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.
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.
Probability distributions for quantum stress tensors measured in a finite time interval
NASA Astrophysics Data System (ADS)
Fewster, Christopher J.; Ford, L. H.
2015-11-01
A meaningful probability distribution for measurements of a quantum stress tensor operator can only be obtained if the operator is averaged in time or in spacetime. This averaging can be regarded as a description of the measurement process. Realistic measurements can be expected to begin and end at finite times, which means that they are described by functions with compact support, which we will also take to be smooth. Here we study the probability distributions for stress tensor operators averaged with such functions of time, in the vacuum state of a massless free field. Our primary aim is to understand the asymptotic form of the distribution which describes the probability of large vacuum fluctuations. Our approach involves asymptotic estimates for the high moments of the distribution. These estimates in turn may be used to obtain estimates for the asymptotic form of the probability distribution. Our results show that averaging over a finite interval results in a probability distribution which falls more slowly than for the case of Lorentzian averaging, and both fall more slowly than exponentially. This indicates that vacuum fluctuations effects can dominate over thermal fluctuations in some circumstances.
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
Quantum integrability of quadratic Killing tensors
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.
Quantum stress tensor for a massive vector field in the space-time of a cylindrical black hole
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.
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.
Model for lightcone fluctuations due to stress tensor fluctuations
NASA Astrophysics Data System (ADS)
Bessa, C. H. G.; De Lorenci, V. A.; Ford, L. H.; Ribeiro, C. C. H.
2016-03-01
We study a model for quantum lightcone fluctuations in which vacuum fluctuations of the electric field and of the squared electric field in a nonlinear dielectric material produce variations in the flight times of probe pulses. When this material has a nonzero third order polarizability, the flight time variations arise from squared electric field fluctuations, and are analogous to effects expected when the stress tensor of a quantized field drives passive spacetime geometry fluctuations. We also discuss the dependence of the squared electric field fluctuations upon the geometry of the material, which in turn determines a sampling function for averaging the squared electric field along the path of the pulse. This allows us to estimate the probability of especially large fluctuations, which is a measure of the probability distribution for quantum stress tensor fluctuations.
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…
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.
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.
Quantum stress in chaotic billiards.
Berggren, Karl-Fredrik; Maksimov, Dmitrii N; Sadreev, Almas F; Höhmann, Ruven; Kuhl, Ulrich; Stöckmann, Hans-Jürgen
2008-06-01
This paper reports on a joint theoretical and experimental study of the Pauli quantum-mechanical stress tensor T_{alphabeta}(x,y) for open two-dimensional chaotic billiards. In the case of a finite current flow through the system the interior wave function is expressed as psi=u+iv . With the assumption that u and v are Gaussian random fields we derive analytic expressions for the statistical distributions for the quantum stress tensor components T_{alphabeta} . The Gaussian random field model is tested for a Sinai billiard with two opposite leads by analyzing the scattering wave functions obtained numerically from the corresponding Schrödinger equation. Two-dimensional quantum billiards may be emulated from planar microwave analogs. Hence we report on microwave measurements for an open two-dimensional cavity and how the quantum stress tensor analog is extracted from the recorded electric field. The agreement with the theoretical predictions for the distributions for T_{alphabeta}(x,y) is quite satisfactory for small net currents. However, a distinct difference between experiments and theory is observed at higher net flow, which could be explained using a Gaussian random field, where the net current was taken into account by an additional plane wave with a preferential direction and amplitude. PMID:18643352
Tensor analysis and curvature in quantum space-time
Namsrai, K.
1987-03-01
Introducing quantum space-time into physics by means of the transformation language of noncommuting coordinates gives a simple scheme of generalizing the tensor analysis. The general covariance principle for the quantum space-time case is discussed, within which one can obtain the covariant structure of basic tensor quantities and the motion equation for a particle in a gravitational field. Definitions of covariant derivatives and curvature are also generalized in the give case. It turns out that the covariant structure of the Riemann-Christoffel curvature tensor is not preserved in quantum space-time. However, if the curvature tensor R/sub ..mu.. nu lambda chi/(z) is redetermined up to the value of the L/sup 2/ term, then its covariant structure is achieved, and it, in turn, allows them to reconstruct the Einstein equation in quantum space-time.
Quantum Monte Carlo simulations with tensor-network states
NASA Astrophysics Data System (ADS)
Song, Jeong Pil; Clay, R. T.
2011-03-01
Matrix-product states, generated by the density-matrix renormalization group method, are among the most powerful methods for simulation of quasi-one dimensional quantum systems. Direct application of a matrix-product state representation fails for two dimensional systems, although a number of tensor-network states have been proposed to generalize the concept for two dimensions. We introduce a useful approximate method replacing a 4-index tensor by two matrices in order to contract tensors in two dimensions. We use this formalism as a basis for variational quantum Monte Carlo, optimizing the matrix elements stochastically. We present results on a two dimensional spinless fermion model including nearest- neighbor Coulomb interactions, and determine the critical Coulomb interaction for the charge density wave state by finite size scaling. This work was supported by the Department of Energy grant DE-FG02-06ER46315.
Covariant statistical mechanics and the stress-energy tensor.
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
Stress tensor from the trace anomaly in Reissner-Nordström spacetimes
NASA Astrophysics Data System (ADS)
Anderson, Paul R.; Mottola, Emil; Vaulin, Ruslan
2007-12-01
The effective action associated with the trace anomaly provides a general algorithm for approximating the expectation value of the stress tensor of conformal matter fields in arbitrary curved spacetimes. In static, spherically symmetric spacetimes, the algorithm involves solving a fourth order linear differential equation in the radial coordinate r for the two scalar auxiliary fields appearing in the anomaly action, and its corresponding stress tensor. By appropriate choice of the homogeneous solutions of the auxiliary field equations, we show that it is possible to obtain finite stress tensors on all Reissner-Nordström event horizons, including the extreme Q=M case. We compare these finite results to previous analytic approximation methods, which yield invariably an infinite stress energy on charged black hole horizons, as well as with detailed numerical calculations that indicate the contrary. The approximation scheme based on the auxiliary field effective action reproduces all physically allowed behaviors of the quantum stress tensor, in a variety of quantum states, for fields of any spin, in the vicinity of the entire family (0≤Q≤M) of RN horizons.
Stress tensor from the trace anomaly in Reissner-Nordstroem spacetimes
Anderson, Paul R.; Mottola, Emil; Vaulin, Ruslan
2007-12-15
The effective action associated with the trace anomaly provides a general algorithm for approximating the expectation value of the stress tensor of conformal matter fields in arbitrary curved spacetimes. In static, spherically symmetric spacetimes, the algorithm involves solving a fourth order linear differential equation in the radial coordinate r for the two scalar auxiliary fields appearing in the anomaly action, and its corresponding stress tensor. By appropriate choice of the homogeneous solutions of the auxiliary field equations, we show that it is possible to obtain finite stress tensors on all Reissner-Nordstroem event horizons, including the extreme Q=M case. We compare these finite results to previous analytic approximation methods, which yield invariably an infinite stress energy on charged black hole horizons, as well as with detailed numerical calculations that indicate the contrary. The approximation scheme based on the auxiliary field effective action reproduces all physically allowed behaviors of the quantum stress tensor, in a variety of quantum states, for fields of any spin, in the vicinity of the entire family (0{<=}Q{<=}M) of RN horizons.
Theory of plasticity based on a new invariant of stress tensor. Two-dimensional stress
NASA Astrophysics Data System (ADS)
Revuzhenko, A. F.; Mikenina, O. A.
2015-10-01
The authors introduce a new stress tensor invariant proportional to a squared intensity of shear stresses versus maximum shear stress. The invariant means a shear stress averaged over three fans-areas along three principal stresses of the stress tensor. The theory is based on the invariant and the associated flow rule. The article gives equations of generalized two-dimensional stress state and an analysis of their types. The authors solve an axisymmetrical problem on limit state around a hole.
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.
OPE of the stress tensors and surface operators
NASA Astrophysics Data System (ADS)
Huang, Xing; Hung, Ling-Yan; Lin, Feng-Li
2015-06-01
We demonstrate that the divergent terms in the OPE of a stress tensor and a line (co-dimension two) operator of general shape in three dimensional spacetime cannot be constructed only from local geometric data depending only on the shape of the line. We verify this holographically for Wilson line operators or equivalently the twist operator corresponding to computing the entanglement entropy using the Ryu-Takayanagi formula. We discuss possible implications of this result.
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).
Detailed stress tensor measurements in a centrifugal compressor vaneless diffuser
Pinarbasi, A.; Johnson, M.W.
1996-04-01
Detailed flow measurements have been made in the vaneless diffuser of a large low-speed centrifugal compressor using hot-wire anemometry. The three time mean velocity components and full stress tensor distributions have been determined on eight measurement plans within the diffuser. High levels of Reynolds stress result in the rapid mixing out of the blade wake. Although high levels of turbulent kinetic energy are found in the passage wake, they are not associated with strong Reynolds stresses and hence the passage wake mixes out only slowly. Low-frequency meandering of the wake position is therefore likely to be responsible for the high kinetic energy levels. The anisotropic nature of the turbulence suggests that Reynolds stress turbulence models are required for CFD modeling of diffuser flows.
Coupling coefficients for tensor product representations of quantum SU(2)
Groenevelt, Wolter
2014-10-15
We study tensor products of infinite dimensional irreducible {sup *}-representations (not corepresentations) of the SU(2) quantum group. We obtain (generalized) eigenvectors of certain self-adjoint elements using spectral analysis of Jacobi operators associated to well-known q-hypergeometric orthogonal polynomials. We also compute coupling coefficients between different eigenvectors corresponding to the same eigenvalue. Since the continuous spectrum has multiplicity two, the corresponding coupling coefficients can be considered as 2 × 2-matrix-valued orthogonal functions. We compute explicitly the matrix elements of these functions. The coupling coefficients can be considered as q-analogs of Bessel functions. As a results we obtain several q-integral identities involving q-hypergeometric orthogonal polynomials and q-Bessel-type functions.
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.
Stress-energy tensor of adiabatic vacuum in Friedmann-Robertson-Walker spacetimes
Kaya, Ali; Tarman, Merve E-mail: merve.tarman@boun.edu.tr
2011-04-01
We compute the leading order contribution to the stress-energy tensor corresponding to the modes of a quantum scalar field propagating in a Friedmann-Robertson-Walker universe with arbitrary coupling to the scalar curvature, whose exact mode functions can be expanded as an infinite adiabatic series. While for a massive field this is a good approximation for all modes when the mass of the field m is larger than the Hubble parameter H, for a massless field only the subhorizon modes with comoving wave-numbers larger than some fixed k{sub *} obeying k{sub *}/a > H can be analyzed in this way. As infinities coming from adiabatic zero, second and fourth order expressions are removed by adiabatic regularization, the leading order finite contribution to the stress-energy tensor is given by the adiabatic order six terms, which we determine explicitly. For massive and massless modes these have the magnitudes H{sup 6}/m{sup 2} and H{sup 6}a{sup 2}/k{sub *}{sup 2}, respectively, and higher order corrections are suppressed by additional powers of (H/m){sup 2} and (Ha/k{sub *}){sup 2}. When the scale factor in the conformal time η is a simple power a(η) = (1/η){sup n}, the stress-energy tensor obeys P = Øρ with Ø = (n−2)/n for massive and Ø = (n−6)/(3n) for massless modes. In that case, the adiabaticity is eventually lost when 0 < n < 1 for massive and when 0 < n < 3/2 for massless fields since in time H/m and Ha/k{sub *} become order one. We discuss the implications of these results for de Sitter and other cosmologically relevant spaces.
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.
11-cis retinal torsion: A QTAIM and stress tensor analysis of the S1 excited state
NASA Astrophysics Data System (ADS)
Maza, Julio R.; Jenkins, Samantha; Kirk, Steven R.
2016-05-01
We investigate torsion about the C11-C12 bond mid-point for the S1 state of 11-cis retinal, using a QTAIM and stress tensor analysis. The QTAIM and stress tensor responses to a torsion ±α increase at a faster rate for the preferred direction of torsion though the CI seam. A QTAIM and stress tensor vector-based analysis provides an alternative way of characterising the asymmetry of the S1 potential energy surface. In the vicinity of the CI seam the ellipticity ε attained minimum values. The application of this analysis to molecular rotary motors is briefly discussed.
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.
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
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).
Renormalized stress-energy tensor near the horizon of a slowly evolving, rotating black hole
NASA Astrophysics Data System (ADS)
Frolov, Valery P.; Thorne, Kip S.
1989-04-01
The renormalized expectation value of the stress-energy tensor
Stress tensor of a quark moving through N=4 thermal plasma
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.
Conservation laws and stress-energy-momentum tensors for systems with background fields
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.
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.
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.
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
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.
Effective gravitational wave stress-energy tensor in alternative theories of gravity
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.
Short distance and initial state effects in inflation: Stress tensor and decoherence
NASA Astrophysics Data System (ADS)
Anderson, Paul R.; Molina-París, Carmen; Mottola, Emil
2005-08-01
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 Schrödinger 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 α 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.
Short distance and initial state effects in inflation: Stress tensor and decoherence
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.
NASA Astrophysics Data System (ADS)
Orús, Román
2012-05-01
In this paper we explore the practical use of the corner transfer matrix and its higher-dimensional generalization, the corner tensor, to develop tensor network algorithms for the classical simulation of quantum lattice systems of infinite size. This exploration is done mainly in one and two spatial dimensions (1D and 2D). We describe a number of numerical algorithms based on corner matrices and tensors to approximate different ground-state properties of these systems. The proposed methods also make use of matrix product operators and projected entangled pair operators and naturally preserve spatial symmetries of the system such as translation invariance. In order to assess the validity of our algorithms, we provide preliminary benchmarking calculations for the spin-1/2 quantum Ising model in a transverse field in both 1D and 2D. Our methods are a plausible alternative to other well-established tensor network approaches such as iDMRG and iTEBD in 1D, and iPEPS and TERG in 2D. The computational complexity of the proposed algorithms is also considered and, in 2D, important differences are found depending on the chosen simulation scheme. We also discuss further possibilities, such as 3D quantum lattice systems, periodic boundary conditions, and real-time evolution. This discussion leads us to reinterpret the standard iTEBD and iPEPS algorithms in terms of corner transfer matrices and corner tensors. Our paper also offers a perspective on many properties of the corner transfer matrix and its higher-dimensional generalizations in the light of novel tensor network methods.
Vacuum stress-energy tensor of a massive scalar field in a wormhole spacetime
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.
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)
Maxwell-Dirac stress-energy tensor in terms of Fierz bilinear currents
NASA Astrophysics Data System (ADS)
Inglis, Shaun; Jarvis, Peter
2016-03-01
We analyse the stress-energy tensor for the self-coupled Maxwell-Dirac system in the bilinear current formalism, using two independent approaches. The first method used is that attributed to Belinfante: starting from the spinor form of the action, the well-known canonical stress-energy tensor is augmented, by extending the Noether symmetry current to include contributions from the Lorentz group, to a manifestly symmetric form. This form admits a transcription to bilinear current form. The second method used is the variational derivation based on the covariant coupling to general relativity. The starting point here at the outset is the transcription of the action using, as independent field variables, both the bilinear currents, together with a gauge invariant vector field (a proxy for the electromagnetic vector potential). A central feature of the two constructions is that they both involve the mapping of the Dirac contribution to the stress-energy from the spinor fields to the equivalent set of bilinear tensor currents, through the use of appropriate Fierz identities. Although this mapping is done at quite different stages, nonetheless we find that the two forms of the bilinear stress-energy tensor agree. Finally, as an application, we consider the reduction of the obtained stress-energy tensor in bilinear form, under the assumption of spherical symmetry.
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
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.
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.
Positive Tensor Network Approach for Simulating Open Quantum Many-Body Systems.
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. PMID:27341253
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.
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.
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. PMID:27232445
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.
The evolution towards the rod-like axisymmetric structure for turbulent stress tensor
NASA Astrophysics Data System (ADS)
Li, Yi
2015-08-01
Modelling the turbulent stress tensor is a main task for both large eddy simulations and methods based on Reynolds averaged Navier-Stokes equations. The turbulent stress is known as the subgrid-scale stress in the former and the Reynolds stress in the latter. In this paper, we examine the observation that the stress tensor tends to evolve towards a rod-like axisymmetric configuration. This observation has been well documented for the subgrid-scale stress. However, for the Reynolds stress, the available data are still too limited to draw a definite conclusion. In the first part of the paper, we show that the tendency is also universal for the Reynolds stress by direct numerical simulations of decaying anisotropic turbulence. To show the universality, it is crucial to examine the decaying process from initial turbulent fields with a wide range of levels of anisotropy. Such initial fields are generated by a novel synthetic turbulence model based on the so-called constrained multi-turnover Lagrangian map. In the second part, we use the direct numerical simulation data to study the dynamical mechanisms of the evolution towards the rod-like structures. Among others, the analyses show that the nonlinear self-interaction term is the driving force of the process, and that the pressure tends to enhance the disk-like axisymmetric structure but overall tends to reduce the anisotropy of the stress tensor. The results shed light on the subtle difference between the pressure and the nonlinear self-interaction terms.
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
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.
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.
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.
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.
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.
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.
Non-abelian symmetries in tensor networks: A quantum symmetry space approach
Weichselbaum, Andreas
2012-12-15
A general framework for non-abelian symmetries is presented for matrix-product and tensor-network states in the presence of well-defined orthonormal local as well as effective basis sets. The two crucial ingredients, the Clebsch-Gordan algebra for multiplet spaces as well as the Wigner-Eckart theorem for operators, are accounted for in a natural, well-organized, and computationally straightforward way. The unifying tensor-representation for quantum symmetry spaces, dubbed QSpace, is particularly suitable to deal with standard renormalization group algorithms such as the numerical renormalization group (NRG), the density matrix renormalization group (DMRG), or also more general tensor networks such as the multi-scale entanglement renormalization ansatz (MERA). In this paper, the focus is on the application of the non-abelian framework within the NRG. A detailed analysis is presented for a fully screened spin- 3/2 three-channel Anderson impurity model in the presence of conservation of total spin, particle-hole symmetry, and SU(3) channel symmetry. The same system is analyzed using several alternative symmetry scenarios based on combinations of U(1){sub charge}, SU(2){sub spin}, SU(2){sub charge}, SU(3){sub channel}, as well as the enveloping symplectic Sp(6) symmetry. These are compared in detail, including their respective dramatic gain in numerical efficiency. In the Appendix, finally, an extensive introduction to non-abelian symmetries is given for practical applications, together with simple self-contained numerical procedures to obtain Clebsch-Gordan coefficients and irreducible operators sets. The resulting QSpace tensors can deal with any set of abelian symmetries together with arbitrary non-abelian symmetries with compact, i.e. finite-dimensional, semi-simple Lie algebras. - Highlights: Black-Right-Pointing-Pointer We introduce a transparent framework for non-abelian symmetries in tensor networks. Black-Right-Pointing-Pointer The framework was successfully
Altimetry data and the elastic stress tensor of subduction zones
NASA Technical Reports Server (NTRS)
Caputo, M.
1985-01-01
The stress field in the lithosphere caused by the distribution of density anomalies associated to the geoidal undulations observed by the GEOS-3 and SEASAT Earth satellites in the Tonga region was studied. Different models of the lithosphere were generated with different assumptions on the density distribution and geometry, all generating a geoid profile almost identical to the observed one. The first model is the Airy isostatic hypothesis which consists of a crust of density 2.85 laying on a lithosphere of density 3.35. The models obtained with different compensation depths give residual shortwavelength anomalies of the order of several tens of mgal and several tens of meters geoidal undulations. It indicates that there is no isostasy of the Airy type in the Tonga region because the observed geoid has very smooth undulation of about 25 m over a distance of 2000 km. The Pratt isostatic hypothesis is used in a model consisting of a crust of variable density laying on a lithosphere of higher density. This model gives smaller residual anomalies but still shows that there is no isostasy of the Pratt type in the Tonga region because the observed geoidal undulation are much smaller and smoother than the residual undulations associated to the Pratt model of isostasy.
Errors induced in triaxial stress tensor calculations using incorrect lattice parameters
Ruud, C.O.; Kozaczek, K.J.
1994-06-01
A number of researchers have proposed that for some metallic alloys, an elaborate procedure is necessary in order to improve the accuracy of the measured triaxial stress tensor. Others have been concerned that the uncertainties in establishing the precise zero-stress lattice parameter of an alloyed and/or cold worked engineering metal could cause significantly more error than would result in ignoring the triaxial stress state and assuming the plane stress condition. This paper illustrates the effect of uncertainties in the zero-stress lattice parameters on the calculated triaxial stress state for zero stress powders of three common engineering alloys, i.e., 1010 steel, 304 stainless steel, and 2024 aluminum. Also, errors due to the incorrect lattice spacing in experimental stress analysis are presented for three examples, i.e., a silicon powder, 304 gainless steel cylinder and a diamond. For cases where the plane strain assumption is justified, the uncertainties due to the stress free lattice parameter can be reduced by a simple measurement.
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.
Proton chemical shift tensors determined by 3D ultrafast MAS double-quantum NMR spectroscopy
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
On the decomposition of stress and strain tensors into spherical and deviatoric parts.
Augusti, G; Martin, J B; Prager, W
1969-06-01
It is well known that Hooke's law for a linearly elastic, isotropic solid may be written in the form of two relations that involve only the spherical or only the deviatoric parts of the tensors of stress and strain. The example of the linearly elastic, transversely isotropic solid is used to show that this decomposition is not, in general, feasible for linearly elastic, anisotropic solids. The discussion is extended to a large class of work-hardening rigid, plastic solids, and it is shown that the considered decomposition can only be achieved for the incompressible solids of this class. PMID:16591754
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
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.
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
Levine, Lyle E; Okoro, Chukwudi; Xu, Ruqing
2015-11-01
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
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.
Inverse approach to Einstein's equations for fluids with vanishing anisotropic stress tensor
NASA Astrophysics Data System (ADS)
Richardson, James; Ishak, Mustapha
2008-02-01
We expand previous work on an inverse approach to Einstein field equations where we include fluids with energy flux and consider the vanishing of the anisotropic stress tensor. We consider the approach using warped product spacetimes of class B1. Although restricted, these spacetimes include many exact solutions of interest to compact object studies and to cosmological models studies. The question explored here is as follows: given a spacetime metric, what fluid flow (timelike congruence), if any, could generate the spacetime via Einstein’s equations? We calculate the flow from the condition of a vanishing anisotropic stress tensor and give results in terms of the metric functions in the three canonical types of coordinates. A condition for perfect fluid sources is also provided. The framework developed is algorithmic and suited for the study and validation of exact solutions using computer algebra systems. The framework can be applied to solutions in comoving and noncomoving frames of reference, and examples in different types of coordinates are worked out.
Stress tensor determination:methodological updates and applications to reservoir stimulation
NASA Astrophysics Data System (ADS)
Martínez-Garzón, P.; Bohnhoff, M.; Kwiatek, G.; Dresen, G. H.
2013-12-01
Studying spatio-temporal variations of the stress field caused by massive fluid injection is relevant towards an improved understanding of geomechanical processes in different types of reservoirs. However, a reliable determination of such stress changes based on inversion of focal mechanisms of induced seismicity requires dense local seismic networks with good azimuthal coverage and low magnitude-detection threshold as well as detailed hydraulic information. At The Geysers geothermal field (California), induced seismicity has been carefully monitored for more than 30 years. While it is evident that local seismicity is related to injection and production operations, it is not trivial to relate the hydraulic parameters from individual wells to the patterns of the crustal stress field and associated seismicity. Earlier attempts to determine the local stress field in the area indicated that the regional tectonic stress field dominates over the stresses induced by reservoir treatment. In this study, we aim to determine potential spatial and temporal variations of the local stress field orientation at The Geysers geothermal site by using fault plane solutions of local events provided by the Northern California Earthquake Data Center. To determine the (deviatoric) stress tensor, we apply different stress inversion schemes including non-linear stress inversion algorithm with Bayesian uncertainty assessment as well as a linear approach with bootstrap resampling. In the first part, we investigated the stress field orientation at different depths using high quality focal mechanisms of induced seismicity over the whole reservoir. The results point out a clear variation of the stress field orientation at reservoir depth (normal regime) with respect to above and below (strike-slip regime). These observations are interpreted as an example of the reduction of horizontal stresses due to the depletion of hydrocarbon and geothermal reservoirs. In the second part, we searched for
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.
Wajsowicz, R.C. )
1993-04-01
Subgrid-scale dissipation of momentum in numerical models of the large-scale ocean circulation is commonly parameterized as a viscous diffusion resulting from the divergence of a stress tensor of the form [omega] = Au. The form of the fourth-order coefficient tensor A is derived for anisotropic dissipation with an axis of rotational symmetry. Sufficient conditions for A to be positive definite for incompressible flows, so guaranteeing a net positive dissipation of kinetic energy, are found. The divergence of the stress tensor, in Cartesian and spherical polar coordinates, is given for A with constant and spatially varying elements. A consistent form of A and [omega] for use in models based on the Arakawa B- and C-grids is also derived. 16 refs.
The stress-energy tensor and the deflection of light in 6-dimensional general relativity
NASA Astrophysics Data System (ADS)
Cocke, W. J.
1996-03-01
We find the stress-energy tensor of a perfect fluid in the 6-dimensional spacetime proposed by Cole. Using the weak-field Newtonian approximation of general relativity gives a constant of proportionality in Einstein's field equations that differs by a factor of 4/6 from the usual one and shows that Cole's extension of the Schwarzschild metric to 6 dimensions is not valid for a gravitating mass of “ordinary” matter. A subsequent evaluation of the deflection of starlight for the 6-d spacetime gives a result that is 4/6 of the 4-d result. We conclude that if spacetime is 6-dimensional, one must find a different way to deal with gravity.
Neoclassical viscous stress tensor for non-linear MHD simulations with XTOR-2F
NASA Astrophysics Data System (ADS)
Mellet, N.; Maget, P.; Lütjens, H.; Meshcheriakov, D.; the Tore Supra Team
2013-04-01
The neoclassical viscous stress tensor is implemented in the non-linear MHD code XTOR-2F (Lütjens and Luciani 2010 J. Comput. Phys. 229 8130-43), allowing consistent bi-fluid simulations of MHD modes, including the metastable branch of neoclassical tearing modes (NTMs) (Carrera et al 1986 Phys. Fluids 29 899-902). Equilibrium flows and bootstrap current from the neoclassical theory are formally recovered in this Chew-Goldberger-Low formulation. The non-linear behaviour of the new model is verified on a test case coming from a Tore Supra non-inductive discharge. A NTM threshold that is larger than with the previous model is obtained. This is due to the fact that the velocity is now part of the bootstrap current and that it differs from the theoretical neoclassical value.
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.
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.
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.
NASA Astrophysics Data System (ADS)
Cho, ChangSoo
2015-04-01
Moment tensor inversion method using waveform is not widely used in identification of fault direction for earthquake but also in identification of explosion experiment such as north korea nuclear test. TDMT inversion code as open source was used for 1-D focal mechanism to moderate earthquake. But TDMT code caused some problems to fit waveform data of earthquake. This software was modified and improved with using the extraction bandwidth for event data and using waveform fitting of maximum cross-correlation with limit of shifting time. Improved algorithm was applied to moderate earthquakes occurred in and around the korean peninsula and showed the result of good data fitting in deriving focal mechanism. CMT centeroid locations were calculated with this algorithm. Earthquakes occurred rarely in the korean peninsula and instrumental recording started from 1990's late. But quality of measurement ground motion is very good after the beginning of instrumental recording. 61 moderate earthquakes occurred analyzed between 2000 to present were analyzed. most of all focal mechanism of earthquake showed strike slip or reverse fault as intraplate earthquake. The horizontal direction of tectonic stress of the korean peninsula is ENE-WSW derived with focal mechanisms that were calculated with 1D moment tensor inversion for moderate earthquake by Zoback(1992)'s method of tectonic stress. 3D-moment tensor inversion method was also developed with simulation code of 3-D viscoelastic finite difference method with ADE(auxiliary differential equation)-PML(perfectly matched layer) and applied to main moderate earthquakes. Forward modeling of 3D seismic wave propagation for moment tensor inversion require much time and expensive cost. Forward simulation with domain decomposition of having only thin model between source and receiver in moment tensor inversion could reduce much time, memory and computational cost in 3D moment tensor inversion even though this method was not more effective
NASA Astrophysics Data System (ADS)
Ran, Ying; Jiang, Shenghan
Phases of matter are sharply defined in the thermodynamic limit. One major challenge of accurately simulating quantum phase diagrams of interacting quantum systems is due to the fact that numerical simulations usually deal with the energy density, a local property of quantum wavefunctions, while identifying different quantum phases generally rely on long-range physics. In this paper we construct generic fully symmetric quantum wavefunctions under certain assumptions using a type of tensor networks: projected entangled pair states, and provide practical simulation algorithms based on them. We find that quantum phases can be organized into crude classes distinguished by short-range physics, which is related to the fractionalization of both on-site symmetries and space-group symmetries. Consequently, our simulation algorithms, which are useful to study long-range physics as well, are expected to be able to sharply determine crude classes in interacting quantum systems efficiently. Examples of these crude classes are demonstrated in half-integer quantum spin systems on the kagome lattice. Limitations and generalizations of our results are discussed. The Alfred P. Sloan fellowship and National Science Foundation under Grant No. DMR-1151440.
Modelling anisotropy and backscatter effects in the subgrid scale stress tensor
NASA Astrophysics Data System (ADS)
Goutorbe, T.; Laurence, D.
1994-12-01
A new Subgrid scale (SGS) model used for Large-Eddy Simulation (LES) is developed by extending the scale-similarity hypothesis. Here a conventional Reynolds averaging is used instead of a test filter, resulting using the resolved (large scale) part of the Reynolds stress tensor. This resolved Reynolds stress (RRS) model, without any eddy viscosity assumption, is shown to properly reproduce the drain and backscatter partition of energy exchange between resolved and subgrid scales (for a channel flow at moderate Reynolds numbers). After assessing these properties by a priori tests (filtering DNS results), LES computations are carried out, determining the model constants by an analytical approach and a dynamic approach. In both cases, backscatter effects can lead to instabilities which are finally cured by introducing a transport equation for the SGS energy. This is felt necessary because when backscatter occurs, both SGS production and Kolmogorov dissipation are negative, so SGS energy must vanish, thus ending backscatter. Only a transport equation for the SGS energy can account for this energy conservation principle which is violated by dynamic approaches, that impose an average procedure. Slight discrepancies appear in the buffer layer which may be attributed to the insufficient resolution of streak structures in the spanwise direction. Thus, an adaptation for the buffer-layer appears to be the last obstacle to construct a model accounting for the most important physical properties required for SGS modeling and applicable for practical applications at high Reynolds numbers.
Tensor numerical methods in quantum chemistry: from Hartree-Fock to excitation energies.
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
Scalar product for the tensor operators of the quantum algebra Ŭq(su2) by the Wigner-Eckart theorem
NASA Astrophysics Data System (ADS)
Fakhri, H.; Nouraddini, M.
2015-07-01
Tensor operators as the irreducible submodules corresponding to the adjoint representation of the quantum algebra Ŭq(su2) are equipped with q-analogue of the Hilbert-Schmidt scalar product by using the Wigner-Eckart theorem. Then, it is used to show that the adjoint representation of the quantum algebra Ŭq(su2) is a *-representation.
Pandey, Manoj Kumar; Ramamoorthy, Ayyalusamy
2013-01-01
There is considerable interest in determining amide-15N chemical shift anisotropy (CSA) tensors from biomolecules and understanding their variation for structural and dynamics studies using solution and solid-state NMR spectroscopy and also by quantum chemical calculations. Due to the difficulties associated with the measurement of CSA tensors from membrane proteins, NMR-based structural studies heavily relied on the CSA tensors determined from model systems, typically single crystals of model peptides. In the present study, the principal components of backbone amide-15N CSA tensor have been determined using density functional theory for a 16.7-kDa membrane-bound paramagnetic heme containing protein, cytochrome b5 (cytb5). All the calculations were performed by taking residues within 5Å distance from the backbone amide-15N nucleus of interest. The calculated amide-15N CSA spans agree less well with our solution NMR data determined for an effective internuclear distance rN-H = 1.023 Å and a constant angle β = 18° that the least shielded component (δ11) makes with the N-H bond. The variation of amide-15N CSA span obtained using quantum chemical calculations is found to be smaller than that obtained from solution NMR measurements, whereas the trends of the variations are found to be in close agreement. We believe that the results reported in this study will be useful in studying the structure and dynamics of membrane proteins and heme-containing proteins, and also membrane-bound protein-protein complexes such as cytochromes-b5-P450. PMID:23268659
NASA Astrophysics Data System (ADS)
Beldjoudi, H.; Delouis, B.; Djellit, H.; Yelles-Chaouche, A.; Gharbi, S.; Abacha, I.
2016-02-01
A moderate earthquake with a moment magnitude of Mw 5.5 struck the Sub-Bibanique region of eastern Algeria on 14 May 2010, killing three people, injuring hundreds of others, and causing moderate damages in the epicentral area, mainly in the villages of Beni-Ilmane and Samma. The focal mechanism of the seismic source for the first shock, obtained by near-field waveform modelling, exhibits left-lateral strike-slip faulting with the first nodal plane oriented at N345°, and right-lateral strike-slip faulting with the second nodal plane oriented at N254°. A second earthquake that struck the region on 16 May 2010, with a moment magnitude of Mw 5.1, was located 9 km SW of the first earthquake. The focal mechanism obtained by waveform modelling showed reverse faulting with nodal planes oriented NE-SW (N25° and N250°). A third earthquake that struck the region on 23 May 2010, with a moment magnitude of Mw 5.2, was located 7 km S of the first shock. The obtained focal mechanism showed a left-lateral strike-slip plane oriented at N12° and a right-lateral strike-slip plane oriented at N257°. Field investigations combined with geological and seismotectonic analyses indicate that the three earthquake shocks were generated by activity on three distinct faults. The second and third shocks were generated on faults oriented WSW-ENE and NNE-SSW, respectively. The regional stress tensor calculated in the region gives an orientation of N340° for the maximum compressive stress direction (σ1) which is close to the horizontal, with a stress shape factor indicating either a compressional or a strike-slip regime.
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.
Quantum mechanical approach to IR intensities via nuclear electric shielding tensors. I. Water
NASA Astrophysics Data System (ADS)
Lazzeretti, P.; Zanasi, R.
1985-08-01
The connection between the nuclear electric shielding and the atomic polar tensors are shown. The electric shielding tensors are related to the polarizability and the magnetizability, and satisfy a constraint condition for the electrostatic equilibrium which is the mixed length-acceleration Thomas-Reiche-Kuhn sum rule. In addition, they can be successfully used to rationalize experimental IR intensity data, which is verified by extended basis set calculations on the water molecule.
Boundary stress-energy tensor and Newton-Cartan geometry in Lifshitz holography
NASA Astrophysics Data System (ADS)
Christensen, Morten H.; Hartong, Jelle; Obers, Niels A.; Rollier, Blaise
2014-01-01
For a specific action supporting z = 2 Lifshitz geometries we identify the Lifshitz UV completion by solving for the most general solution near the Lifshitz boundary. We identify all the sources as leading components of bulk fields which requires a vielbein formalism. This includes two linear combinations of the bulk gauge field and timelike vielbein where one asymptotes to the boundary timelike vielbein and the other to the boundary gauge field. The geometry induced from the bulk onto the boundary is a novel extension of Newton-Cartan geometry that we call torsional Newton-Cartan (TNC) geometry. There is a constraint on the sources but its pairing with a Ward identity allows one to reduce the variation of the on-shell action to unconstrained sources. We compute all the vevs along with their Ward identities and derive conditions for the boundary theory to admit conserved currents obtained by contracting the boundary stress-energy tensor with a TNC analogue of a conformal Killing vector. We also obtain the anisotropic Weyl anomaly that takes the form of a Hořava-Lifshitz action defined on a TNC geometry. The Fefferman-Graham expansion contains a free function that does not appear in the variation of the on-shell action. We show that this is related to an irrelevant deformation that selects between two different UV completions.
NASA Astrophysics Data System (ADS)
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.
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
NASA Astrophysics Data System (ADS)
Brüsewitz, C.; Vetter, U.; Hofsäss, H.
2015-02-01
We present ab-initio calculations of the independent components of gradient elastic tensors, so-called gradient elastic constants, which relate electric field gradient tensors to stress or strain tensors. The constants of cubic and hexagonal metals, MAX phases, and zinc oxide were determined within the framework of density functional theory by using the augmented plane waves plus local orbitals method implemented in the WIEN2k code. Comparison with experimental gradient elastic constants and electric field gradients' stress dependencies suggest an accuracy of about 30% of the calculated constants, independent of the probe that detects the field gradient being self- or foreign-atom. Changes in the electric field gradient take place by strain-induced asymmetric occupations of the p and d states in the valence region for all investigated materials. Volume and structural dependencies of the electric field gradient can directly be determined from this fundamental approach and are, for hexagonal closed packed metals, consistent with vanishing electric field gradients around ideal close packing and volume dependencies larger than one. The concept of these calculations is applicable in any hyperfine interaction method and, thus, can be used to gain information about intrinsic strains in systems where the experimental gradient elastic constants are inaccessible.
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.
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.
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
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
NASA Astrophysics Data System (ADS)
Moretti, Valter
1999-08-01
We conclude the rigorous analysis of a previous paper [V. Moretti, Commun. Math. Phys. 201, 327 (1999)] concerning the relation between the (Euclidean) point-splitting approach and the local ζ-function procedure to renormalize physical quantities at one-loop in (Euclidean) Quantum Field Theory in curved space-time. The case of the stress tensor is now considered in general D-dimensional closed manifolds for positive scalar operators -Δ+V(x). Results obtained formally in previous works [in the case D=4 and V(x)=ξR(x)+m2] are rigorously proven and generalized. It is also proven that, in static Euclidean manifolds, the method is compatible with Lorentzian-time analytic continuations. It is proven that the result of the ζ-function procedure is the same obtained from an improved version of the point-splitting method which uses a particular choice of the term w0(x,y) in the Hadamard expansion of the Green's function, given in terms of heat-kernel coefficients. This version of the point-splitting procedure works for any value of the field mass m. If D is even, the result is affected by an arbitrary one-parameter class of (conserved in absence of external source) symmetric tensors, dependent on the geometry locally, and it gives rise to the general correct trace expression containing the renormalized field fluctuations as well as the conformal anomaly term. Furthermore, it is proven that, in the case D=4 and V(x)=ξR(x)+m2, the given procedure reduces to the Euclidean version of Wald's improved point-splitting procedure provided the arbitrary mass scale present in the ζ-function is chosen opportunely. It is finally argued that the found point-splitting method should work generally, also dropping the hypothesis of a closed manifold, and not depending on the ζ-function procedure. This fact is indeed checked in the Euclidean section of Minkowski space-time for A=-Δ+m2 where the method gives rise to the correct Minkowski stress tensor for m2⩾0 automatically.
Improving the performance of tensor matrix vector multiplication in quantum chemistry codes.
Gropp, W. D.; Kaushik, D. K.; Minkoff, M.; Smith, B. F.
2008-05-08
Cumulative reaction probability (CRP) calculations provide a viable computational approach to estimate reaction rate coefficients. However, in order to give meaningful results these calculations should be done in many dimensions (ten to fifteen). This makes CRP codes memory intensive. For this reason, these codes use iterative methods to solve the linear systems, where a good fraction of the execution time is spent on matrix-vector multiplication. In this paper, we discuss the tensor product form of applying the system operator on a vector. This approach shows much better performance and provides huge savings in memory as compared to the explicit sparse representation of the system matrix.
Piezo-optic tensor of crystals from quantum-mechanical calculations
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.
Piezo-optic tensor of crystals from quantum-mechanical calculations
NASA Astrophysics Data System (ADS)
Erba, A.; Ruggiero, M. T.; Korter, T. M.; Dovesi, R.
2015-10-01
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.
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
NASA Astrophysics Data System (ADS)
Brajanovski, Miroslav
2011-11-01
I present an algorithm that uses cross-dipole wireline data only in order to estimate the HTI stiffness tensor for sandstone formations under in-situ asymmetric lateral (azimuthal) stress conditions. The algorithm is based on the generalization of terms "excess compliance" and "fracture weakness" developed within the linear slip interface theory for fractured rocks and is applied here to describe the effect of grain contacts in loose sandstones. I introduce the term "plane of weakness" being oriented (aligned) orthogonal to the minimal horizontal principal stress direction in order to describe the overall effective weakness of sandstone caused by the different principal stresses. For the quantification of this phenomenon I use the anisotropic Gassmann model. As a result I am able to calculate a HTI stiffness tensor for the interval length of a saturated sandstone formation and the respective Thomsen's parameters. The input data required for these calculations have to be provided by wireline logging and will consist of porosity, density, P-wave velocity, fast and slow shear wave velocities and oil-water saturation ratio. The algorithm in its current form is applicable to sandstone reservoirs only. Its limitation is based on two assumptions, which state that all the measured anisotropy is induced by the present stress in sandstone and that the unstressed sandstone would be nearly isotropic. From a technical viewpoint this algorithm can be implemented fairly easily in data acquisition and interpretation software relying on correct estimation of anisotropy parameters. It is also cheap because it does not require any additional measurements apart from the cross-dipole logging.
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.
Struppe, Jochem; Zhang, Yong; Rozovsky, Sharon
2015-01-01
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 77Se NMR properties and how those can in turn be employed to study biological systems. We report the solid-state 77Se NMR measurements of the L-selenocystine chemical shift tensor, which provides the first experimental chemical shift tensor information of selenocysteine-containing systems. Quantum chemical calculations of L-selenocystine models were performed to help understand various structural effects on 77Se 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. 77Se 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
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
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.
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.
NASA Astrophysics Data System (ADS)
D'Amico, Sebastiano; Cammarata, Laura; Cangemi, Marianna; Cavallaro, Danilo; Di Martino, Roberto Maria; Firetto Carlino, Marco
2014-12-01
The main goal of this study is to provide moment tensor solutions for small and moderate earthquakes of the Matese seismic sequence in southern Italy for the period of December 2013-January 2014. We estimate the focal mechanisms of 31 earthquakes with local magnitudes related to the Matese earthquake seismic sequence (December 2013-January 2014) in Southern-Central Italy which are recorded by the broadband stations of the Italian National Seismic Network and the Mediterranean Very Broadband Seismographic Network (MedNet) run by the Istituto Nazionale di Geofisica e Vulcanologia (INGV). The solutions show that normal faulting is the prevailing style of seismic deformation in agreement with the local faults mapped out in the area. Comparisons with already published solutions and with seismological and geological information available allowed us to properly interpret the moment tensor solutions in the frame of the seismic sequence evolution and also to furnish additional information about less energetic seismic phases. Focal data were inverted to obtain the seismogenic stress in the study area. The results are compatible with the major tectonic domain of the area.
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).
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.
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.
NASA Astrophysics Data System (ADS)
Tao, Bo; Katz, Joseph; Meneveau, Charles
2001-11-01
Based on the 3-D velocity measurements in the core region of a square duct at ReH ~ 1.2 × 10^5, the tensorial alignment of the deviatoric SGS stress (τ_ij^d) relative to the filtered strain-rate tensor (tildeS_ij) was shown to have a bi-modal behavior (Tao, et al. 2001). To gain further insight into the statistical geometry of τ_ij^d, we employ the Germano decomposition (Leonard 1974; Germano 1986), τ_ij = \\cal L_ij+\\cal C_ij+\\cal R_ij, and investigate the alignments of the individual stress components. Here the Leonard and SGS Reynolds stresses are computed from the data according to \\cal L_ij=widetildetildeu_itildeuj - tildetildeui tildetildeu_j, and \\cal R_ij = widetildeu'_iu'j - widetildeu'_iwidetildeu'_j, where u'_i=u_i-tildeu_i. The alignment between \\cal L_ij and tildeS_ij again exhibits the bi-modal trend, and the alignment angle is about 40^o. The alignment between \\cal R_ij and tildeS_ij, on the other hand, is similar to an eddy viscosity configuration, even though the pdf peak is fairly broad. The strongest alignment is between the most contracting tildeS_ij eigenvector and the most extensive \\cal R_ij eigenvector. These trends exist throughout conditional samplings based on several resolved scale parameters. Surprisingly, of the three contributors to τ_ij^d, the cross stress \\cal C_ij shows the least significant alignment trends with tildeS_ij. Analysis of the alignment of the vorticity vector with \\calL_ij, \\cal C_ij, and \\cal R_ij will also be presented.
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.
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
Highly entangled tensor networks
NASA Astrophysics Data System (ADS)
Gu, Yingfei; Bulmash, Daniel; Qi, Xiao-Liang
Tensor network states are used to represent many-body quantum state, e.g., a ground state of local Hamiltonian. In this talk, we will provide a systematic way to produce a family of highly entangled tensor network states. These states are entangled in a special way such that the entanglement entropy of a subsystem follows the Ryu-Takayanagi formula, i.e. the entropy is proportional to the minimal area geodesic surface bounding the boundary region. Our construction also provide an intuitive understanding of the Ryu-Takayanagi formula by relating it to a wave propagation process. We will present examples in various geometries.
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.
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
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.
Tensor visualizations in computational geomechanics
NASA Astrophysics Data System (ADS)
Jeremi, Boris; Scheuermann, Gerik; Frey, Jan; Yang, Zhaohui; Hamann, Bernd; Joy, Kenneth I.; Hagen, Hans
2002-08-01
We present a novel technique for visualizing tensors in three dimensional (3D) space. Of particular interest is the visualization of stress tensors resulting from 3D numerical simulations in computational geomechanics. To this end we present three different approaches to visualizing tensors in 3D space, namely hedgehogs, hyperstreamlines and hyperstreamsurfaces. We also present a number of examples related to stress distributions in 3D solids subjected to single and load couples. In addition, we present stress visualizations resulting from single-pile and pile-group computations. The main objective of this work is to investigate various techniques for visualizing general Cartesian tensors of rank 2 and it's application to geomechanics problems.
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.
NASA Astrophysics Data System (ADS)
Wang, Ling; Gu, Zheng-Cheng; Verstraete, Frank; Wen, Xiang-Gang
We study this model using the cluster update algorithm for tensor product states (TPSs). We find that the ground state energies at finite sizes and in the thermodynamic limit are in good agreement with the exact diagonalization study. At the largest bond dimension available D = 9 and through finite size scaling of the magnetization order near the transition point, we accurately determine the critical point J2c1 = 0 . 53 (1) J1 and the critical exponents β = 0 . 50 (4) . In the intermediate region we find a paramagnetic ground state without any static valence bond solid (VBS) order, supported by an exponentially decaying spin-spin correlation while a power law decaying dimer-dimer correlation. By fitting a universal scaling function for the spin-spin correlation we find the critical exponents ν = 0 . 68 (3) and ηs = 0 . 34 (6) , which is very close to the observed critical exponents for deconfined quantum critical point (DQCP) in other systems. Thus our numerical results strongly suggest a Landau forbidden phase transition from Neel order to VBS order at J2c1 = 0 . 53 (1) J1 . This project is supported by the EU Strep project QUEVADIS, the ERC Grant QUERG, and the FWF SFB Grants FoQuS and ViCoM; and the Institute for Quantum Information and Matter.
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.
NASA Astrophysics Data System (ADS)
Brown, Eric
2008-10-01
Some of the most beautiful and complex theories in physics are formulated in the language of tensors. While powerful, these methods are sometimes daunting to the uninitiated. I will introduce the use of Clifford Algebra as a practical alternative to the use of tensors. Many physical quantities can be represented in an indexless form. The boundary between the classical and the quantum worlds becomes a little more transparent. I will review some key concepts, and then talk about some of the things that I am doing with this interesting and powerful tool. Of note to some will be the development of rigid body dynamics for a game engine. Others may be interested in expressing the connection on a spin bundle. My intent is to prove to the audience that there exists an accessible mathematical tool that can be employed to probe the most difficult of topics in physics.
Energy Science and Technology Software Center (ESTSC)
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).
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
CAST: Contraction Algorithm for Symmetric Tensors
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.
NASA Astrophysics Data System (ADS)
Bousso, Raphael; Fisher, Zachary; Leichenauer, Stefan; Wall, Aron C.
2016-03-01
We propose a universal inequality that unifies the Bousso bound with the classical focusing theorem. Given a surface σ that need not lie on a horizon, we define a finite generalized entropy Sgen as the area of σ in Planck units, plus the von Neumann entropy of its exterior. Given a null congruence N orthogonal to σ , the rate of change of Sgen per unit area defines a quantum expansion. We conjecture that the quantum expansion cannot increase along N . This extends the notion of universal focusing to cases where quantum matter may violate the null energy condition. Integrating the conjecture yields a precise version of the Strominger-Thompson quantum Bousso bound. Applied to locally parallel light-rays, the conjecture implies a novel inequality, the quantum null energy condition, a lower bound on the stress tensor in terms of the second derivative of the von Neumann entropy. We sketch a proof of the latter relation in quantum field theory.
Tensor Algebra Library for NVidia Graphics Processing Units
Energy Science and Technology Software Center (ESTSC)
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
Tensor Algebra Library for NVidia Graphics Processing Units
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).
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.
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
Stress-directed compositional patterning of SiGe substrates for lateral quantum barrier manipulation
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.
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.
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
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.
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
Tensor network decompositions in the presence of a global symmetry
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.
NASA Astrophysics Data System (ADS)
Kontou, Eleni-Alexandra; Olum, Ken D.
2015-12-01
Quantum inequalities are constraints on how negative the weighted average of the renormalized stress-energy tensor of a quantum field can be. A null-projected quantum inequality can be used to prove the averaged null energy condition, which would then rule out exotic phenomena such as wormholes and time machines. In this work we derive such an inequality for a massless minimally coupled scalar field, working to first order of the Riemann tensor and its derivatives. We then use this inequality to prove the averaged null energy condition on achronal geodesics in a curved background that obeys the null convergence condition.
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.
Reduction of exciton mass by uniaxial stress in GaAs/AlGaAs quantum wells
NASA Astrophysics Data System (ADS)
Loginov, D. K.; Grigoryev, P. S.; Efimov, Yu. P.; Eliseev, S. A.; Lovtcius, V. A.; Petrov, V. V.; Ubyivovk, E. V.; Ignatiev, I. V.
2016-08-01
It is experimentally shown that the pressure applied along the twofold symmetry axis of a heterostructure with a wide GaAs/AlGaAs quantum well leads to considerable modification of the polariton reflectance spectra. This effect is treated as the stress-induced decrease of the heavy-hole exciton mass. Theoretical modeling of the effect supports this assumption. The 5\\%-decrease of the exciton mass is obtained at pressure P=0.23 GPa.
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.
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.
First-Principles calculation of surface stress evolution of Ge quantum dots
NASA Astrophysics Data System (ADS)
Lu, Guang-Hong; Cuma, Martin; Liu, Feng
2004-03-01
Ge quantum dots (huts) form on Si(001) surface after growth of a wetting layer of 3-4 monolayers, having a highly ordered structure bounded by (105) facets. Surface stress/strain plays an important role in their stabilization. Recent experiments [1,2] of Ge growth on Si(105) surface have suggested a continuous evolution toward compression with increasing Ge coverage to stabilize Ge/Si(105) facets. However, quantitative information of surface stress of Ge/Si(105) facet, and hence the surface stress on Ge dots is still lacking, which causes a big gap in our understanding. Therefore, we have performed large-scale first-principles calculations to evaluate evolution of surface energy and surface stress in the Ge-covered Si (105) surface, as a function of Ge coverage. We show a very large tensile surface stress present in clean Si(105) surface induced by surface reconstruction, which continuously evolve toward compression with increasing Ge coverage, confirming the qualitative suggestion by experiments. Quantitatively, only moderate reduction of tensile surface stress occurs for the first two layers of Ge deposition, and the surface stress actually remains to be tensile until 5-layer of Ge coverage. This work is supported by DOE. [1] Y. Fujikawa, K. Akiyama, T. Nagao, T. Sakurai, M.G. Lagally, T. Hashimoto, Y. Morikawa, and K. Terakura, Phys. Rev. Lett. 88, 176101 (2002) [2] P. Raiteri,D.B. Migas, L. Miglio, A. Rastelli, and H. von Kanel, Phys. Rev. Lett. 88, 256103 (2002)
A Communication-Optimal Framework for Contracting Distributed Tensors
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.
Superquadric glyphs for symmetric second-order tensors.
Schultz, Thomas; Kindlmann, Gordon L
2010-01-01
Symmetric second-order tensor fields play a central role in scientific and biomedical studies as well as in image analysis and feature-extraction methods. The utility of displaying tensor field samples has driven the development of visualization techniques that encode the tensor shape and orientation into the geometry of a tensor glyph. With some exceptions, these methods work only for positive-definite tensors (i.e. having positive eigenvalues, such as diffusion tensors). We expand the scope of tensor glyphs to all symmetric second-order tensors in two and three dimensions, gracefully and unambiguously depicting any combination of positive and negative eigenvalues. We generalize a previous method of superquadric glyphs for positive-definite tensors by drawing upon a larger portion of the superquadric shape space, supplemented with a coloring that indicates the quadratic form (including eigenvalue sign). We show that encoding arbitrary eigenvalue magnitudes requires design choices that differ fundamentally from those in previous work on traceless tensors that arise in the study of liquid crystals. Our method starts with a design of 2-D tensor glyphs guided by principles of scale-preservation and symmetry, and creates 3-D glyphs that include the 2-D glyphs in their axis-aligned cross-sections. A key ingredient of our method is a novel way of mapping from the shape space of three-dimensional symmetric second-order tensors to the unit square. We apply our new glyphs to stress tensors from mechanics, geometry tensors and Hessians from image analysis, and rate-of-deformation tensors in computational fluid dynamics. PMID:20975202
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.
NASA Astrophysics Data System (ADS)
Beig, Robert; Krammer, Werner
2004-02-01
For a conformally flat 3-space, we derive a family of linear second-order partial differential operators which sends vectors into trace-free, symmetric 2-tensors. These maps, which are parametrized by conformal Killing vectors on the 3-space, are such that the divergence of the resulting tensor field depends only on the divergence of the original vector field. In particular, these maps send source-free electric fields into TT tensors. Moreover, if the original vector field is the Coulomb field on {\\bb R}^3\\backslash \\lbrace0\\rbrace , the resulting tensor fields on {\\bb R}^3\\backslash \\lbrace0\\rbrace are nothing but the family of TT tensors originally written by Bowen and York.
Bandgap tuning with thermal residual stresses induced in a quantum dot.
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
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.
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.
Uni10: an open-source library for tensor network algorithms
NASA Astrophysics Data System (ADS)
Kao, Ying-Jer; Hsieh, Yun-Da; Chen, Pochung
2015-09-01
We present an object-oriented open-source library for developing tensor network algorithms written in C++ called Uni10. With Uni10, users can build a symmetric tensor from a collection of bonds, while the bonds are constructed from a list of quantum numbers associated with different quantum states. It is easy to label and permute the indices of the tensors and access a block associated with a particular quantum number. Furthermore a network class is used to describe arbitrary tensor network structure and to perform network contractions efficiently. We give an overview of the basic structure of the library and the hierarchy of the classes. We present examples of the construction of a spin-1 Heisenberg Hamiltonian and the implementation of the tensor renormalization group algorithm to illustrate the basic usage of the library. The library described here is particularly well suited to explore and fast prototype novel tensor network algorithms and to implement highly efficient codes for existing algorithms.
Orthogonal tensor decompositions
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].
Residual stress induced crystalline to amorphous phase transformation in Nb2O5 quantum dots
NASA Astrophysics Data System (ADS)
Dhawan, Sahil; Dhawan, Tanuj; Vedeshwar, Agnikumar G.
2014-07-01
Nb2O5 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 Nb2O5 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 (∂Eg/∂P)T = -29.3 meV/GPa. From this study, the crystalline to amorphous transformation in tetragonal form of M-Nb2O5 has been determined to be at about 14 GPa. Both pressure coefficient of band gap and crystalline to amorphous transition for tetragonal M-Nb2O5 have been determined for the first time in the literature.
Coordinate independent expression for transverse trace-free tensors
NASA Astrophysics Data System (ADS)
Conboye, Rory
2016-01-01
The transverse and trace-free (TT) part of the extrinsic curvature represents half of the dynamical degrees of freedom of the gravitational field in the 3 + 1 formalism. As such, it is part of the freely specifiable initial data for numerical relativity. Though TT tensors in three-space possess only two component degrees of freedom, they cannot ordinarily be given solely by two scalar potentials. Such expressions have been derived, however, in coordinate form, for all TT tensors in flat space which are also translationally or axially symmetric (Conboye and Murchadha 2014 Class. Quantum Grav. 31 085019). Since TT tensors are conformally covariant, these also give TT tensors in conformally flat space. In this article, the work above has been extended by giving a coordinate-independent expression for these TT tensors. The translational and axial symmetry conditions have also been generalized to invariance along any hypersurface orthogonal Killing vector.
Ground state fidelity from tensor network representations.
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
Anomalous photoluminescence in CdSe quantum-dot solids at high pressure due to nonuniform stress.
Grant, Christian D; Crowhurst, Jonathan C; Hamel, Sebastien; Williamson, Andrew J; Zaitseva, Natalia
2008-06-01
The application of static high pressure provides a means to precisely control and investigate many fundamental and unique properties of nanoparticles. CdSe is a model quantum-dot system, the behavior of which under high pressure has been extensively studied; however, the effect of nonuniform stresses on this system has not been fully appreciated. Photoluminescence data obtained from CdSe quantum-dot solids in different stress environments varying from purely uniform to highly nonuniform are presented. Small deviations from a uniform stress distribution profoundly affect the electronic properties of this system. In nonuniform stress environments, a pronounced flattening of the photoluminescence enegy is observed above 3 GPa. The observations are validated with theoretical calculations obtained using an all-atom semiempirical pseudopotential technique. This effect must be considered when investigating other potentially pressure-mediated phenomena. PMID:18481798
Tensor hypercontraction. II. Least-squares renormalization.
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
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.
Complex responses to Si quantum dots accumulation in carp liver tissue: Beyond oxidative stress.
Serban, Andreea Iren; Stanca, Loredana; Sima, Cornelia; Staicu, Andrea Cristina; Zarnescu, Otilia; Dinischiotu, Anca
2015-09-01
The use of quantum dots (QDs) in biomedical applications is limited due to their inherent toxicity caused by the heavy metal core of the particles. Consequently, silicon-based QDs are expected to display diminished toxicity. We investigated the in vivo effects induced by Si/SiO2 QDs intraperitoneally injected in crucian carp liver. The QDs contained a crystalline Si core encased in a SiO2 shell, with a size between 2.75 and 11.25nm and possess intrinsic fluorescence (Ex 325nm/Em ∼690nm). Tissue fluorescence microscopy analysis revealed the presence of QDs in the liver for at least 2weeks after injection. Although protein and lipid oxidative stress markers showed the onset of oxidative stress, the hepatic tissue exhibited significant antioxidant adaptations (increase of antioxidant enzymes, recovery of glutathione levels), sustained by the activation of Hsp30 and Hsp70 chaperoning proteins. The increased activity of cyclooxigenase-2 (COX-2) and matrix metalloproteinases (MMPs) support the idea that Si/SiO2 QDs have a potential to induce inflammatory response, a scenario also indicated by the profile of Hsp60 and Hsp90 heat shock proteins. MMPs profile and the recovery of oxidative stress markers suggested a tissue remodelation phase after 3weeks from QDs administration. PMID:26079203
Quantum Efficiency Loss after PID Stress: Wavelength Dependence on Cell Surface and Cell Edge
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.
Quantum mechanics based multiscale modeling of stress-induced phase transformations in iron
NASA Astrophysics Data System (ADS)
Lew, A.; Caspersen, K.; Carter, E. A.; Ortiz, M.
2006-06-01
The ground state crystal structure of Fe, ferromagnetic body-centered cubic (bcc), undergoes a stress-induced martensitic phase transformation to a hexagonally close-packed (hcp) structure. Both bcc and hcp have been observed to coexist over a large range deformations, such that the nonlinearities in the constitutive behavior of each phase need to be included for an accurate description. We present herein a methodology to construct high-fidelity quantum mechanics based nonlinear elastic energy densities, amenable to be included in microstructural optimization procedures like sequential lamination. We use the model to show that the transition pressure (TP) has a strong dependence on relatively small amounts of shear deformation, and to investigate the value of the TP under uniaxial compressions, presumably found in shock-loaded materials. Results hint that more complex deformation patterns may need be present to be consistent with measured experimental values.
NASA Astrophysics Data System (ADS)
Palmkvist, Jakob
2014-01-01
We introduce an infinite-dimensional Lie superalgebra which is an extension of the U-duality Lie algebra of maximal supergravity in D dimensions, for 3 ⩽ D ⩽ 7. The level decomposition with respect to the U-duality Lie algebra gives exactly the tensor hierarchy of representations that arises in gauge deformations of the theory described by an embedding tensor, for all positive levels p. We prove that these representations are always contained in those coming from the associated Borcherds-Kac-Moody superalgebra, and we explain why some of the latter representations are not included in the tensor hierarchy. The most remarkable feature of our Lie superalgebra is that it does not admit a triangular decomposition like a (Borcherds-)Kac-Moody (super)algebra. Instead the Hodge duality relations between level p and D - 2 - p extend to negative p, relating the representations at the first two negative levels to the supersymmetry and closure constraints of the embedding tensor.
Palmkvist, Jakob
2014-01-15
We introduce an infinite-dimensional Lie superalgebra which is an extension of the U-duality Lie algebra of maximal supergravity in D dimensions, for 3 ⩽ D ⩽ 7. The level decomposition with respect to the U-duality Lie algebra gives exactly the tensor hierarchy of representations that arises in gauge deformations of the theory described by an embedding tensor, for all positive levels p. We prove that these representations are always contained in those coming from the associated Borcherds-Kac-Moody superalgebra, and we explain why some of the latter representations are not included in the tensor hierarchy. The most remarkable feature of our Lie superalgebra is that it does not admit a triangular decomposition like a (Borcherds-)Kac-Moody (super)algebra. Instead the Hodge duality relations between level p and D − 2 − p extend to negative p, relating the representations at the first two negative levels to the supersymmetry and closure constraints of the embedding tensor.
Faster identification of optimal contraction sequences for tensor networks.
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. PMID:25314572
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.
Visualizing Tensor Normal Distributions at Multiple Levels of Detail.
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
NASA Astrophysics Data System (ADS)
Ghaffarnejad, H.; Neyad, H.; Mojahedi, M. A.
2013-08-01
We obtain renormalized stress tensor of a mass-less, charge-less dynamical quantum scalar field, minimally coupled with a spherically symmetric static Lukewarm black hole. In two dimensional analog the minimal coupling reduces to the conformal coupling and the stress tensor is found to be determined by the nonlocal contribution of the anomalous trace and some additional parameters in close relation to the work presented by Christensen and Fulling. Lukewarm black holes are a special class of Reissner-Nordström-de Sitter space times where its electric charge is equal to its mass. Having the obtained renormalized stress tensor we attempt to obtain a time-independent solution of the well known metric back reaction equation. Mathematical derivations predict that the final state of an evaporating quantum Lukewarm black hole reduces to a remnant stable mini black hole with moved locations of the horizons. Namely the perturbed black hole (cosmological) horizon is compressed (extended) to scales which is smaller (larger) than the corresponding classical radius of the event horizons. Hence there is not obtained an deviation on the cosmic sensor-ship hypothesis.
Conformal killing tensors and covariant Hamiltonian dynamics
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.
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.
Evaluation of Bayesian tensor estimation using tensor coherence
NASA Astrophysics Data System (ADS)
Kim, Dae-Jin; Kim, In-Young; Jeong, Seok-Oh; Park, Hae-Jeong
2009-06-01
Fiber tractography, a unique and non-invasive method to estimate axonal fibers within white matter, constructs the putative streamlines from diffusion tensor MRI by interconnecting voxels according to the propagation direction defined by the diffusion tensor. This direction has uncertainties due to the properties of underlying fiber bundles, neighboring structures and image noise. Therefore, robust estimation of the diffusion direction is essential to reconstruct reliable fiber pathways. For this purpose, we propose a tensor estimation method using a Bayesian framework, which includes an a priori probability distribution based on tensor coherence indices, to utilize both the neighborhood direction information and the inertia moment as regularization terms. The reliability of the proposed tensor estimation was evaluated using Monte Carlo simulations in terms of accuracy and precision with four synthetic tensor fields at various SNRs and in vivo human data of brain and calf muscle. Proposed Bayesian estimation demonstrated the relative robustness to noise and the higher reliability compared to the simple tensor regression.
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.
Quantum field theory in spaces with closed time-like curves. [Gott space
Boulware, D.G.
1992-01-01
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 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.
Quantum field theory in spaces with closed time-like curves
Boulware, D.G.
1992-12-31
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.
Gogny interactions with tensor terms
NASA Astrophysics Data System (ADS)
Anguiano, M.; Lallena, A. M.; Co', G.; De Donno, V.; Grasso, M.; Bernard, R. N.
2016-07-01
We present a perturbative approach to include tensor terms in the Gogny interaction. We do not change the values of the usual parameterisations, with the only exception of the spin-orbit term, and we add tensor terms whose only free parameters are the strengths of the interactions. We identify observables sensitive to the presence of the tensor force in Hartree-Fock, Hartree-Fock-Bogoliubov and random phase approximation calculations. We show the need of including two tensor contributions, at least: a pure tensor term and a tensor-isospin term. We show results relevant for the inclusion of the tensor term for single-particle energies, charge-conserving magnetic excitations and Gamow-Teller excitations.
Mott, P.H.; Argon, A.S. ); Suter, U.W. Massachusetts Institute of Technology, Cambridge, MA )
1992-07-01
A definition of the local atomic strain increments in three dimensions and an algorithm for computing them is presented. An arbitrary arrangement of atoms is tessellated in to Delaunay tetrahedra, identifying interstices, and Voronoi polyhedra, identifying atomic domains. The deformation gradient increment tensor for interstitial space is obtained from the displacement increments of the corner atoms of Delaunay tetrahedra. The atomic site strain increment tensor is then obtained by finding the intersection of the Delaunay tetrahedra with the Voronoi polyhedra, accumulating the individual deformation gradient contributions of the intersected Delaunay tetrahedra into the Voronoi polyhedra. An example application is discussed, showing how the atomic strain clarifies the relative local atomic movement for a polymeric glass treated at the atomic level. 6 refs. 10 figs.
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.
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
Tensor part of the Skyrme energy density functional: Spherical nuclei
NASA Astrophysics Data System (ADS)
Lesinski, T.; Bender, M.; Bennaceur, K.; Duguet, T.; Meyer, J.
2007-07-01
We perform a systematic study of the impact of the J2 tensor term in the Skyrme energy functional on properties of spherical nuclei. In the Skyrme energy functional, the tensor terms originate from both zero-range central and tensor forces. We build a set of 36 parametrizations, covering a wide range of the parameter space of the isoscalar and isovector tensor term coupling constants with a fit protocol very similar to that of the successful SLy parametrizations. We analyze the impact of the tensor terms on a large variety of observables in spherical mean-field calculations, such as the spin-orbit splittings and single-particle spectra of doubly-magic nuclei, the evolution of spin-orbit splittings along chains of semi-magic nuclei, mass residuals of spherical nuclei, and known anomalies of radii. The major findings of our study are as follows: (i) Tensor terms should not be added perturbatively to existing parametrizations; a complete refit of the entire parameter set is imperative. (ii) The free variation of the tensor terms does not lower the χ2 within a standard Skyrme energy functional. (iii) For certain regions of the parameter space of their coupling constants, the tensor terms lead to instabilities of the spherical shell structure, or even to the coexistence of two configurations with different spherical shell structures. (iv) The standard spin-orbit interaction does not scale properly with the principal quantum number, such that single-particle states with one or several nodes have too large spin-orbit splittings, whereas those of nodeless intruder levels are tentatively too small. Tensor terms with realistic coupling constants cannot cure this problem. (v) Positive values of the coupling constants of proton-neutron and like-particle tensor terms allow for a qualitative description of the evolution of spin-orbit splittings in chains of Ca, Ni, and Sn isotopes. (vi) For the same values of the tensor term coupling constants, however, the overall agreement of
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
Quantum fluctuations of radiation pressure
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.
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.
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.
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.
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.
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
A hierarchy of topological tensor network states
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.
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.
Competition between the tensor light shift and nonlinear Zeeman effect
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.
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.
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
The proton nuclear magnetic shielding tensors in biphenyl: experiment and theory.
Schönborn, Frank; Schmitt, Heike; Zimmermann, Herbert; Haeberlen, Ulrich; Corminboeuf, Clémence; Grossmann, Gisbert; Heine, Thomas
2005-07-01
Line-narrowing multiple pulse techniques are applied to a spherical sample crystal of biphenyl. The 10 different proton shielding tensors in this compound are determined. The accuracy level for the tensor components is 0.3 ppm. The assignment of the measured tensors to the corresponding proton sites is given careful attention. Intermolecular shielding contributions are calculated by the induced magnetic point dipole model with empirical atom and bond susceptibilities (distant neighbours) and by a new quantum chemical method (near neighbours). Subtracting the intermolecular contributions from the (correctly assigned) measured shielding tensors leads to isolated-molecule shielding tensors for which there are symmetry relations. Compliance to these relations is the criterion for the correct assignment. The success of this program indicates that intermolecular proton shielding contributions can be calculated to better than 0.5 ppm. The isolated-molecule shielding tensors obtained from experiment and calculated intermolecular contributions are compared with isolated-molecule quantum chemical results. Expressed in the icosahedral tensor representation, the rms differences of the respective tensor components are below 0.5 ppm for all proton sites in biphenyl. In the isolated molecule, the least shielded direction of all protons is the perpendicular to the molecular plane. For the para proton, the intermediate principal direction is along the C-H bond. It is argued that these relations also hold for the protons in the isolated benzene molecule. PMID:15949748
Quantum reverse hypercontractivity
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.
MATLAB tensor classes for fast algorithm prototyping.
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.
NASA Astrophysics Data System (ADS)
Su, Dan; Dou, Xiuming; Wu, Xuefei; Liao, Yongping; Zhou, Pengyu; Ding, Kun; Ni, Haiqiao; Niu, Zhichuan; Zhu, Haijun; Jiang, Desheng; Sun, Baoquan
2016-04-01
Exciton and biexciton emission energies as well as excitonic fine-structure splitting (FSS) in single InAs/GaAs quantum dots (QDs) have been continuously tuned in situ in an optical cryostat using a developed uniaxial stress device. With increasing tensile stress, the red shift of excitonic emission is up to 5 nm; FSS decreases firstly and then increases monotonically, reaching a minimum value of approximately 10 μeV; biexciton binding energy decreases from 460 to 106 μeV. This technique provides a simple and convenient means to tune QD structural symmetry, exciton energy and biexciton binding energy and can be used for generating entangled and indistinguishable photons.
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.
Moment tensors of ten witwatersrand mine tremors
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.
Visualizing second order tensor fields with hyperstreamlines
NASA Technical Reports Server (NTRS)
Delmarcelle, Thierry; Hesselink, Lambertus
1993-01-01
Hyperstreamlines are a generalization to second order tensor fields of the conventional streamlines used in vector field visualization. As opposed to point icons commonly used in visualizing tensor fields, hyperstreamlines form a continuous representation of the complete tensor information along a three-dimensional path. This technique is useful in visulaizing both symmetric and unsymmetric three-dimensional tensor data. Several examples of tensor field visualization in solid materials and fluid flows are provided.
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.
Diffusion tensor image registration using tensor geometry and orientation features.
Yang, Jinzhong; Shen, Dinggang; Davatzikos, Christos; Verma, Ragini
2008-01-01
This paper presents a method for deformable registration of diffusion tensor (DT) images that integrates geometry and orientation features into a hierarchical matching framework. The geometric feature is derived from the structural geometry of diffusion and characterizes the shape of the tensor in terms of prolateness, oblateness, and sphericity of the tensor. Local spatial distributions of the prolate, oblate, and spherical geometry are used to create an attribute vector of geometric feature for matching. The orientation feature improves the matching of the WM fiber tracts by taking into account the statistical information of underlying fiber orientations. These features are incorporated into a hierarchical deformable registration framework to develop a diffusion tensor image registration algorithm. Extensive experiments on simulated and real brain DT data establish the superiority of this algorithm for deformable matching of diffusion tensors, thereby aiding in atlas creation. The robustness of the method makes it potentially useful for group-based analysis of DT images acquired in large studies to identify disease-induced and developmental changes. PMID:18982691
Quantum fields in curved spacetime
NASA Astrophysics Data System (ADS)
Hollands, Stefan; Wald, Robert M.
2015-04-01
We review the theory of quantum fields propagating in an arbitrary, classical, globally hyperbolic spacetime. Our review emphasizes the conceptual issues arising in the formulation of the theory and presents known results in a mathematically precise way. Particular attention is paid to the distributional nature of quantum fields, to their local and covariant character, and to microlocal spectrum conditions satisfied by physically reasonable states. We review the Unruh and Hawking effects for free fields, as well as the behavior of free fields in deSitter spacetime and FLRW spacetimes with an exponential phase of expansion. We review how nonlinear observables of a free field, such as the stress-energy tensor, are defined, as well as time-ordered-products. The "renormalization ambiguities" involved in the definition of time-ordered products are fully characterized. Interacting fields are then perturbatively constructed. Our main focus is on the theory of a scalar field, but a brief discussion of gauge fields is included. We conclude with a brief discussion of a possible approach towards a nonperturbative formulation of quantum field theory in curved spacetime and some remarks on the formulation of quantum gravity.
Proof of the quantum null energy condition
NASA Astrophysics Data System (ADS)
Bousso, Raphael; Fisher, Zachary; Koeller, Jason; Leichenauer, Stefan; Wall, Aron C.
2016-01-01
We prove the quantum null energy condition (QNEC), a lower bound on the stress tensor in terms of the second variation in a null direction of the entropy of a region. The QNEC arose previously as a consequence of the quantum focusing conjecture, a proposal about quantum gravity. The QNEC itself does not involve gravity, so a proof within quantum field theory is possible. Our proof is somewhat nontrivial, suggesting that there may be alternative formulations of quantum field theory that make the QNEC more manifest. Our proof applies to free and super-renormalizable bosonic field theories, and to any points that lie on stationary null surfaces. An example is Minkowski space, where any point p and null vector ka define a null plane N (a Rindler horizon). Given any codimension-2 surface Σ that contains p and lies on N , one can consider the von Neumann entropy Sout of the quantum state restricted to one side of Σ . A second variation Sout'' can be defined by deforming Σ along N , in a small neighborhood of p with area A . The QNEC states that ⟨Tk k(p )⟩≥ℏ/2 π lim A →0 Sout''/A .
A Framework for Load Balancing of Tensor Contraction Expressions via Dynamic Task Partitioning
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.
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.
Invariant Crease Lines for Topological and Structural Analysis of Tensor Fields
Tricoche, Xavier; Kindlmann, Gordon; Westin, Carl-Fredrik
2009-01-01
We introduce a versatile framework for characterizing and extracting salient structures in three-dimensional symmetric second-order tensor fields. The key insight is that degenerate lines in tensor fields, as defined by the standard topological approach, are exactly crease (ridge and valley) lines of a particular tensor invariant called mode. This reformulation allows us to apply well-studied approaches from scientific visualization or computer vision to the extraction of topological lines in tensor fields. More generally, this main result suggests that other tensor invariants, such as anisotropy measures like fractional anisotropy (FA), can be used in the same framework in lieu of mode to identify important structural properties in tensor fields. Our implementation addresses the specific challenge posed by the non-linearity of the considered scalar measures and by the smoothness requirement of the crease manifold computation. We use a combination of smooth reconstruction kernels and adaptive refinement strategy that automatically adjust the resolution of the analysis to the spatial variation of the considered quantities. Together, these improvements allow for the robust application of existing ridge line extraction algorithms in the tensor context of our problem. Results are proposed for a diffusion tensor MRI dataset, and for a benchmark stress tensor field used in engineering research. PMID:18989019
Srivastava, Swati; Pant, Aakanksha; Trivedi, Shalini; Pandey, Rakesh
2016-03-01
Curcumin (CUR) and β-caryophellene (BCP) are well known bioactive phytomolecules which are known to reduce oxidative stress in living organisms. Therefore, the present study was envisaged to explore the possible effects of CUR and BCP in suppression of cadmium quantum dots (CdTe QDs) induced toxicity in Caenorhabditis elegans. CdTe QD are luminescent nanoparticles extensively exploited for in vivo imaging, but long term bioaccumulation confer deleterious effects on living organisms. The 24-h LC50 and LC100 of CdTe QD were found to be 18.40μg/ml and 100μg/ml respectively. The CdTe QD exposure elevated HSP-16.2 expression mediating induction of the stress response. The CdTe QD lethality was due to increment in ROS and decline in SOD and GST expression. The present study demonstrates improved survival in BCP (50μM) and CUR (20μM) treated worms by over 60% (P<0.01) and 50% (P<0.029) in CdTe QD (100μg/ml) exposed worms. Furthermore, BCP and CUR attenuate oxidative stress triggered by QD. The present study for the first time demonstrates CdTe QD toxicity remediation via BCP and CUR. The future investigations can unravel underlying protective effects of phytomolceules for remediating cyotoxicolgical effects of QDs. PMID:26773363
Tensor Target Polarization at TRIUMF
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.
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.
... sudden negative change, such as losing a job, divorce, or illness Traumatic stress, which happens when you ... stress, so you can avoid more serious health effects. NIH: National Institute of Mental Health
Spacetimes with Semisymmetric Energy-Momentum Tensor
NASA Astrophysics Data System (ADS)
De, U. C.; Velimirović, Ljubica
2015-06-01
The object of the present paper is to introduce spacetimes with semisymmetric energy-momentum tensor. At first we consider the relation R( X, Y)ṡ T=0, that is, the energy-momentum tensor T of type (0,2) is semisymmetric. It is shown that in a general relativistic spacetime if the energy-momentum tensor is semisymmetric, then the spacetime is also Ricci semisymmetric and the converse is also true. Next we characterize the perfect fluid spacetime with semisymmetric energy-momentum tensor. Then, we consider conformally flat spacetime with semisymmetric energy-momentum tensor. Finally, we cited some examples of spacetimes admitting semisymmetric energy-momentum tensor.
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.
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.
Bounds on corner entanglement in quantum critical states
NASA Astrophysics Data System (ADS)
Bueno, Pablo; Witczak-Krempa, William
2016-01-01
The entanglement entropy in many gapless quantum systems receives a contribution from the corners in the entangling surface in 2+1d, which is characterized by a universal function a (θ ) depending on the opening angle θ , and contains pertinent low energy information. For conformal field theories (CFTs), the leading expansion coefficient in the smooth limit θ →π yields the stress tensor two-point function coefficient CT. Little is known about a (θ ) beyond that limit. Here, we show that the next term in the smooth limit expansion contains information beyond the two- and three-point correlators of the stress tensor. We conjecture that it encodes four-point data, making it much richer. Further, we establish strong constraints on this and higher-order smooth-limit coefficients. We also show that a (θ ) is lower-bounded by a nontrivial function multiplied by the central charge CT, e.g., a (π /2 ) ≥(π2ln2 ) CT/6 . This bound for 90-degree corners is nearly saturated by all known results, including recent numerics for the interacting Wilson-Fisher quantum critical points (QCPs). A bound is also given for the Rényi entropies. We illustrate our findings using O(N ) QCPs, free boson and Dirac fermion CFTs, strongly coupled holographic ones, and other models. Exact results are also given for Lifshitz quantum critical points, and for conical singularities in 3+1d.
Quantum games as quantum types
NASA Astrophysics Data System (ADS)
Delbecque, Yannick
In this thesis, we present a new model for higher-order quantum programming languages. The proposed model is an adaptation of the probabilistic game semantics developed by Danos and Harmer [DH02]: we expand it with quantum strategies which enable one to represent quantum states and quantum operations. Some of the basic properties of these strategies are established and then used to construct denotational semantics for three quantum programming languages. The first of these languages is a formalisation of the measurement calculus proposed by Danos et al. [DKP07]. The other two are new: they are higher-order quantum programming languages. Previous attempts to define a denotational semantics for higher-order quantum programming languages have failed. We identify some of the key reasons for this and base the design of our higher-order languages on these observations. The game semantics proposed in this thesis is the first denotational semantics for a lambda-calculus equipped with quantum types and with extra operations which allow one to program quantum algorithms. The results presented validate the two different approaches used in the design of these two new higher-order languages: a first one where quantum states are used through references and a second one where they are introduced as constants in the language. The quantum strategies presented in this thesis allow one to understand the constraints that must be imposed on quantum type systems with higher-order types. The most significant constraint is the fact that abstraction over part of the tensor product of many unknown quantum states must not be allowed. Quantum strategies are a new mathematical model which describes the interaction between classical and quantum data using system-environment dialogues. The interactions between the different parts of a quantum system are described using the rich structure generated by composition of strategies. This approach has enough generality to be put in relation with other
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.
Variational Monte Carlo simulations using tensor-product projected states
NASA Astrophysics Data System (ADS)
Sikora, Olga; Chang, Hsueh-Wen; Chou, Chung-Pin; Pollmann, Frank; Kao, Ying-Jer
2015-04-01
We propose an efficient numerical method, which combines the advantages of recently developed tensor-network based methods and standard trial wave functions, to study the ground-state properties of quantum many-body systems. In this approach, we apply a projector in the form of a tensor-product operator to an input wave function, such as a Jastrow-type or Hartree-Fock wave function, and optimize the tensor elements via variational Monte Carlo. The entanglement already contained in the input wave function can considerably reduce the bond dimensions compared to the regular tensor-product state representation. In particular, this allows us to also represent states that do not obey the area law of entanglement entropy. In addition, for fermionic systems, the fermion sign structure can be encoded in the input wave function. We show that the optimized states provide good approximations of the ground-state energy and correlation functions in the cases of two-dimensional bosonic and fermonic systems.
Spherical tensor analysis of nuclear magnetic resonance signals.
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
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.
Tensor mode backreaction during slow-roll inflation
NASA Astrophysics Data System (ADS)
Marozzi, G.; Vacca, G. P.
2014-08-01
We consider the backreaction of the long wavelength tensor modes produced during a slow-roll inflationary regime driven by a single scalar field in a spatially flat Friedmann-Lemaître-Robertson-Walker background geometry. We investigate the effects on nonlocal observables such as the effective (averaged) expansion rate and equation of state at second order in cosmological perturbation theory. The coupling between scalar and tensor perturbations induces at second-order new tensor backreaction terms beyond the one already present in a de Sitter background. We analyze in detail the effects seen by the class of observers comoving with the inflaton field (taken as a clock) and the class of free-falling observers. In both cases the quantum backreaction is at least 1/ɛ (with ɛ the slow-roll parameter) larger than the one which can be naively inferred from a de Sitter background. In particular, we compute the effect for a free massive inflaton model and obtain in both cases a quantum correction on the background expansion rate of the order of H4/(m2MPl2). A short discussion on the issue of the breakdown of perturbation theory is given.
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.
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.
Viability of vector-tensor theories of gravity
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.
NASA Astrophysics Data System (ADS)
Wéber, Zoltán
2009-08-01
Linear inversion of three-component waveform data for the time-varying moment tensor rate functions (MTRFs) is a powerful method for studying seismic sources. After finding the MTRFs, however, we should try to represent an earthquake by just one moment tensor and one source time function (STF), if possible. This approach is particularly justified when dealing with weak local events. Unfortunately, extraction of a moment tensor and STF from the MTRFs is essentially a non-linear inverse problem. In this paper, we introduce an iterative Lp norm minimization technique to retrieve the best moment tensor and STF from the MTRFs obtained by waveform inversion. To allow only forward slip during the rupture process, we impose a positivity constraint on the STF. The error analysis, carried out by using Monte Carlo simulation, allows us to estimate and display the uncertainties of the retrieved source parameters. On the basis of the resulting moment tensor uncertainties, the statistical significance of the double-couple, compensated linear vector dipole and volumetric parts of the solution can be readily assessed. Tests on synthetic data indicate that the proposed algorithm gives good results for both simple and complex sources. Confidence zones for the retrieved STFs are usually fairly large. The mechanisms, on the other hand, are mostly well resolved. The scalar seismic moments are also determined with acceptable accuracy. If the MTRFs cannot resolve the complex nature of a source, the method yields the average source mechanism. If the subevents are well separated in time, their mechanisms can be estimated by appropriately splitting the MTRFs into subintervals. The method has also been applied to two local earthquakes that occurred in Hungary. The isotropic component of the moment tensor solutions is insignificant, implying the tectonic nature of the investigated events. The principal axes of the source mechanisms agree well with the main stress pattern published for the
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.
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.
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).
An efficient tensor transpose algorithm for multicore CPU, Intel Xeon Phi, and NVidia Tesla GPU
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).
An efficient tensor transpose algorithm for multicore CPU, Intel Xeon Phi, and NVidia Tesla GPU
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
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.
Constraint algebra of general relativity from a formal continuum limit of canonical tensor model
NASA Astrophysics Data System (ADS)
Sasakura, Naoki; Sato, Yuki
2015-10-01
Canonical tensor model (CTM for short below) is a rank-three tensor model formulated as a totally constrained system in the canonical formalism. In the classical case, the constraints form a first-class constraint Poisson algebra with structures similar to that of the ADM formalism of general relativity, qualifying CTM as a possible discrete formalism for quantum gravity. In this paper, we show that, in a formal continuum limit, the constraint Poisson algebra of CTM with no cosmological constant exactly reproduces that of the ADM formalism. To this end, we obtain the expression of the metric tensor field in general relativity in terms of one of the dynamical rank-three tensors in CTM, and determine the correspondence between the constraints of CTM and those of the ADM formalism. On the other hand, the cosmological constant term of CTM seems to induce non-local dynamics, and is inconsistent with an assumption about locality of the continuum limit.
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.
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.
Gravitational scalar-tensor theory
NASA Astrophysics Data System (ADS)
Naruko, Atsushi; Yoshida, Daisuke; Mukohyama, Shinji
2016-05-01
We consider a new form of gravity theories in which the action is written in terms of the Ricci scalar and its first and second derivatives. Despite the higher derivative nature of the action, the theory is ghost-free under an appropriate choice of the functional form of the Lagrangian. This model possesses 2 + 2 physical degrees of freedom, namely 2 scalar degrees and 2 tensor degrees. We exhaust all such theories with the Lagrangian of the form f(R,{({{\
Nontraditional tensor decompositions and applications.
Bader, Brett William
2010-07-01
This presentation will discuss two tensor decompositions that are not as well known as PARAFAC (parallel factors) and Tucker, but have proven useful in informatics applications. Three-way DEDICOM (decomposition into directional components) is an algebraic model for the analysis of 3-way arrays with nonsymmetric slices. PARAFAC2 is a related model that is less constrained than PARAFAC and allows for different objects in one mode. Applications of both models to informatics problems will be shown.
Local virial and tensor theorems.
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
Random Tensors and Planted Cliques
NASA Astrophysics Data System (ADS)
Brubaker, S. Charles; Vempala, Santosh S.
The r-parity tensor of a graph is a generalization of the adjacency matrix, where the tensor’s entries denote the parity of the number of edges in subgraphs induced by r distinct vertices. For r = 2, it is the adjacency matrix with 1’s for edges and - 1’s for nonedges. It is well-known that the 2-norm of the adjacency matrix of a random graph is O(sqrt{n}). Here we show that the 2-norm of the r-parity tensor is at most f(r)sqrt{n}log^{O(r)}n, answering a question of Frieze and Kannan [1] who proved this for r = 3. As a consequence, we get a tight connection between the planted clique problem and the problem of finding a vector that approximates the 2-norm of the r-parity tensor of a random graph. Our proof method is based on an inductive application of concentration of measure.
Generalised tensor fluctuations and inflation
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.
QIN, YU; WANG, HUAN; LIU, ZHENG-YUN; LIU, JIE; WU, JIN-ZHU
2015-01-01
Realgar (As4S4) has been used in traditional Chinese medicines for treatment of malignancies. However, the poor water solubility of realgar limits its clinical application. To overcome this problem, realgar quantum dots (RQDs; 5.48±1.09 nm) were prepared by a photoluminescence method. The mean particle size was characterized by high-resolution transmission electron microscopy and scanning electron microscopy. Our recent studies revealed that the RQDs were effective against tumor growth in tumor-bearing mice without producing apparent toxicity. The present study investigated their anticancer effects and mechanisms in human hepatocellular carcinoma (HepG2) cells. The HepG2 cells and human normal liver (L02) cells were used to determine the cytotoxicity of RQDs. The portion of apoptotic and dead cells were measured by flow cytometry with Annexin V-fluorescein isothiocyanate/propidium iodide double staining. Apoptosis-related proteins and genes were examined by western blot analysis and reverse transcription-quantitative polymerase chain reaction, and the mitochondrial membrane potential was assayed by confocal microscope with JC-1 as a probe. RQDs exhibited cytotoxicity in a concentration-dependent manner and HepG2 cells were more sensitive compared with normal L02 cells. At 15 µg/ml, 20% of the cells were apoptotic, while 60% of the cells were necrotic at 30 µg/ml. The anti-apoptosis protein Bcl-2 was dose-dependently decreased, while pro-apoptotic protein Bax was increased. There was a loss of mitochondrial membrane potential and expression of the stress genes C/EBP-homologous protein 10 and glucose-regulated protein 78 was increased by RQDs. RQDs were effective in the inhibition of HepG2 cell proliferation and this effect was due to induction of apoptosis and necrosis through endoplasmic reticulum stress. PMID:26405541
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
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.
Sparse alignment for robust tensor learning.
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
Tensor SOM and tensor GTM: Nonlinear tensor analysis by topographic mappings.
Iwasaki, Tohru; Furukawa, Tetsuo
2016-05-01
In this paper, we propose nonlinear tensor analysis methods: the tensor self-organizing map (TSOM) and the tensor generative topographic mapping (TGTM). TSOM is a straightforward extension of the self-organizing map from high-dimensional data to tensorial data, and TGTM is an extension of the generative topographic map, which provides a theoretical background for TSOM using a probabilistic generative model. These methods are useful tools for analyzing and visualizing tensorial data, especially multimodal relational data. For given n-mode relational data, TSOM and TGTM can simultaneously organize a set of n-topographic maps. Furthermore, they can be used to explore the tensorial data space by interactively visualizing the relationships between modes. We present the TSOM algorithm and a theoretical description from the viewpoint of TGTM. Various TSOM variations and visualization techniques are also described, along with some applications to real relational datasets. Additionally, we attempt to build a comprehensive description of the TSOM family by adapting various data structures. PMID:26991392
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.
Quantum Gravity in More than Four Dimensions.
NASA Astrophysics Data System (ADS)
Vaz, Cenalo
Ever since its inception, Einstein's general relativity has been considered a most remarkable theory. It is generally believed today, that the classical theory is well understood. Nevertheless, in the pursuit of a deeper understanding of physics in terms of a 'grand' unification of forces, one would like to quantize the theory, thus bringing it under the known forces of nature. We will address the possibility that space-time is of dimension greater that four. In the pursuit of Einstein's dream of a unification of physical interactions, many interesting ideas have been developed. Beginning with Weyl and Kaluza, we have progressed to strings and superstrings. The thing that is common to all these theories is the requirement of a space-time of more than four dimensions. To explain the apparent dimensionality of space-time, the extra dimensions are thought to form some compact manifold of extremely small characteristic size. While Kaluza's theory implicitly assumes that Einstein's gravity is classically correct in any number of dimensions, superstring phenomenology may suggest otherwise. Generalizations to Einstein's gravity are indicated, and the gravitational Casimir energy is explicitly approximated on a background configuration M^4 times S^6, on a ten dimensional space-time. Weyl invariance is particularly interesting to the quantum gravitationalist. One finds that energy momentum tensor of the Weyl invariant quantum field picks up an anomalous trace, which is related to particle production by the curved background. We therefore compute the conformal anomaly for a conformally coupled scalar field and consider some of its consequences. We then suggest that the conformal anomaly, when combined with the perfect fluid hypothesis, can be used to determine the complete energy momentum tensor of the quantum field in certain backgrounds. Christensen has suggested that by imposing some 'natural' conditions to be obeyed by the renormalized stress tensor, one could avoid most
Optimizing Tensor Contraction Expressions for Hybrid CPU-GPU Execution
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.
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.
Bayes method for low rank tensor estimation
NASA Astrophysics Data System (ADS)
Suzuki, Taiji; Kanagawa, Heishiro
2016-03-01
We investigate the statistical convergence rate of a Bayesian low-rank tensor estimator, and construct a Bayesian nonlinear tensor estimator. The problem setting is the regression problem where the regression coefficient forms a tensor structure. This problem setting occurs in many practical applications, such as collaborative filtering, multi-task learning, and spatio-temporal data analysis. The convergence rate of the Bayes tensor estimator is analyzed in terms of both in-sample and out-of-sample predictive accuracies. It is shown that a fast learning rate is achieved without any strong convexity of the observation. Moreover, we extend the tensor estimator to a nonlinear function estimator so that we estimate a function that is a tensor product of several functions.
Gravitoelectromagnetic analogy based on tidal tensors
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.
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.
Inflationary tensor perturbations after BICEP2.
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