examined in comparison with respective state-of-art methods. Specifically, the performance of tensor scale based image filtering is compared with gradient and Weickert’s structure tensor based diffusive filtering algorithms. Also, the performance of tensor scale based n-linear interpolation is evaluated in comparison with standard n-linear and windowed-sinc interpolation methods. PMID:26236148

  17. A hitchhiker's guide to diffusion tensor imaging.

    PubMed

    Soares, José M; Marques, Paulo; Alves, Victor; Sousa, Nuno

    2013-01-01

    Diffusion Tensor Imaging (DTI) studies are increasingly popular among clinicians and researchers as they provide unique insights into brain network connectivity. However, in order to optimize the use of DTI, several technical and methodological aspects must be factored in. These include decisions on: acquisition protocol, artifact handling, data quality control, reconstruction algorithm, and visualization approaches, and quantitative analysis methodology. Furthermore, the researcher and/or clinician also needs to take into account and decide on the most suited software tool(s) for each stage of the DTI analysis pipeline. Herein, we provide a straightforward hitchhiker's guide, covering all of the workflow's major stages. Ultimately, this guide will help newcomers navigate the most critical roadblocks in the analysis and further encourage the use of DTI. PMID:23486659

  18. f(R)-gravity from Killing tensors

    NASA Astrophysics Data System (ADS)

    Paliathanasis, Andronikos

    2016-04-01

    We consider f(R)-gravity in a Friedmann-Lemaître-Robertson-Walker spacetime with zero spatial curvature. We apply the Killing tensors of the minisuperspace in order to specify the functional form of f(R) and for the field equations to be invariant under Lie-Bäcklund transformations, which are linear in momentum (contact symmetries). Consequently, the field equations to admit quadratic conservation laws given by Noether’s theorem. We find three new integrable f(R)-models, for which, with the application of the conservation laws, we reduce the field equations to a system of two first-order ordinary differential equations. For each model we study the evolution of the cosmological fluid. We find that for each integrable model the cosmological fluid has an equation of state parameter, in which there is linear behavior in terms of the scale factor which describes the Chevallier, Polarski and Linder parametric dark energy model.

  19. Chiral perturbation theory with tensor sources

    SciTech Connect

    Cata, Oscar; Cata, Oscar; Mateu, Vicent

    2007-05-21

    We construct the most general chirally-invariant Lagrangian for mesons in the presence of external sources coupled to the tensor current \\bar psi sigma_mu nu psi. In order to have only even terms in the chiral expansion, we consider the new source of O(p2). With this choice, we build the even-parity effective Lagrangian up to the p6-order (NLO). While there are only 4 new terms at the p4-order, at p6-order we find 78 terms for n_f=2 and 113 terms for n_f=3. We provide a detailed discussion on the different mechanisms that ensure that our final set of operators is complete and non-redundant. We also examine the odd-parity sector, to conclude that the first operators appear at the p8-order (NNLO).

  20. A hitchhiker's guide to diffusion tensor imaging

    PubMed Central

    Soares, José M.; Marques, Paulo; Alves, Victor; Sousa, Nuno

    2012-01-01

    Diffusion Tensor Imaging (DTI) studies are increasingly popular among clinicians and researchers as they provide unique insights into brain network connectivity. However, in order to optimize the use of DTI, several technical and methodological aspects must be factored in. These include decisions on: acquisition protocol, artifact handling, data quality control, reconstruction algorithm, and visualization approaches, and quantitative analysis methodology. Furthermore, the researcher and/or clinician also needs to take into account and decide on the most suited software tool(s) for each stage of the DTI analysis pipeline. Herein, we provide a straightforward hitchhiker's guide, covering all of the workflow's major stages. Ultimately, this guide will help newcomers navigate the most critical roadblocks in the analysis and further encourage the use of DTI. PMID:23486659

  1. Tensor decomposition in potential energy surface representations.

    PubMed

    Ostrowski, Lukas; Ziegler, Benjamin; Rauhut, Guntram

    2016-09-14

    In order to reduce the operation count in vibration correlation methods, e.g., vibrational configuration interaction (VCI) theory, a tensor decomposition approach has been applied to the analytical representations of multidimensional potential energy surfaces (PESs). It is shown that a decomposition of the coefficients within the individual n-mode coupling terms in a multimode expansion of the PES is feasible and allows for convenient contractions of one-dimensional integrals with these newly determined factor matrices. Deviations in the final VCI frequencies of a set of small molecules were found to be negligible once the rank of the factors matrices is chosen appropriately. Recommendations for meaningful ranks are provided and different algorithms are discussed. PMID:27634247

  2. Electroproduction of tensor mesons in QCD

    NASA Astrophysics Data System (ADS)

    Braun, V. M.; Kivel, N.; Strohmaier, M.; Vladimirov, A. A.

    2016-06-01

    Due to multiple possible polarizations hard exclusive production of tensor mesons by virtual photons or in heavy meson decays offers interesting possibilities to study the helicity structure of the underlying short-distance process. Motivated by the first measurement of the transition form factor γ∗γ → f 2(1270) at large momentum transfers by the BELLE collaboration we present an improved QCD analysis of this reaction in the framework of collinear factorization including contributions of twist-three quark-antiquark-gluon operators and an estimate of soft end-point corrections using light-cone sum rules. The results appear to be in good agreement with the data, in particular the predicted scaling behavior is reproduced in all cases.

  3. A hitchhiker's guide to diffusion tensor imaging.

    PubMed

    Soares, José M; Marques, Paulo; Alves, Victor; Sousa, Nuno

    2013-01-01

    Diffusion Tensor Imaging (DTI) studies are increasingly popular among clinicians and researchers as they provide unique insights into brain network connectivity. However, in order to optimize the use of DTI, several technical and methodological aspects must be factored in. These include decisions on: acquisition protocol, artifact handling, data quality control, reconstruction algorithm, and visualization approaches, and quantitative analysis methodology. Furthermore, the researcher and/or clinician also needs to take into account and decide on the most suited software tool(s) for each stage of the DTI analysis pipeline. Herein, we provide a straightforward hitchhiker's guide, covering all of the workflow's major stages. Ultimately, this guide will help newcomers navigate the most critical roadblocks in the analysis and further encourage the use of DTI.

  4. Conductivity of pure graphene: Theoretical approach using the polarization tensor

    NASA Astrophysics Data System (ADS)

    Klimchitskaya, G. L.; Mostepanenko, V. M.

    2016-06-01

    We obtain analytic expressions for the conductivity of pristine (pure) graphene in the framework of the Dirac model using the polarization tensor in (2+1) dimensions defined along the real frequency axis. It is found that at both zero and nonzero temperature T the in-plane and out-of-plane conductivities of graphene are equal to each other with a high precision and essentially do not depend on the wave vector. At T =0 the conductivity of graphene is real and equal to σ0=e2/(4 ℏ ) up to small nonlocal corrections in accordance with many authors. At some fixed T ≠0 the real part of the conductivity varies between zero at low frequencies ω and σ0 for optical ω . If ω is fixed, the conductivity varies between σ0 at low T and zero at high T . The imaginary part of the conductivity of graphene is shown to depend on the ratio of ω to T . In accordance with the obtained asymptotic expressions, at fixed T it varies from infinity at ω =0 to a negative minimum value reached at some ω , and then approaches to zero with further increase of ω . At fixed ω the imaginary part of the conductivity varies from zero at T =0 , reaches a negative minimum at some T , and then goes to infinity together with T . The numerical computations of both the real and imaginary parts of the conductivity are performed. The above results are obtained in the framework of quantum electrodynamics at nonzero temperature and can be generalized for graphene samples with nonzero mass gap parameter and chemical potential.

  5. Non-classical conditional probability and the quantum no-cloning theorem

    NASA Astrophysics Data System (ADS)

    Niestegge, Gerd

    2015-09-01

    The quantum mechanical no-cloning theorem for pure states is generalized and transfered to the quantum logics with a conditional probability calculus in a rather abstract, though simple and basic fashion without relying on a tensor product construction or finite dimension as required in other generalizations.

  6. State-independent experimental test of quantum contextuality in an indivisible system.

    PubMed

    Zu, C; Wang, Y-X; Deng, D-L; Chang, X-Y; Liu, K; Hou, P-Y; Yang, H-X; Duan, L-M

    2012-10-12

    We report the first state-independent experimental test of quantum contextuality on a single photonic qutrit (three-dimensional system), based on a recent theoretical proposal [Phys. Rev. Lett. 108, 030402 (2012)]. Our experiment spotlights quantum contextuality in its most basic form, in a way that is independent of either the state or the tensor product structure of the system.

  7. Development of a vector-tensor system to measure the absolute magnetic flux density and its gradient in magnetically shielded rooms

    SciTech Connect

    Voigt, J.; Knappe-Grüneberg, S.; Gutkelch, D.; Neuber, S.; Schnabel, A.; Burghoff, M.; Haueisen, J.

    2015-05-15

    Several experiments in fundamental physics demand an environment of very low, homogeneous, and stable magnetic fields. For the magnetic characterization of such environments, we present a portable SQUID system that measures the absolute magnetic flux density vector and the gradient tensor. This vector-tensor system contains 13 integrated low-critical temperature (LTc) superconducting quantum interference devices (SQUIDs) inside a small cylindrical liquid helium Dewar with a height of 31 cm and 37 cm in diameter. The achievable resolution depends on the flux density of the field under investigation and its temporal drift. Inside a seven-layer mu-metal shield, an accuracy better than ±23 pT for the components of the static magnetic field vector and ±2 pT/cm for each of the nine components of the gradient tensor is reached by using the shifting method.

  8. Development of a vector-tensor system to measure the absolute magnetic flux density and its gradient in magnetically shielded rooms.

    PubMed

    Voigt, J; Knappe-Grüneberg, S; Gutkelch, D; Haueisen, J; Neuber, S; Schnabel, A; Burghoff, M

    2015-05-01

    Several experiments in fundamental physics demand an environment of very low, homogeneous, and stable magnetic fields. For the magnetic characterization of such environments, we present a portable SQUID system that measures the absolute magnetic flux density vector and the gradient tensor. This vector-tensor system contains 13 integrated low-critical temperature (LTc) superconducting quantum interference devices (SQUIDs) inside a small cylindrical liquid helium Dewar with a height of 31 cm and 37 cm in diameter. The achievable resolution depends on the flux density of the field under investigation and its temporal drift. Inside a seven-layer mu-metal shield, an accuracy better than ±23 pT for the components of the static magnetic field vector and ±2 pT/cm for each of the nine components of the gradient tensor is reached by using the shifting method.

  9. Full Moment Tensor Analysis of Western US Explosions, Earthquakes, Collapses, and Volcanic Events Using a Regional Waveform Inversion

    NASA Astrophysics Data System (ADS)

    Ford, S. R.; Dreger, D. S.; Walter, W. R.

    2006-12-01

    Seismic moment tensor analysis at regional distances commonly involves solving for the deviatoric moment tensor and decomposing it to characterize the tectonic earthquake source. The full seismic moment tensor solution can also recover the isotropic component of the seismic source, which is theoretically dominant in explosions and collapses, and present in volcanic events. Analysis of events with demonstrably significant isotropic energy can aid in understanding the source processes of volcanic and geothermal seismic events and the monitoring of nuclear explosions. Using a regional time-domain waveform inversion for the complete moment tensor we calculate the deviatoric and isotropic source components for several explosions at the Nevada Test Site (NTS) and earthquakes, collapses, and volcanic events in the surrounding region of the NTS (Western US). The events separate into specific populations according to their deviation from a pure double-couple and ratio of isotropic to deviatoric energy. The separation allows for anomalous event identification and discrimination of explosions, earthquakes, and collapses. Analysis of the source principal axes can characterize the regional stress field, and tectonic release due to explosions. Error in the moment tensor solutions and source parameters is also calculated. We investigate the sensitivity of the moment tensor solutions to Green's functions calculated with imperfect Earth models, inaccurate event locations, and data with a low signal-to-noise ratio. We also test the performance of the method under a range of recording conditions from excellent azimuthal coverage to cases of sparse coverage as might be expected for smaller events. This analysis will be used to determine the magnitude range where well-constrained solutions can be obtained.

  10. Affinity learning with diffusion on tensor product graph.

    PubMed

    Yang, Xingwei; Prasad, Lakshman; Latecki, Longin Jan

    2013-01-01

    In many applications, we are given a finite set of data points sampled from a data manifold and represented as a graph with edge weights determined by pairwise similarities of the samples. Often the pairwise similarities (which are also called affinities) are unreliable due to noise or due to intrinsic difficulties in estimating similarity values of the samples. As observed in several recent approaches, more reliable similarities can be obtained if the original similarities are diffused in the context of other data points, where the context of each point is a set of points most similar to it. Compared to the existing methods, our approach differs in two main aspects. First, instead of diffusing the similarity information on the original graph, we propose to utilize the tensor product graph (TPG) obtained by the tensor product of the original graph with itself. Since TPG takes into account higher order information, it is not a surprise that we obtain more reliable similarities. However, it comes at the price of higher order computational complexity and storage requirement. The key contribution of the proposed approach is that the information propagation on TPG can be computed with the same computational complexity and the same amount of storage as the propagation on the original graph. We prove that a graph diffusion process on TPG is equivalent to a novel iterative algorithm on the original graph, which is guaranteed to converge. After its convergence we obtain new edge weights that can be interpreted as new, learned affinities. We stress that the affinities are learned in an unsupervised setting. We illustrate the benefits of the proposed approach for data manifolds composed of shapes, images, and image patches on two very different tasks of image retrieval and image segmentation. With learned affinities, we achieve the bull's eye retrieval score of 99.99 percent on the MPEG-7 shape dataset, which is much higher than the state-of-the-art algorithms. When the data

  11. A viscoelastic Unitary Crack-Opening strain tensor for crack width assessment in fractured concrete structures

    NASA Astrophysics Data System (ADS)

    Sciumè, Giuseppe; Benboudjema, Farid

    2016-09-01

    A post-processing technique which allows computing crack width in concrete is proposed for a viscoelastic damage model. Concrete creep is modeled by means of a Kelvin-Voight cell while the damage model is that of Mazars in its local form. Due to the local damage approach, the constitutive model is regularized with respect to finite element mesh to avoid mesh dependency in the computed solution (regularization is based on fracture energy). The presented method is an extension to viscoelasticity of the approach proposed by Matallah et al. (Int. J. Numer. Anal. Methods Geomech. 34(15):1615-1633, 2010) for a purely elastic damage model. The viscoelastic Unitary Crack-Opening (UCO) strain tensor is computed accounting for evolution with time of surplus of stress related to damage; this stress is obtained from decomposition of the effective stress tensor. From UCO the normal crack width is then derived accounting for finite element characteristic length in the direction orthogonal to crack. This extension is quite natural and allows for accounting of creep impact on opening/closing of cracks in time dependent problems. A graphical interpretation of the viscoelastic UCO using Mohr's circles is proposed and application cases together with a theoretical validation are presented to show physical consistency of computed viscoelastic UCO.

  12. Tensor classification of structure in smoothed particle hydrodynamics density fields

    NASA Astrophysics Data System (ADS)

    Forgan, Duncan; Bonnell, Ian; Lucas, William; Rice, Ken

    2016-04-01

    As hydrodynamic simulations increase in scale and resolution, identifying structures with non-trivial geometries or regions of general interest becomes increasingly challenging. There is a growing need for algorithms that identify a variety of different features in a simulation without requiring a `by eye' search. We present tensor classification as such a technique for smoothed particle hydrodynamics (SPH). These methods have already been used to great effect in N-Body cosmological simulations, which require smoothing defined as an input free parameter. We show that tensor classification successfully identifies a wide range of structures in SPH density fields using its native smoothing, removing a free parameter from the analysis and preventing the need for tessellation of the density field, as required by some classification algorithms. As examples, we show that tensor classification using the tidal tensor and the velocity shear tensor successfully identifies filaments, shells and sheet structures in giant molecular cloud simulations, as well as spiral arms in discs. The relationship between structures identified using different tensors illustrates how different forces compete and co-operate to produce the observed density field. We therefore advocate the use of multiple tensors to classify structure in SPH simulations, to shed light on the interplay of multiple physical processes.

  13. DTI segmentation using an information theoretic tensor dissimilarity measure.

    PubMed

    Wang, Zhizhou; Vemuri, Baba C

    2005-10-01

    In recent years, diffusion tensor imaging (DTI) has become a popular in vivo diagnostic imaging technique in Radiological sciences. In order for this imaging technique to be more effective, proper image analysis techniques suited for analyzing these high dimensional data need to be developed. In this paper, we present a novel definition of tensor "distance" grounded in concepts from information theory and incorporate it in the segmentation of DTI. In a DTI, the symmetric positive definite (SPD) diffusion tensor at each voxel can be interpreted as the covariance matrix of a local Gaussian distribution. Thus, a natural measure of dissimilarity between SPD tensors would be the Kullback-Leibler (KL) divergence or its relative. We propose the square root of the J-divergence (symmetrized KL) between two Gaussian distributions corresponding to the diffusion tensors being compared and this leads to a novel closed form expression for the "distance" as well as the mean value of a DTI. Unlike the traditional Frobenius norm-based tensor distance, our "distance" is affine invariant, a desirable property in segmentation and many other applications. We then incorporate this new tensor "distance" in a region based active contour model for DTI segmentation. Synthetic and real data experiments are shown to depict the performance of the proposed model.

  14. Degeneracy-aware interpolation of 3D diffusion tensor fields

    NASA Astrophysics Data System (ADS)

    Bi, Chongke; Takahashi, Shigeo; Fujishiro, Issei

    2012-01-01

    Visual analysis of 3D diffusion tensor fields has become an important topic especially in medical imaging for understanding microscopic structures and physical properties of biological tissues. However, it is still difficult to continuously track the underlying features from discrete tensor samples, due to the absence of appropriate interpolation schemes in the sense that we are able to handle possible degeneracy while fully respecting the smooth transition of tensor anisotropic features. This is because the degeneracy may cause rotational inconsistency of tensor anisotropy. This paper presents such an approach to interpolating 3D diffusion tensor fields. The primary idea behind our approach is to resolve the possible degeneracy through optimizing the rotational transformation between a pair of neighboring tensors by analyzing their associated eigenstructure, while the degeneracy can be identified by applying a minimum spanning tree-based clustering algorithm to the original tensor samples. Comparisons with existing interpolation schemes will be provided to demonstrate the advantages of our scheme, together with several results of tracking white matter fiber bundles in a human brain.

  15. Cosmological implications of modified gravity induced by quantum metric fluctuations

    NASA Astrophysics Data System (ADS)

    Liu, Xing; Harko, Tiberiu; Liang, Shi-Dong

    2016-08-01

    We investigate the cosmological implications of modified gravities induced by the quantum fluctuations of the gravitational metric. If the metric can be decomposed as the sum of the classical and of a fluctuating part, of quantum origin, then the corresponding Einstein quantum gravity generates at the classical level modified gravity models with a non-minimal coupling between geometry and matter. As a first step in our study, after assuming that the expectation value of the quantum correction can be generally expressed in terms of an arbitrary second order tensor constructed from the metric and from the thermodynamic quantities characterizing the matter content of the Universe, we derive the (classical) gravitational field equations in their general form. We analyze in detail the cosmological models obtained by assuming that the quantum correction tensor is given by the coupling of a scalar field and of a scalar function to the metric tensor, and by a term proportional to the matter energy-momentum tensor. For each considered model we obtain the gravitational field equations, and the generalized Friedmann equations for the case of a flat homogeneous and isotropic geometry. In some of these models the divergence of the matter energy-momentum tensor is non-zero, indicating a process of matter creation, which corresponds to an irreversible energy flow from the gravitational field to the matter fluid, and which is direct consequence of the non-minimal curvature-matter coupling. The cosmological evolution equations of these modified gravity models induced by the quantum fluctuations of the metric are investigated in detail by using both analytical and numerical methods, and it is shown that a large variety of cosmological models can be constructed, which, depending on the numerical values of the model parameters, can exhibit both accelerating and decelerating behaviors.

  16. Quantum memory Quantum memory

    NASA Astrophysics Data System (ADS)

    Le Gouët, Jean-Louis; Moiseev, Sergey

    2012-06-01

    Interaction of quantum radiation with multi-particle ensembles has sparked off intense research efforts during the past decade. Emblematic of this field is the quantum memory scheme, where a quantum state of light is mapped onto an ensemble of atoms and then recovered in its original shape. While opening new access to the basics of light-atom interaction, quantum memory also appears as a key element for information processing applications, such as linear optics quantum computation and long-distance quantum communication via quantum repeaters. Not surprisingly, it is far from trivial to practically recover a stored quantum state of light and, although impressive progress has already been accomplished, researchers are still struggling to reach this ambitious objective. This special issue provides an account of the state-of-the-art in a fast-moving research area that makes physicists, engineers and chemists work together at the forefront of their discipline, involving quantum fields and atoms in different media, magnetic resonance techniques and material science. Various strategies have been considered to store and retrieve quantum light. The explored designs belong to three main—while still overlapping—classes. In architectures derived from photon echo, information is mapped over the spectral components of inhomogeneously broadened absorption bands, such as those encountered in rare earth ion doped crystals and atomic gases in external gradient magnetic field. Protocols based on electromagnetic induced transparency also rely on resonant excitation and are ideally suited to the homogeneous absorption lines offered by laser cooled atomic clouds or ion Coulomb crystals. Finally off-resonance approaches are illustrated by Faraday and Raman processes. Coupling with an optical cavity may enhance the storage process, even for negligibly small atom number. Multiple scattering is also proposed as a way to enlarge the quantum interaction distance of light with matter. The

  17. Separate universes in loop quantum cosmology: Framework and applications

    NASA Astrophysics Data System (ADS)

    Wilson-Ewing, Edward

    2016-06-01

    I present a streamlined review of how the separate universe approach to cosmological perturbation theory can be used to study the dynamics of long-wavelength scalar perturbations in loop quantum cosmology (LQC), and then use it to calculate how long-wavelength curvature perturbations evolve across the LQC bounce assuming a constant equation of state. A similar calculation is possible for tensor modes using results from a complementary approach to cosmological perturbation theory in LQC based on an effective Hamiltonian constraint. An interesting result is that the tensor-to-scalar ratio can be suppressed or amplified by quantum gravity effects during the bounce, depending on the equation of state of the matter field dominating the dynamics. In particular, if the equation of state lies between - 1/3 and 1, the value of the tensor-to-scalar ratio will be suppressed during the bounce, in some cases significantly.

  18. Computational studies of quantum spin systems

    NASA Astrophysics Data System (ADS)

    Wang, Ling

    Quantum spin models are important for studying the magnetic behavior of strongly correlated electronic insulators. Specifically, the 2D S = 1/2 Heisenberg model closely captures the antiferromagnetic state of CuO2 layers of the high-Tc superconductor parent compounds at half band filling. Introducing competing interactions or disorder can drive quantum phase transitions to other new states. I use the stochastic series expansion (SSE) quantum Monte Carlo (QMC) method and finite-size scaling to study the quantum critical points of two Heisenberg bilayers, each with intra- and inter-plane couplings J and J⊥. Tuning the inter- to intra-layer coupling constant ratio g = J⊥ /J drives a quantum phase transition between the Neel ordered state and a quantum disordered state. I discuss the ground-state finite-size scaling properties of three different quantities and extract the critical value of the coupling ratio gc. The results improve gc by more than an order of magnitude over the previous best estimates. Upon doping with static non-magnetic impurities, (e.g., substituting Cu with Zn), the cuprate layer is driven through a percolation phase transition. While the static properties are described by 2D classical percolation, the dynamical properties are quantum mechanical. I use exact diagonalization to calculate the lowest excitation gap Delta and use SSE to study an upper bound for Delta obtained from sum rules. Scaling the gap distribution with the cluster length L, a dynamic exponent z ≈ 2Df is obtained, where Df is the fractal dimensionality of the percolating cluster. I present several arguments showing that the low-energy excitations are due to weakly coupled effective moments formed owing to local imbalance in sublattice occupation. Many interesting quantum spin models lead to negative signs in the importance weight used in QMC sampling, and thus this method cannot be used. Matrix product states (MPSs) and tensor product states (TPSs) have recently been

  19. Trace anomaly on a quantum spacetime manifold

    SciTech Connect

    Spallucci, Euro; Smailagic, Anais; Nicolini, Piero

    2006-04-15

    In this paper we investigate the trace anomaly in a space-time where single events are delocalized as a consequence of short distance quantum coordinate fluctuations. We obtain a modified form of heat kernel asymptotic expansion which does not suffer from short distance divergences. Calculation of the trace anomaly is performed using an IR regulator in order to circumvent the absence of UV infinities. The explicit form of the trace anomaly is presented and the corresponding 2D Polyakov effective action and energy-momentum tensor are obtained. The vacuum expectation value of the energy-momentum tensor in the Boulware, Hartle-Hawking and Unruh vacua is explicitly calculated in a rt section of a recently found, noncommutative inspired, Schwarzschild-like solution of the Einstein equations. The standard short distance divergences in the vacuum expectation values are regularized in agreement with the absence of UV infinities removed by quantum coordinate fluctuations.

  20. Effects of realistic tensor force on nuclear structure

    SciTech Connect

    Nakada, H.

    2012-10-20

    First-order tensor-force effects on nuclear structure are investigated in the self-consistent mean-field and RPA calculations with the M3Y-type semi-realistic interactions, which contain the realistic tensor force. The tensor force plays a key role in Z- or N-dependence of the shell structure, and in transitions involving spin degrees-of-freedom. It is demonstrated that the semi-realistic interactions successfully describe the N-dependence of the shell structure in the proton-magic nuclei (e.g. Ca and Sn), and the magnetic transitions (e.g. M1 transition in {sup 208}Pb).

  1. Extracting the diffusion tensor from molecular dynamics simulation with Milestoning

    SciTech Connect

    Mugnai, Mauro L.; Elber, Ron

    2015-01-07

    We propose an algorithm to extract the diffusion tensor from Molecular Dynamics simulations with Milestoning. A Kramers-Moyal expansion of a discrete master equation, which is the Markovian limit of the Milestoning theory, determines the diffusion tensor. To test the algorithm, we analyze overdamped Langevin trajectories and recover a multidimensional Fokker-Planck equation. The recovery process determines the flux through a mesh and estimates local kinetic parameters. Rate coefficients are converted to the derivatives of the potential of mean force and to coordinate dependent diffusion tensor. We illustrate the computation on simple models and on an atomically detailed system—the diffusion along the backbone torsions of a solvated alanine dipeptide.

  2. Abelian tensor hierarchy in 4D N = 1 conformal supergravity

    NASA Astrophysics Data System (ADS)

    Aoki, Shuntaro; Higaki, Tetsutaro; Yamada, Yusuke; Yokokura, Ryo

    2016-09-01

    We consider Abelian tensor hierarchy in four-dimensional N = 1 supergravity in the conformal superspace formalism, where the so-called covariant approach is used to antisymmetric tensor fields. We introduce p-form gauge superfields as superforms in the conformal superspace. We solve the Bianchi identities under the constraints for the super-forms. As a result, each of form fields is expressed by a single gauge invariant superfield. We also show the relation between the superspace formalism and the superconformal tensor calculus.

  3. The general dielectric tensor for bi-kappa magnetized plasmas

    NASA Astrophysics Data System (ADS)

    Gaelzer, R.; Ziebell, L. F.; Meneses, A. R.

    2016-06-01

    In this paper, we derive the dielectric tensor for a plasma containing particles described by an anisotropic superthermal (bi-kappa) velocity distribution function. The tensor components are written in terms of the two-variables kappa plasma special functions, recently defined by Gaelzer and Ziebell [Phys. Plasmas 23, 022110 (2016)]. We also obtain various new mathematical properties for these functions, which are useful for the analytical treatment, numerical implementation, and evaluation of the functions and, consequently, of the dielectric tensor. The formalism developed here and in the previous paper provides a mathematical framework for the study of electromagnetic waves propagating at arbitrary angles and polarizations in a superthermal plasma.

  4. Extracting the diffusion tensor from molecular dynamics simulation with Milestoning.

    PubMed

    Mugnai, Mauro L; Elber, Ron

    2015-01-01

    We propose an algorithm to extract the diffusion tensor from Molecular Dynamics simulations with Milestoning. A Kramers-Moyal expansion of a discrete master equation, which is the Markovian limit of the Milestoning theory, determines the diffusion tensor. To test the algorithm, we analyze overdamped Langevin trajectories and recover a multidimensional Fokker-Planck equation. The recovery process determines the flux through a mesh and estimates local kinetic parameters. Rate coefficients are converted to the derivatives of the potential of mean force and to coordinate dependent diffusion tensor. We illustrate the computation on simple models and on an atomically detailed system-the diffusion along the backbone torsions of a solvated alanine dipeptide.

  5. Quantum Communication

    NASA Astrophysics Data System (ADS)

    Weinfurter, Harald; Zeilinger, Anton

    Quantum entanglement lies at the heart of the new field of quantum communication and computation. For a long time, entanglement was seen just as one of those fancy features which make quantum mechanics so counterintuitive. But recently, quantum information theory has shown the tremendous importance of quantum correlations for the formulation of new methods of information transfer and for algorithms exploiting the capabilities of quantum computers.This chapter describes the first experimental realizations of quantum communication schemes using entangled photon pairs. We show how to make communication secure against eavesdropping using entanglement-based quantum cryptography, how to increase the information capacity of a quantum channel by quantum dense coding and, finally, how to communicate quantum information itself in the process of quantum teleportation.

  6. Intermediate quantum statistics for identical objects

    SciTech Connect

    Kuryshkin, V.V.

    1988-11-01

    Methods to construct various algebras of creation and annihilation operators of physical objects in complex quantum state spaces with a nonnegative metric are proposed. All allowed algebras for the cases of identical nonrelativistic systems in the second quantization of the Schrodinger equation, of identical quanta of relativistic tensor fields, and of identical quanta of relativistic spinor fields are constructed. A comparison of the obtained algebras with the well-known algebras of this type (Fermi, Bose, para-Fermi, and superalgebras) is given.

  7. Quantum-mechanical instability of the Kerr-Newman black-hole interior

    SciTech Connect

    Hiscock, W.A.

    1980-04-15

    The behavior of the conserved stress-energy tensor of a quantized massless field in a Kerr-Newman black-hole space-time is studied. In the Unruh vacuum state, and under the assumption that certain stress-energy tensor components are analytic functions of a, the Kerr angular momentum parameter, it is shown that the stress-energy tensor must diverge on at least one of the two inner event horizons. A weaker assumption, simple continuity, suffices to guarantee that the stress-energy tensor diverges on the inner horizon of all slowly rotating Kerr-Newman black holes. This perturbation singularity invalidates the Kerr-Newman interior as a counterexample to strong cosmic censorship, and closes off the ''space bridge'' to other asymptotically flat exterior ''universes.''

  8. Quantum Weyl invariance and cosmology

    NASA Astrophysics Data System (ADS)

    Dabholkar, Atish

    2016-09-01

    Equations for cosmological evolution are formulated in a Weyl invariant formalism to take into account possible Weyl anomalies. Near two dimensions, the renormalized cosmological term leads to a nonlocal energy-momentum tensor and a slowly decaying vacuum energy. A natural generalization to four dimensions implies a quantum modification of Einstein field equations at long distances. It offers a new perspective on time-dependence of couplings and naturalness with potentially far-reaching consequences for the cosmological constant problem, inflation, and dark energy.

  9. Quantum cosmology near two dimensions

    NASA Astrophysics Data System (ADS)

    Bautista, Teresa; Dabholkar, Atish

    2016-08-01

    We consider a Weyl-invariant formulation of gravity with a cosmological constant in d -dimensional spacetime and show that near two dimensions the classical action reduces to the timelike Liouville action. We show that the renormalized cosmological term leads to a nonlocal quantum momentum tensor which satisfies the Ward identities in a nontrivial way. The resulting evolution equations for an isotropic, homogeneous universe lead to slowly decaying vacuum energy and power-law expansion. We outline the implications for the cosmological constant problem, inflation, and dark energy.

  10. Airborne full tensor magnetic gradiometry surveys in the Thuringian basin, Germany

    NASA Astrophysics Data System (ADS)

    Queitsch, M.; Schiffler, M.; Goepel, A.; Stolz, R.; Meyer, M.; Meyer, H.; Kukowski, N.

    2013-12-01

    In this contribution we introduce a newly developed fully operational full tensor magnetic gradiometer (FTMG) instrument based on Superconducting Quantum Interference Devices (SQUIDs) and show example data acquired in 2012 within the framework of the INFLUINS (Integrated Fluid Dynamics in Sedimentary basins) project. This multidisciplinary project aims for a better understanding of movements and interaction between shallow and deep fluids in the Thuringian Basin in the center of Germany. In contrast to mapping total magnetic field intensity (TMI) in conventional airborne magnetic surveys for industrial exploration of mineral deposits and sedimentary basins, our instrument measures all components of the magnetic field gradient tensor using highly sensitive SQUID gradiometers. This significantly constrains the solutions of the inverse problem. Furthermore, information on the ratio between induced and remanent magnetization is obtained. Special care has been taken to reduce motion noise while acquiring data in airborne operation. Therefore, the sensors are mounted in a nonmagnetic and aerodynamically shaped bird made of fiberglas with a high drag tail which stabilizes the bird even at low velocities. The system is towed by a helicopter and kept at 30m above ground during data acquisition. Additionally, the system in the bird incorporates an inertial unit for geo-referencing and enhanced motion noise compensation, a radar altimeter for topographic correction and a GPS system for high precision positioning. Advanced data processing techniques using reference magnetometer and inertial unit data result in a very low system noise of less than 60 pT/m peak to peak in airborne operation. To show the performance of the system we present example results from survey areas within the Thuringian basin and along its bordering highlands. The mapped gradient tensor components show a high correlation to existing geologic maps. Furthermore, the measured gradient components indicate

  11. A new two-dimensional, limited, zone-centered tensor artificial viscosity

    SciTech Connect

    Clover, M.; Cranfill, C.

    1997-12-01

    It is the goal of this paper to describe a fully multidimensional, limited discretization viscosity. The authors prefer discretization to artificial because it arises naturally from discretizing the momentum equation of fluid dynamics. By this is meant that the velocity-dependent stress tensor is not arbitrary, as has been assumed since von Neumann`s paper of 1952, but unavoidable, if a method of weak solution is used to solve the Euler equations. This weak solution method--due to Harten, Lax and van Leer [1985]--shows that Q arises in order to numerically conserve momentum, when the equation is integrated over a finite space and time interval. Understanding the ramifications of this insight lead to the construction of a tensor Q that is the sum of a number of dyadic terms (one per dimension). Thus, the k- and l-directed viscosities of k-l mesh codes is to be understood as the two dyadic terms corresponding to the two eigenvalues of the strain-rate tensor in 2-D (where the assumption had not been explicitly stated that the faces of the control volume--on which the stresses push--are orthogonal or parallel to the eigenvectors of the strain-rate). Calculating velocity jumps within zones to higher order and using limiters is done with the same degree of ad hoc rigor as in Godunov codes. The structure of this paper is to reprise certain results from 1-d analysis of a momentum equation, in order to highlight certain lessons that, when understood, enable one to easily generalize to higher dimension. The authors will also present some results on analytic test problems that this Q produces in a Free-Lagrange hydro code.

  12. Antisymmetric rank-2 tensor unparticle physics

    SciTech Connect

    Hur, Taeil; Ko, P.; Wu Xiaohong

    2007-11-01

    We present the phenomenology of antisymmetric rank-2 tensor unparticle operator O{sub U,A}{sup {mu}}{sup {nu}} with scaling dimension d{sub U}. We consider the physical effects of operator O{sub U,A}{sup {mu}}{sup {nu}} in Z{sup 0} boson invisible decays Z{sup 0}{yields}U, Z{sup 0}{yields}bb channel, the electroweak precision observable S parameter, and the muon anomalous magnetic dipole moment. The Z{sup 0} boson invisible decay gives a very stringent constraint in the ({lambda}{sub U},M{sub U}) plane, and only small r{identical_to}{lambda}{sub U}/M{sub U} < or approx. 0.1 is favored, when {lambda}{sub U} is order of several 100 GeV. When the phenomenological parameter {mu}, which parameterizes the scale invariance breaking, goes to 0, the S parameter and the muon (g-2) diverge for 1

  13. Objective Tinnitus and the Tensor Tympani Muscle.

    PubMed

    Rock

    1995-01-01

    Objective tinnitus (OT) may be caused by contraction of the tensor tympani muscle (TTM). The more forcefully the TTM contracts, the greater the intensity of the OT heard. Forceful closure of both eyelids can reflexively cause OT by contracting the TTM. The Forceful Eyelid Closure Syndrome (FECS) was reported at the Proceedings of the Second International Tinnitus Seminar in 1983.(1) FECS consists of several factors: (1) Objective tinnitus (2) An associated waning of hearing primarily of the lower frequencies, as much as 45 dB at 125 Hz, 30 to 40 dB at 250 Hz ascending to the patient's norm at 2000 Hz and approximately a 5 to 10 dB at 4000 Hz and 5 to 20 dB at 8000 Hz (3) Retraction of the manubrium and posterior mid-third of the tympanic membrane (TM) at the malleus-umbo area as seen under the otomicroscope (OM) in 25% (108) of 432 ears examined (4) These same ears were 75% (324) positive for increased impedance at maximum compliance with FEC. Of the patients studied, 25% had no response under the otomicroscope or by impedance audiometry.

  14. PHYSLIB: A C++ tensor class library

    SciTech Connect

    Budge, K.G.

    1991-10-09

    C++ is the first object-oriented programming language which produces sufficiently efficient code for consideration in computation-intensive physics and engineering applications. In addition, the increasing availability of massively parallel architectures requires novel programming techniques which may prove to be relatively easy to implement in C++. For these reasons, Division 1541 at Sandia National Laboratories is devoting considerable resources to the development of C++ libraries. This document describes the first of these libraries to be released, PHYSLIB, which defines classes representing Cartesian vectors and (second-order) tensors. This library consists of the header file physlib.h, the inline code file physlib.inl, and the source file physlib.C. The library is applicable to both three-dimensional and two-dimensional problems; the user selects the 2-D version of the library by defining the symbol TWO D in the header file physlib.h and recompiling physlib.C and his own code. Alternately, system managers may wish to provide duplicate header and object modules of each dimensionality. This code was produced under the auspices of Sandia National Laboratories, a federally-funded research center administered for the United States Department of Energy on a non-profit basis by AT T. This code is available to US citizens, and institutions under research, government use and/or commercial license agreements.

  15. Dark matter dispersion tensor in perturbation theory

    NASA Astrophysics Data System (ADS)

    Aviles, Alejandro

    2016-03-01

    We compute the dark matter velocity dispersion tensor up to third order in perturbation theory using the Lagrangian formalism, revealing growing solutions at the third and higher orders. Our results are general and can be used for any other perturbative formalism. As an application, corrections to the matter power spectrum are calculated, and we find that some of them have the same structure as those in the effective field theory of large-scale structure, with "EFT-like" coefficients that grow quadratically with the linear growth function and are further suppressed by powers of the logarithmic linear growth factor f ; other corrections present additional k dependence. Due to the velocity dispersions, there exists a free-streaming scale that suppresses the whole 1-loop power spectrum. Furthermore, we find that as a consequence of the nonlinear evolution, the free-streaming length is shifted towards larger scales, wiping out more structure than that expected in linear theory. Therefore, we argue that the formalism developed here is better suited for a perturbation treatment of warm dark matter or neutrino clustering, where the velocity dispersion effects are well known to be important. We discuss implications related to the nature of dark matter.

  16. Hidden symmetries and killing tensors on curved spaces

    SciTech Connect

    Ianus, S.; Visinescu, M.; Vilcu, G. E.

    2010-11-15

    Higher-order symmetries corresponding to Killing tensors are investigated. The intimate relation between Killing-Yano tensors and nonstandard supersymmetries is pointed out. In the Dirac theory on curved spaces, Killing-Yano tensors generate Dirac-type operators involved in interesting algebraic structures as dynamical algebras or even infinite dimensional algebras or superalgebras. The general results are applied to space-times which appear in modern studies. One presents the infinite dimensional superalgebra of Dirac type operators on the 4-dimensional Euclidean Taub-NUT space that can be seen as a twisted loop algebra. The existence of the conformal Killing-Yano tensors is investigated for some spaces with mixed 3-Sasakian structures.

  17. Reducing tensor magnetic gradiometer data for unexploded ordnance detection

    USGS Publications Warehouse

    Bracken, Robert E.; Brown, Philip J.

    2005-01-01

    We performed a survey to demonstrate the effectiveness of a prototype tensor magnetic gradiometer system (TMGS) for detection of buried unexploded ordnance (UXO). In order to achieve a useful result, we designed a data-reduction procedure that resulted in a realistic magnetic gradient tensor and devised a simple way of viewing complicated tensor data, not only to assess the validity of the final resulting tensor, but also to preview the data at interim stages of processing. The final processed map of the surveyed area clearly shows a sharp anomaly that peaks almost directly over the target UXO. This map agrees well with a modeled map derived from dipolar sources near the known target locations. From this agreement, it can be deduced that the reduction process is valid, making the prototype TMGS a foundation for development of future systems and processes.

  18. Visualization of 2-D and 3-D Tensor Fields

    NASA Technical Reports Server (NTRS)

    Hesselink, Lambertus

    1997-01-01

    In previous work we have developed a novel approach to visualizing second order symmetric 2-D tensor fields based on degenerate point analysis. At degenerate points the eigenvalues are either zero or equal to each other, and the hyper-streamlines about these points give rise to tri-sector or wedge points. These singularities and their connecting hyper-streamlines determine the topology of the tensor field. In this study we are developing new methods for analyzing and displaying 3-D tensor fields. This problem is considerably more difficult than the 2-D one, as the richness of the data set is much larger. Here we report on our progress and a novel method to find , analyze and display 3-D degenerate points. First we discuss the theory, then an application involving a 3-D tensor field, the Boussinesq problem with two forces.

  19. Visualization of 2-D and 3-D Tensor Fields

    NASA Technical Reports Server (NTRS)

    Hesselink, Lambertus

    1995-01-01

    In previous work we have developed a novel approach to visualizing second order symmetric 2-D tensor fields based on degenerate point analysis. At degenerate points the eigenvalues are either zero or equal to each other, and the hyperstreamlines about these points give rise to trisector or wedge points. These singularities and their connecting hyperstreamlines determine the topology of the tensor field. In this study we are developing new methods for analyzing and displaying 3-D tensor fields. This problem is considerably more difficult than the 2-D one, as the richness of the data set is much larger. Here we report on our progress and a novel method to find, analyze and display 3-D degenerate points. First we discuss the theory, then an application involving a 3-D tensor field, the Boussinesq problem with two forces.

  20. Inflationary power spectra with quantum holonomy corrections

    SciTech Connect

    Mielczarek, Jakub

    2014-03-01

    In this paper we study slow-roll inflation with holonomy corrections from loop quantum cosmology. It was previously shown that, in the Planck epoch, these corrections lead to such effects as singularity avoidance, metric signature change and a state of silence. Here, we consider holonomy corrections affecting the phase of cosmic inflation, which takes place away from the Planck epoch. Both tensor and scalar power spectra of primordial inflationary perturbations are computed up to the first order in slow-roll parameters and V/ρ{sub c}, where V is a potential of the scalar field and ρ{sub c} is a critical energy density (expected to be of the order of the Planck energy density). Possible normalizations of modes at short scales are discussed. In case the normalization is performed with use of the Wronskian condition applied to adiabatic vacuum, the tensor and scalar spectral indices are not quantum corrected in the leading order. However, by choosing an alternative method of normalization one can obtain quantum corrections in the leading order. Furthermore, we show that the holonomy-corrected equations of motion for tensor and scalar modes can be derived based on effective background metrics. This allows us to show that the classical Wronskian normalization condition is well defined for the cosmological perturbations with holonomy corrections.

  1. Quantum simulation

    NASA Astrophysics Data System (ADS)

    Georgescu, I. M.; Ashhab, S.; Nori, Franco

    2014-01-01

    Simulating quantum mechanics is known to be a difficult computational problem, especially when dealing with large systems. However, this difficulty may be overcome by using some controllable quantum system to study another less controllable or accessible quantum system, i.e., quantum simulation. Quantum simulation promises to have applications in the study of many problems in, e.g., condensed-matter physics, high-energy physics, atomic physics, quantum chemistry, and cosmology. Quantum simulation could be implemented using quantum computers, but also with simpler, analog devices that would require less control, and therefore, would be easier to construct. A number of quantum systems such as neutral atoms, ions, polar molecules, electrons in semiconductors, superconducting circuits, nuclear spins, and photons have been proposed as quantum simulators. This review outlines the main theoretical and experimental aspects of quantum simulation and emphasizes some of the challenges and promises of this fast-growing field.

  2. Turbulence constitutive modeling of the square root of the Reynolds stress.

    PubMed

    Ariki, Taketo

    2015-11-01

    A methodology for turbulence constitutive modeling is discussed on the basis of the square-root tensor of the Reynolds stress. The present methodology can satisfy the realizability condition for the Reynolds stress proposed by Schumann [Phys. Fluids 20, 721 (1977)] in a more general manner than the conventional methodologies. The definition and uniqueness of the square-root tensor have been discussed, and its boundary condition has been properly obtained consistently with that of the Reynolds stress. Examples of possible constitutive models of both tensor-expansion and transport-equation types have been proposed. PMID:26651782

  3. Turbulence constitutive modeling of the square root of the Reynolds stress

    NASA Astrophysics Data System (ADS)

    Ariki, Taketo

    2015-11-01

    A methodology for turbulence constitutive modeling is discussed on the basis of the square-root tensor of the Reynolds stress. The present methodology can satisfy the realizability condition for the Reynolds stress proposed by Schumann [Phys. Fluids 20, 721 (1977)], 10.1063/1.861942 in a more general manner than the conventional methodologies. The definition and uniqueness of the square-root tensor have been discussed, and its boundary condition has been properly obtained consistently with that of the Reynolds stress. Examples of possible constitutive models of both tensor-expansion and transport-equation types have been proposed.

  4. The atomic anisotropic displacement tensor – completing the picture.

    PubMed

    Thorkildsen, Gunnar; Larsen, Helge B

    2015-07-01

    A simplified approach for calculating the equivalent isotropic displacement parameter is presented and the transformation property of the tensor representation U to point-group operations is analysed. Complete tables have been compiled for the restrictions imposed upon the tensor owing to the site symmetry associated with all special positions as listed in Hahn [(2011), International Tables for Crystallography, Vol. A, Space-group Symmetry, 5th revised ed. Chichester: John Wiley and Sons, Ltd]. PMID:26131902

  5. Beyond-standard-model tensor interaction and hadron phenomenology

    SciTech Connect

    Courtoy, Aurore; Baessler, Stefan; Gonzalez-Alonso, Martin; Liuti, Simonetta

    2015-10-15

    Here, we evaluate the impact of recent developments in hadron phenomenology on extracting possible fundamental tensor interactions beyond the standard model. We show that a novel class of observables, including the chiral-odd generalized parton distributions, and the transversity parton distribution function can contribute to the constraints on this quantity. Experimental extractions of the tensor hadronic matrix elements, if sufficiently precise, will provide a, so far, absent testing ground for lattice QCD calculations.

  6. Beyond-Standard-Model Tensor Interaction and Hadron Phenomenology.

    PubMed

    Courtoy, Aurore; Baeßler, Stefan; González-Alonso, Martín; Liuti, Simonetta

    2015-10-16

    We evaluate the impact of recent developments in hadron phenomenology on extracting possible fundamental tensor interactions beyond the standard model. We show that a novel class of observables, including the chiral-odd generalized parton distributions, and the transversity parton distribution function can contribute to the constraints on this quantity. Experimental extractions of the tensor hadronic matrix elements, if sufficiently precise, will provide a, so far, absent testing ground for lattice QCD calculations. PMID:26550868

  7. Exactly soluble quantum wormhole in two dimensions

    SciTech Connect

    Kim, Won Tae; Son, Edwin J.; Yoon, Myung Seok

    2004-11-15

    We are presenting a quantum traversable wormhole in an exactly soluble two-dimensional model. This is different from previous works since the exotic negative energy that supports the wormhole is generated from the quantization of classical energy-momentum tensors. This explicit illustration shows the quantum-mechanical energy can be used as a candidate for the exotic source. As for the traversability, after a particle travels through the wormhole, the static initial wormhole geometry gets a back reaction which spoils the wormhole structure. However, it may still maintain the initial structure along with the appropriate boundary condition.

  8. Observational constraints on loop quantum cosmology.

    PubMed

    Bojowald, Martin; Calcagni, Gianluca; Tsujikawa, Shinji

    2011-11-18

    In the inflationary scenario of loop quantum cosmology in the presence of inverse-volume corrections, we give analytic formulas for the power spectra of scalar and tensor perturbations convenient to compare with observations. Since inverse-volume corrections can provide strong contributions to the running spectral indices, inclusion of terms higher than the second-order runnings in the power spectra is crucially important. Using the recent data of cosmic microwave background and other cosmological experiments, we place bounds on the quantum corrections.

  9. Contact Tensor in a p-Wave Fermi Gas with Anisotropic Feshbach Resonances

    NASA Astrophysics Data System (ADS)

    Yoshida, Shuhei M.; Ueda, Masahito

    2016-05-01

    Recent theoretical and experimental investigations have revealed that a Fermi gas with a p-wave Feshbach resonance has universal relations between the system's high-momentum behavior and thermodynamics. A new feature introduced by the p-wave interaction is anisotropy in the Feshbach resonances; three degenerate p-wave resonances split according to the magnetic quantum number of the closed-channel molecules | m | due to the magnetic dipole-dipole interaction. Here, we investigate the consequences of the anisotropy. We show that the momentum distribution has a high-momentum asymptote nk ~k-2 ∑ m, m' = - 1 1 >Cm, m'Y1m * (\\kcirc)Y1m' (\\kcirc) , in which we introduce the p-wave contact tensor Cm ,m'. In contrast to the previous studies, it has nine components. We identify them as the number, angular momentum, and nematicity of the closed-channel molecules. We also discuss two examples, the anisotropic p-wave superfluid and a gas confined in a cigar-shaped trap, which exhibit a nematicity component in the p-wave contact tensor.

  10. Tensor polarization dependent fragmentation functions and e+e-→V π X at high energies

    NASA Astrophysics Data System (ADS)

    Chen, Kai-bao; Yang, Wei-hua; Wei, Shu-yi; Liang, Zuo-tang

    2016-08-01

    We present the systematic results for three-dimensional fragmentation functions of spin-1 hadrons defined via the quark-quark correlator. There are totally 72 such fragmentation functions, among them 18 are twist-2, 36 are twist-3 and 18 are twist-4. We also present the relationships between the twist-3 parts and those defined via the quark-gluon-quark correlator obtained from the QCD equation of motion. We show that the two particle semi-inclusive hadron production process e+e-→V π X at high energies is one of the best places to study the three-dimensional tensor polarization dependent fragmentation functions. We present the general kinematic analysis of this process and show that the cross section should be expressed in terms of 81 independent structure functions. After that we present parton model results for the hadronic tensor, the structure functions, and the azimuthal and spin asymmetries in terms of these gauge invariant fragmentation functions at the leading order perturbative quantum chromodynamics up to twist-3.

  11. Conservation of energy-momentum tensor in fermionic superfluid phase: Effects of U(1) broken symmetry

    NASA Astrophysics Data System (ADS)

    He, Yan; Guo, Hao

    2016-07-01

    Respecting the conservation laws of momentum and energy in a many body theory is very important for understanding the transport phenomena. The previous conserving approximation requires that the self-energy of a single particle could be written as a functional derivative of a full dressed Green's function. This condition can not be satisfied in the G0 G t-matrix or pair fluctuation theory which emphasizes the fermion pairing with a stronger than the Bardeen-Cooper-Schrieffer (BCS) attraction. In the previous work [1], we have shown that when the temperature is above the superfluid transition temperature Tc, the G0 G t-matrix theory can be put into a form that satisfies the stress tensor Ward identity (WI) or local form of conservation laws by introducing a new type of vertex correction. In this paper, we will extend the above conservation approximation to the superfluid phase in the BCS mean field level. To establish the stress tensor WI, we have to include the fluctuation of the order parameter or the contribution from the Goldstone mode. The result will be useful for understanding the transport properties such as the behavior of the viscosity of Fermionic gases in the superfluid phases.

  12. Representing Matrix Cracks Through Decomposition of the Deformation Gradient Tensor in Continuum Damage Mechanics Methods

    NASA Technical Reports Server (NTRS)

    Leone, Frank A., Jr.

    2015-01-01

    A method is presented to represent the large-deformation kinematics of intraply matrix cracks and delaminations in continuum damage mechanics (CDM) constitutive material models. The method involves the additive decomposition of the deformation gradient tensor into 'crack' and 'bulk material' components. The response of the intact bulk material is represented by a reduced deformation gradient tensor, and the opening of an embedded cohesive interface is represented by a normalized cohesive displacement-jump vector. The rotation of the embedded interface is tracked as the material deforms and as the crack opens. The distribution of the total local deformation between the bulk material and the cohesive interface components is determined by minimizing the difference between the cohesive stress and the bulk material stress projected onto the cohesive interface. The improvements to the accuracy of CDM models that incorporate the presented method over existing approaches are demonstrated for a single element subjected to simple shear deformation and for a finite element model of a unidirectional open-hole tension specimen. The material model is implemented as a VUMAT user subroutine for the Abaqus/Explicit finite element software. The presented deformation gradient decomposition method reduces the artificial load transfer across matrix cracks subjected to large shearing deformations, and avoids the spurious secondary failure modes that often occur in analyses based on conventional progressive damage models.

  13. Application of the implicit TENSOR code to studies of containment of undergound nuclear tests

    SciTech Connect

    Burton, D. E.; Bryan, J. B.; Lettis, Jr., L. A.; Rambo, J. T.

    1982-02-01

    The TENSOR code, a two-dimensional finite-difference code, has been used extensively for the solution of stress wave propagation problems in materials, particularly those associated with the containment of underground nuclear test. These problems are typically characterized by shock waves at early times and by nearly incompressible flow at later times. To address this type of problem more economically, an implicit Newmark time integration has been implemented. Implicit differencing requires the solution of a coupled system of equations, by either direct or interative methods. An iterative technique has been selected to reduce the impact of the algorithm on the code structure and because it is the more economical method when only modest increases in timestep are desired. Although the algorithm is similar in some respects to the ICE method of Harlow and Amsden, substantial differences are required by the involvement of a complete stress tensor (instead of a scalar pressure) and by the highly nonlinear nature of the earth material constitutive relations.

  14. Discriminating induced seismicity from natural earthquakes using moment tensors and source spectra

    NASA Astrophysics Data System (ADS)

    Zhang, Hongliang; Eaton, David W.; Li, Ge; Liu, Yajing; Harrington, Rebecca M.

    2016-02-01

    Earthquake source mechanisms and spectra can provide important clues to aid in discriminating between natural and induced events. In this study, we calculate moment tensors and stress drop values for eight recent induced earthquakes in the Western Canadian Sedimentary Basin with magnitudes between 3.2 and 4.4, as well as a nearby magnitude 5.3 event that is interpreted as a natural earthquake. We calculate full moment tensor solutions by performing a waveform-fitting procedure based on a 1-D transversely isotropic velocity model. In addition to a dominant double-couple (DC) signature that is common to nearly all events, most induced events exhibit significant non-double-couple components. A parameter sensitivity analysis indicates that spurious non-DC components are negligible if the signal to noise ratio (SNR) exceeds 10 and if the 1-D model differs from the true velocity structure by less than 5%. Estimated focal depths of induced events are significantly shallower than the typical range of focal depths for intraplate earthquakes in the Canadian Shield. Stress drops of the eight induced events were estimated using a generalized spectral-fitting method and fall within the typical range of 2 to 90 MPa for tectonic earthquakes. Elastic moduli changes due to the brittle damage production at the source, presence of multiple intersecting fractures, dilatant jogs created at the overlapping areas of multiple fractures, or non-planar pre-existing faults may explain the non-DC components for induced events.

  15. An Iterative Reweighted Method for Tucker Decomposition of Incomplete Tensors

    NASA Astrophysics Data System (ADS)

    Yang, Linxiao; Fang, Jun; Li, Hongbin; Zeng, Bing

    2016-09-01

    We consider the problem of low-rank decomposition of incomplete multiway tensors. Since many real-world data lie on an intrinsically low dimensional subspace, tensor low-rank decomposition with missing entries has applications in many data analysis problems such as recommender systems and image inpainting. In this paper, we focus on Tucker decomposition which represents an Nth-order tensor in terms of N factor matrices and a core tensor via multilinear operations. To exploit the underlying multilinear low-rank structure in high-dimensional datasets, we propose a group-based log-sum penalty functional to place structural sparsity over the core tensor, which leads to a compact representation with smallest core tensor. The method for Tucker decomposition is developed by iteratively minimizing a surrogate function that majorizes the original objective function, which results in an iterative reweighted process. In addition, to reduce the computational complexity, an over-relaxed monotone fast iterative shrinkage-thresholding technique is adapted and embedded in the iterative reweighted process. The proposed method is able to determine the model complexity (i.e. multilinear rank) in an automatic way. Simulation results show that the proposed algorithm offers competitive performance compared with other existing algorithms.

  16. An Introduction to Tensors for Students of Physics and Engineering

    NASA Technical Reports Server (NTRS)

    Kolecki, Joseph C.

    2002-01-01

    Tensor analysis is the type of subject that can make even the best of students shudder. My own post-graduate instructor in the subject took away much of the fear by speaking of an implicit rhythm in the peculiar notation traditionally used, and helped us to see how this rhythm plays its way throughout the various formalisms. Prior to taking that class, I had spent many years "playing" on my own with tensors. I found the going to be tremendously difficult but was able, over time, to back out some physical and geometrical considerations that helped to make the subject a little more transparent. Today, it is sometimes hard not to think in terms of tensors and their associated concepts. This article, prompted and greatly enhanced by Marlos Jacob, whom I've met only by e-mail, is an attempt to record those early notions concerning tensors. It is intended to serve as a bridge from the point where most undergraduate students "leave off" in their studies of mathematics to the place where most texts on tensor analysis begin. A basic knowledge of vectors, matrices, and physics is assumed. A semi-intuitive approach to those notions underlying tensor analysis is given via scalars, vectors, dyads, triads, and higher vector products. The reader must be prepared to do some mathematics and to think. For those students who wish to go beyond this humble start, I can only recommend my professor's wisdom: find the rhythm in the mathematics and you will fare pretty well.

  17. Improving RESTORE for robust diffusion tensor estimation: a simulation study

    NASA Astrophysics Data System (ADS)

    Chang, Lin-Ching

    2010-03-01

    Diffusion tensor magnetic resonance imaging (DT-MRI) is increasingly used in clinical research and applications for its ability to depict white matter tracts and for its sensitivity to microstructural and architectural features of brain tissue. However, artifacts are common in clinical DT-MRI acquisitions. Signal perturbations produced by such artifacts can be severe and neglecting to account for their contribution can result in erroneous diffusion tensor values. The Robust Estimation of Tensors by Outlier Rejection (RESTORE) has been demonstrated to be an effective method for improving tensor estimation on a voxel-by-voxel basis in the presence of artifactual data points in diffusion weighted images. Despite the very good performance of the RESTORE algorithm, there are some limitations and opportunities for improvement. Instabilities in tensor estimation using RESTORE have been observed in clinical human brain data. Those instabilities can come from the intrinsic high frequency spin inflow effects in non-DWIs or from excluding too many data points from the fitting. This paper proposes several practical constraints to the original RESTORE method. Results from Monte Carlo simulation indicate that the improved RESTORE method reduces the instabilities in tensor estimation observed from the original RESTORE method.

  18. Global nuclear structure effects of the tensor interaction

    SciTech Connect

    Zalewski, M.; Olbratowski, P.; Rafalski, M.; Werner, T. R.; Satula, W.; Wyss, R. A.

    2009-12-15

    A direct fit of the isoscalar spin-orbit (SO) and both isoscalar and isovector tensor coupling constants to the f{sub 5/2}-f{sub 7/2} SO splittings in {sup 40}Ca, {sup 56}Ni, and {sup 48}Ca nuclei requires a drastic reduction of the isoscalar SO strength and strong attractive tensor coupling constants. The aim of this work is to address further consequences of these strong attractive tensor and weak SO fields on binding energies, nuclear deformability, and high-spin states. In particular, the contribution to the nuclear binding energy from the tensor field shows a generic magic structure with tensorial magic numbers N(Z)=14,32,56, or 90, corresponding to the maximum spin asymmetries in 1d{sub 5/2}, 1f{sub 7/2}+2p{sub 3/2}, 1g{sub 9/2}+2d{sub 5/2}, and 1h{sub 11/2}+2f{sub 7/2} single-particle configurations, respectively, and that these numbers are smeared out by pairing correlations and deformation effects. The consequences of strong attractive tensor fields and weak SO interaction for nuclear stability at the drip lines are also examined, particularly those close to the tensorial doubly magic nuclei. The possibility of an entirely new tensor-force-driven deformation effect is discussed.

  19. Bayesian CP Factorization of Incomplete Tensors with Automatic Rank Determination.

    PubMed

    Zhao, Qibin; Zhang, Liqing; Cichocki, Andrzej

    2015-09-01

    CANDECOMP/PARAFAC (CP) tensor factorization of incomplete data is a powerful technique for tensor completion through explicitly capturing the multilinear latent factors. The existing CP algorithms require the tensor rank to be manually specified, however, the determination of tensor rank remains a challenging problem especially for CP rank . In addition, existing approaches do not take into account uncertainty information of latent factors, as well as missing entries. To address these issues, we formulate CP factorization using a hierarchical probabilistic model and employ a fully Bayesian treatment by incorporating a sparsity-inducing prior over multiple latent factors and the appropriate hyperpriors over all hyperparameters, resulting in automatic rank determination. To learn the model, we develop an efficient deterministic Bayesian inference algorithm, which scales linearly with data size. Our method is characterized as a tuning parameter-free approach, which can effectively infer underlying multilinear factors with a low-rank constraint, while also providing predictive distributions over missing entries. Extensive simulations on synthetic data illustrate the intrinsic capability of our method to recover the ground-truth of CP rank and prevent the overfitting problem, even when a large amount of entries are missing. Moreover, the results from real-world applications, including image inpainting and facial image synthesis, demonstrate that our method outperforms state-of-the-art approaches for both tensor factorization and tensor completion in terms of predictive performance.

  20. Conditions for quantum interference in cognitive sciences.

    PubMed

    Yukalov, Vyacheslav I; Sornette, Didier

    2014-01-01

    We present a general classification of the conditions under which cognitive science, concerned, e.g. with decision making, requires the use of quantum theoretical notions. The analysis is done in the frame of the mathematical approach based on the theory of quantum measurements. We stress that quantum effects in cognition can arise only when decisions are made under uncertainty. Conditions for the appearance of quantum interference in cognitive sciences and the conditions when interference cannot arise are formulated. PMID:24259280