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-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.
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.
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
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.
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.
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
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.
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
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
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.
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.
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.
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.
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
2015-03-01
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
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
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.
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
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).
Tensor Algebra Library for NVidia Graphics Processing Units
2015-03-16
This is a general purpose math library implementing basic tensor algebra operations on NVidia GPU accelerators. This software is a tensor algebra library that can perform basic tensor algebra operations, including tensor contractions, tensor products, tensor additions, etc., on NVidia GPU accelerators, asynchronously with respect to the CPU host. It supports a simultaneous use of multiple NVidia GPUs. Each asynchronous API function returns a handle which can later be used for querying the completion ofmore » the corresponding tensor algebra operation on a specific GPU. The tensors participating in a particular tensor operation are assumed to be stored in local RAM of a node or GPU RAM. The main research area where this library can be utilized is the quantum many-body theory (e.g., in electronic structure theory).« less
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.
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.
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)
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].
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.
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.
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
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.
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.
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.
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. [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.
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.
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.
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.
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.
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
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
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.
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.
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.
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.
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,{({{\
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
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.
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.
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
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.
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
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.
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.
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.
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
Wormholes, the weak energy condition, and scalar-tensor gravity
NASA Astrophysics Data System (ADS)
Shaikh, Rajibul; Kar, Sayan
2016-07-01
We obtain a large class of Lorentzian wormhole spacetimes in scalar-tensor gravity, for which the matter stress energy does satisfy the weak energy condition. Our constructions have zero Ricci scalar and an everywhere finite, nonzero scalar field profile. Interpreting the scalar-tensor gravity as an effective on-brane theory resulting from a two-brane Randall-Sundrum model of warped extra dimensions, it is possible to link wormhole existence with that of extra dimensions. We study the geometry, matter content, gravitational redshift and circular orbits in such wormholes and argue that our examples are perhaps among those which may have some observational relevance in astrophysics in the future. We also study traversability and find that our wormholes are indeed traversable for values of the metric parameters satisfying the weak energy condition.
Some classes of renormalizable tensor models
NASA Astrophysics Data System (ADS)
Geloun, Joseph Ben; Livine, Etera R.
2013-08-01
We identify new families of renormalizable tensor models from anterior renormalizable tensor models via a mapping capable of reducing or increasing the rank of the theory without having an effect on the renormalizability property. Mainly, a version of the rank 3 tensor model as defined by Ben Geloun and Samary [Ann. Henri Poincare 14, 1599 (2013); e-print arXiv:1201.0176 [hep-th
Curvature tensors unified field equations on SEXn
NASA Astrophysics Data System (ADS)
Chung, Kyung Tae; Lee, Il Young
1988-09-01
We study the curvature tensors and field equations in the n-dimensional SE manifold SEXn. We obtain several basic properties of the vectors S λ and U λ and then of the SE curvature tensor and its contractions, such as a generalized Ricci identity, a generalized Bianchi identity, and two variations of the Bianchi identity satisfied by the SE Einstein tensor. Finally, a system of field equations is discussed in SEXn and one of its particular solutions is constructed and displayed.
Anisotropic fractional diffusion tensor imaging
Meerschaert, Mark M; Magin, Richard L; Ye, Allen Q
2015-01-01
Traditional diffusion tensor imaging (DTI) maps brain structure by fitting a diffusion model to the magnitude of the electrical signal acquired in magnetic resonance imaging (MRI). Fractional DTI employs anomalous diffusion models to obtain a better fit to real MRI data, which can exhibit anomalous diffusion in both time and space. In this paper, we describe the challenge of developing and employing anisotropic fractional diffusion models for DTI. Since anisotropy is clearly present in the three-dimensional MRI signal response, such models hold great promise for improving brain imaging. We then propose some candidate models, based on stochastic theory.
A uniform parameterization of moment tensors
NASA Astrophysics Data System (ADS)
Tape, C.; Tape, W.
2015-12-01
A moment tensor is a 3 x 3 symmetric matrix that expresses an earthquake source. We construct a parameterization of the five-dimensional space of all moment tensors of unit norm. The coordinates associated with the parameterization are closely related to moment tensor orientations and source types. The parameterization is uniform, in the sense that equal volumes in the coordinate domain of the parameterization correspond to equal volumes of moment tensors. Uniformly distributed points in the coordinate domain therefore give uniformly distributed moment tensors. A cartesian grid in the coordinate domain can be used to search efficiently over moment tensors. We find that uniformly distributed moment tensors have uniformly distributed orientations (eigenframes), but that their source types (eigenvalue triples) are distributed so as to favor double couples. An appropriate choice of a priori moment tensor probability is a prerequisite for parameter estimation. As a seemingly sensible choice, we consider the homogeneous probability, in which equal volumes of moment tensors are equally likely. We believe that it will lead to improved characterization of source processes.
Fast stray field computation on tensor grids
Exl, L.; Auzinger, W.; Bance, S.; Gusenbauer, M.; Reichel, F.; Schrefl, T.
2012-01-01
A direct integration algorithm is described to compute the magnetostatic field and energy for given magnetization distributions on not necessarily uniform tensor grids. We use an analytically-based tensor approximation approach for function-related tensors, which reduces calculations to multilinear algebra operations. The algorithm scales with N4/3 for N computational cells used and with N2/3 (sublinear) when magnetization is given in canonical tensor format. In the final section we confirm our theoretical results concerning computing times and accuracy by means of numerical examples. PMID:24910469
Spectral expansions of homogeneous and isotropic tensor-valued random fields
NASA Astrophysics Data System (ADS)
Malyarenko, Anatoliy; Ostoja-Starzewski, Martin
2016-06-01
We establish spectral expansions of tensor-valued homogeneous and isotropic random fields in terms of stochastic integrals with respect to orthogonal scattered random measures previously known only for the case of tensor rank 0. The fields under consideration take values in the 3-dimensional Euclidean space {E^3} and in the space {S^2(E^3)} of symmetric rank 2 tensors over {E^3}. We find a link between the theory of random fields and the theory of finite-dimensional convex compact sets. These random fields furnish stepping-stone for models of rank 1 and rank 2 tensor-valued fields in continuum physics, such as displacement, velocity, stress, strain, providing appropriate conditions (such as the governing equation or positive-definiteness) are imposed.
Some remarks on the genesis of scalar-tensor theories
NASA Astrophysics Data System (ADS)
Goenner, Hubert
2012-08-01
Between 1941 and 1962, scalar-tensor theories of gravitation were suggested four times by different scientists in four different countries. The earliest originator, the Swiss mathematician W. Scherrer, was virtually unknown until now whereas the chronologically latest pair gave their names to a multitude of publications on Brans-Dicke theory. P. Jordan, one of the pioneers of quantum mechanics and quantum field theory, and Y. Thiry, known by his book on celestial mechanics, a student of the mathematician Lichnerowicz, complete the quartet. Diverse motivations for and conceptual interpretations of their theories will be discussed as well as relations among them. Also, external factors like language, citation habits, or closeness to the mainstream are considered. It will become clear why Brans-Dicke theory, although structurally a déjà-vu, superseded all the other approaches.
Elliptic Relaxation of a Tensor Representation of the Pressure-Strain and Dissipation Rate
NASA Technical Reports Server (NTRS)
Carlson, John R.; Gatski, Thomas B.
2002-01-01
A formulation to include the effects of wall-proximity in a second moment closure model is presented that utilizes a tensor representation for the redistribution term in the Reynolds stress equations. 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. DNS data and Reynolds stress solutions using a full differential approach at channel Reynolds number of 590 are compared to the new model.
3D reconstruction of tensors and vectors
Defrise, Michel; Gullberg, Grant T.
2005-02-17
Here we have developed formulations for the reconstruction of 3D tensor fields from planar (Radon) and line-integral (X-ray) projections of 3D vector and tensor fields. Much of the motivation for this work is the potential application of MRI to perform diffusion tensor tomography. The goal is to develop a theory for the reconstruction of both Radon planar and X-ray or line-integral projections because of the flexibility of MRI to obtain both of these type of projections in 3D. The development presented here for the linear tensor tomography problem provides insight into the structure of the nonlinear MRI diffusion tensor inverse problem. A particular application of tensor imaging in MRI is the potential application of cardiac diffusion tensor tomography for determining in vivo cardiac fiber structure. One difficulty in the cardiac application is the motion of the heart. This presents a need for developing future theory for tensor tomography in a motion field. This means developing a better understanding of the MRI signal for diffusion processes in a deforming media. The techniques developed may allow the application of MRI tensor tomography for the study of structure of fiber tracts in the brain, atherosclerotic plaque, and spine in addition to fiber structure in the heart. However, the relations presented are also applicable to other fields in medical imaging such as diffraction tomography using ultrasound. The mathematics presented can also be extended to exponential Radon transform of tensor fields and to other geometric acquisitions such as cone beam tomography of tensor fields.
NASA Astrophysics Data System (ADS)
Orús, Román
2014-10-01
This is a partly non-technical introduction to selected topics on tensor network methods, based on several lectures and introductory seminars given on the subject. It should be a good place for newcomers to get familiarized with some of the key ideas in the field, specially regarding the numerics. After a very general introduction we motivate the concept of tensor network and provide several examples. We then move on to explain some basics about Matrix Product States (MPS) and Projected Entangled Pair States (PEPS). Selected details on some of the associated numerical methods for 1d and 2d quantum lattice systems are also discussed.
Nonlocal correction to the energy-momentum tensor for φ 3 theory in six dimensions
NASA Astrophysics Data System (ADS)
Wu, Feng
2015-10-01
Applying the background field method, we construct by explicit computation the leading-order nonlocal quantum correction to the on-shell effective action for φ ^3 theory in six dimensions. We then use the resulting action to obtain the nonlocal correction to the energy-momentum tensor. At leading order, we find that this nonlocal correction modifies the virial current when the scalar field is minimally coupled to gravity. This is to be compared to the classically Weyl invariant case, where it only corrects the traceless part of the energy-momentum tensor.
Ji, Qingbin; Li, Lei; Zhang, Wei; Wang, Jia; Liu, Peichi; Xie, Yahong; Yan, Tongxing; Yang, Wei; Chen, Weihua; Hu, Xiaodong
2016-08-24
The existence of high threading dislocation density (TDD) in GaN-based epilayers is a long unsolved problem, which hinders further applications of defect-sensitive GaN-based devices. Multiple-modulation of epitaxial lateral overgrowth (ELOG) is used to achieve high-quality GaN template on a novel serpentine channel patterned sapphire substrate (SCPSS). The dislocation blocking brought by the serpentine channel patterned mask, coupled with repeated dislocation bending, can reduce the dislocation density to a yet-to-be-optimized level of ∼2 × 10(5) to 2 × 10(6) cm(-2). About 80% area utilization rate of GaN with low TDD and stress relaxation is obtained. The periodical variations of dislocation density, optical properties and residual stress in GaN-based epilayers on SCPSS are analyzed. The quantum efficiency of InGaN/GaN multiple quantum wells (MQWs) on it can be increased by 52% compared with the conventional sapphire substrate. The reduced nonradiative recombination centers, the enhanced carrier localization, and the suppressed quantum confined Stark effect, are the main determinants of improved luminous performance in MQWs on SCPSS. This developed ELOG on serpentine shaped mask needs no interruption and regrowth, which can be a promising candidate for the heteroepitaxy of semipolar/nonpolar GaN and GaAs with high quality. PMID:27484167
Chambers, David W
2008-01-01
We all experience stress as a regular, and sometimes damaging and sometimes useful, part of our daily lives. In our normal ups and downs, we have our share of exhaustion, despondency, and outrage--matched with their corresponding positive moods. But burnout and workaholism are different. They are chronic, dysfunctional, self-reinforcing, life-shortening habits. Dentists, nurses, teachers, ministers, social workers, and entertainers are especially susceptible to burnout; not because they are hard-working professionals (they tend to be), but because they are caring perfectionists who share control for the success of what they do with others and perform under the scrutiny of their colleagues (they tend to). Workaholics are also trapped in self-sealing cycles, but the elements are ever-receding visions of control and using constant activity as a barrier against facing reality. This essay explores the symptoms, mechanisms, causes, and successful coping strategies for burnout and workaholism. It also takes a look at the general stress response on the physiological level and at some of the damage American society inflicts on itself. PMID:18846841
Asymmetric tensor analysis for flow visualization.
Zhang, Eugene; Yeh, Harry; Lin, Zhongzang; Laramee, Robert S
2009-01-01
The gradient of a velocity vector field is an asymmetric tensor field which can provide critical insight that is difficult to infer from traditional trajectory-based vector field visualization techniques. We describe the structures in the eigenvalue and eigenvector fields of the gradient tensor and how these structures can be used to infer the behaviors of the velocity field. To illustrate the structures in asymmetric tensor fields, we introduce the notions of eigenvalue and eigenvector manifolds. These concepts afford a number of theoretical results that clarify the connections between symmetric and antisymmetric components in tensor fields. In addition, these manifolds naturally lead to partitions of tensor fields, which we use to design effective visualization strategies. Both eigenvalue manifold and eigenvector manifold are supported by a tensor reparameterization with physical meaning. This allows us to relate our tensor analysis to physical quantities such as rotation, angular deformation, and dilation, which provide physical interpretation of our tensor-driven vector field analysis in the context of fluid mechanics. To demonstrate the utility of our approach, we have applied our visualization techniques and interpretation to the study of the Sullivan Vortex as well as computational fluid dynamics simulation data. PMID:19008559
Matrix Representation and Tensor Analysis of Courses
ERIC Educational Resources Information Center
Tait, W. H.
1975-01-01
A discussion of how a tensor theory can be adapted to provide a fully quantitative analysis of a social system. A social tensor is developed from the physical analogue and used to analyze the structure of an education course. (Author/HB)
Inflation and alternatives with blue tensor spectra
Wang, Yi; Xue, Wei E-mail: wei.xue@sissa.it
2014-10-01
We study the tilt of the primordial gravitational waves spectrum. A hint of blue tilt is shown from analyzing the BICEP2 and POLARBEAR data. Motivated by this, we explore the possibilities of blue tensor spectra from the very early universe cosmology models, including null energy condition violating inflation, inflation with general initial conditions, and string gas cosmology, etc. For the simplest G-inflation, blue tensor spectrum also implies blue scalar spectrum. In general, the inflation models with blue tensor spectra indicate large non-Gaussianities. On the other hand, string gas cosmology predicts blue tensor spectrum with highly Gaussian fluctuations. If further experiments do confirm the blue tensor spectrum, non-Gaussianity becomes a distinguishing test between inflation and alternatives.
NASA Astrophysics Data System (ADS)
Malecki, A.; Potdevin, G.; Biernath, T.; Eggl, E.; Willer, K.; Lasser, T.; Maisenbacher, J.; Gibmeier, J.; Wanner, A.; Pfeiffer, F.
2014-02-01
Here we introduce a new concept for x-ray computed tomography that yields information about the local micro-morphology and its orientation in each voxel of the reconstructed 3D tomogram. Contrary to conventional x-ray CT, which only reconstructs a single scalar value for each point in the 3D image, our approach provides a full scattering tensor with multiple independent structural parameters in each volume element. In the application example shown in this study, we highlight that our method can visualize sub-pixel fiber orientations in a carbon composite sample, hence demonstrating its value for non-destructive testing applications. Moreover, as the method is based on the use of a conventional x-ray tube, we believe that it will also have a great impact in the wider range of material science investigations and in future medical diagnostics. The authors declare no competing financial interests.
Depth inpainting by tensor voting.
Kulkarni, Mandar; Rajagopalan, Ambasamudram N
2013-06-01
Depth maps captured by range scanning devices or by using optical cameras often suffer from missing regions due to occlusions, reflectivity, limited scanning area, sensor imperfections, etc. In this paper, we propose a fast and reliable algorithm for depth map inpainting using the tensor voting (TV) framework. For less complex missing regions, local edge and depth information is utilized for synthesizing missing values. The depth variations are modeled by local planes using 3D TV, and missing values are estimated using plane equations. For large and complex missing regions, we collect and evaluate depth estimates from self-similar (training) datasets. We align the depth maps of the training set with the target (defective) depth map and evaluate the goodness of depth estimates among candidate values using 3D TV. We demonstrate the effectiveness of the proposed approaches on real as well as synthetic data. PMID:24323102
NASA Astrophysics Data System (ADS)
Lazar, Markus; Agiasofitou, Eleni
2014-12-01
The present work provides fundamental quantities in generalized elasticity and dislocation theory of quasicrystals. In a clear and straightforward manner, the three-dimensional Green tensor of generalized elasticity theory and the extended displacement vector for an arbitrary extended force are derived. Next, in the framework of dislocation theory of quasicrystals, the solutions of the field equations for the extended displacement vector and the extended elastic distortion tensor are given; that is, the generalized Burgers equation for arbitrary sources and the generalized Mura-Willis formula, respectively. Moreover, important quantities of the theory of dislocations as the Eshelby stress tensor, Peach-Koehler force, stress function tensor and the interaction energy are derived for general dislocations. The application to dislocation loops gives rise to the generalized Burgers equation, where the displacement vector can be written as a sum of a line integral plus a purely geometric part. Finally, using the Green tensor, all other dislocation key-formulas for loops, known from the theory of anisotropic elasticity, like the Peach-Koehler stress formula, Mura-Willis equation, Volterra equation, stress function tensor and the interaction energy are derived for quasicrystals.
Evaluation of the Tensor Polynomial and Hoffman strength theories for composite materials
NASA Technical Reports Server (NTRS)
Narayanaswami, R.; Adelman, H. M.
1977-01-01
The Hoffman theory and the Tensor Polynomial (Tsai-Wu) theory with the stress interaction term set equal to zero have been found to be preferred alternatives to the general Tensor Polynomial theory for predicting strength of filamentary composite laminae. These theories were used to predict failure of off-axis boron/epoxy and E-glass/epoxy test specimens and gave excellent agreement with available experimental results. A numerical experiment was also performed to estimate the errors for ten different composite systems under six different loadings. The maximum error in predicted failure loads among all cases was below 10 percent. These results suggest that the Hoffman failure theory and the Tensor Polynomial theory with the stress interaction term equal to zero can predict failure of practical filamentary composite materials under general biaxial loading with sufficient accuracy for engineering applications.
Advances on tensor network theory: symmetries, fermions, entanglement, and holography
NASA Astrophysics Data System (ADS)
Orús, Román
2014-11-01
This is a short review on selected theory developments on tensor network (TN) states for strongly correlated systems. Specifically, we briefly review the effect of symmetries in TN states, fermionic TNs, the calculation of entanglement Hamiltonians from projected entangled pair states (PEPS), and the relation between the multi-scale entanglement renormalization ansatz (MERA) and the AdS/CFT or gauge/gravity duality. We stress the role played by entanglement in the emergence of several physical properties and objects through the TN language. Some recent results along these lines are also discussed.
Acceleration of Streamed Tensor Contraction Expressions on GPGPU-based Clusters
Ma, Wenjing; Krishnamoorthy, Sriram; Villa, Oreste; Kowalski, Karol
2010-09-20
Tensor contractions are generalized multidimensional matrix multiplication operations that widely occur in quantum chemistry. Efficient execution of tensor contractions on GPUs requires tackling several challenges to be addressed, including index permutation and small dimension-sizes reducing thread block utilization. In this paper, we present our approach to automatically generate CUDA code to execute tensor contractions on GPUs, including management of data movement between CPU and GPU. GPU-enabled code is generated for the most expensive contractions in CCSD(T) and incorporated into NWChem, a popular computational chemistry suite. We demonstrate speedup over a factor of 8.4 using one core per node and over 2.6 when utilizing the entire system using hybrid CPU+GPU solution with 2 GPUs and 5 cores. We finally analyze the behavior of the application on future GPU systems.
A General Method of Selecting Quantum Channel for Bidirectional Quantum Teleportation
NASA Astrophysics Data System (ADS)
Fu, Hong-Zi; Tian, Xiu-Lao; Hu, Yang
2014-06-01
Based on tensor representation and Bell basis measurement in bidirectional quantum teleportation, a criterion that can be used to judge whether a four-qubit quantum state can be regarded as quantum channel or not in bidirectional teleportation is suggested and a theoretical scheme of bidirectional teleportation via four-qubit state as the quantum channel is proposed. In accordance with this criterion we give a general method of selecting quantum channel in bidirectional teleportation, which is determined by the channel parameter matrix R in the Bell basis measurement. This general method provide a theoretical basis for quantum channel selection in bidirectional quantum teleportation experiments.
Ding, F; Singh, R; Plumhof, J D; Zander, T; Krápek, V; Chen, Y H; Benyoucef, M; Zwiller, V; Dörr, K; Bester, G; Rastelli, A; Schmidt, O G
2010-02-12
We study the effect of an external biaxial stress on the light emission of single InGaAs/GaAs(001) quantum dots placed onto piezoelectric actuators. With increasing compression, the emission blueshifts and the binding energies of the positive trion (X+) and biexciton (XX) relative to the neutral exciton (X) show a monotonic increase. This phenomenon is mainly ascribed to changes in electron and hole localization and it provides a robust method to achieve color coincidence in the emission of X and XX, which is a prerequisite for the possible generation of entangled photon pairs via the recently proposed "time reordering" scheme. PMID:20366855
NASA Astrophysics Data System (ADS)
Sameer, M. Ikhdair; Majid, Hamzavi
2013-09-01
Approximate analytical solutions of the Dirac equation for Tietz—Hua (TH) potential including Coulomb-like tensor (CLT) potential with arbitrary spin—orbit quantum number κ are obtained within the Pekeris approximation scheme to deal with the spin—orbit coupling terms κ(κ ± 1)r-2. Under the exact spin and pseudospin symmetric limitation, bound state energy eigenvalues and associated unnormalized two-component wave functions of the Dirac particle in the field of both attractive and repulsive TH potential with tensor potential are found using the parametric Nikiforov—Uvarov (NU) method. The cases of the Morse oscillator with tensor potential, the generalized Morse oscillator with tensor potential, and the non-relativistic limits have been investigated.
Low uncertainty method for inertia tensor identification
NASA Astrophysics Data System (ADS)
Barreto, J. P.; Muñoz, L. E.
2016-02-01
The uncertainty associated with the experimental identification of the inertia tensor can be reduced by implementing adequate rotational and translational motions in the experiment. This paper proposes a particular 3D trajectory that improves the experimental measurement of the inertia tensor of rigid bodies. Such a trajectory corresponds to a motion in which the object is rotated around a large number of instantaneous axes, while the center of gravity remains static. The uncertainty in the inertia tensor components obtained with this practice is reduced by 45% in average, compared with those calculated using simple rotations around three perpendicular axes (Roll, Pitch, Yaw).
Tensor methods for large, sparse unconstrained optimization
Bouaricha, A.
1996-11-01
Tensor methods for unconstrained optimization were first introduced by Schnabel and Chow [SIAM J. Optimization, 1 (1991), pp. 293-315], who describe these methods for small to moderate size problems. This paper extends these methods to large, sparse unconstrained optimization problems. This requires an entirely new way of solving the tensor model that makes the methods suitable for solving large, sparse optimization problems efficiently. We present test results for sets of problems where the Hessian at the minimizer is nonsingular and where it is singular. These results show that tensor methods are significantly more efficient and more reliable than standard methods based on Newton`s method.
Incremental Discriminant Analysis in Tensor Space
Chang, Liu; Weidong, Zhao; Tao, Yan; Qiang, Pu; Xiaodan, Du
2015-01-01
To study incremental machine learning in tensor space, this paper proposes incremental tensor discriminant analysis. The algorithm employs tensor representation to carry on discriminant analysis and combine incremental learning to alleviate the computational cost. This paper proves that the algorithm can be unified into the graph framework theoretically and analyzes the time and space complexity in detail. The experiments on facial image detection have shown that the algorithm not only achieves sound performance compared with other algorithms, but also reduces the computational issues apparently. PMID:26339229
Time Evolution of Modeled Reynolds Stresses in Planar Homogeneous Flows
NASA Technical Reports Server (NTRS)
Jongen, T.; Gatski, T. B.
1997-01-01
The analytic expression of the time evolution of the Reynolds stress anisotropy tensor in all planar homogeneous flows is obtained by exact integration of the modeled differential Reynolds stress equations. The procedure is based on results of tensor representation theory, is applicable for general pressure-strain correlation tensors, and can account for any additional turbulence anisotropy effects included in the closure. An explicit solution of the resulting system of scalar ordinary differential equations is obtained for the case of a linear pressure-strain correlation tensor. The properties of this solution are discussed, and the dynamic behavior of the Reynolds stresses is studied, including limit cycles and sensitivity to initial anisotropies.
ConnesFusionTensorProduct/Photon GluonFusion in Mitochondria
NASA Astrophysics Data System (ADS)
Wh-Maksoed, Prodi Of Physics Ui, Depok 16415-Indonesia; Ssi, Wh-Maksoed
2016-05-01
As in AJ Wassermann distinguished of classical invariant theory & quantum invariant theory subfactor, in S. Palcoux:``From Neveu-Schwarz Subfactors & Connes Fusion'' described the subfactor theory & Witt-algebra whereas Andreas Thom's explanation about ConnesFusionTensorProduct/CFTP related Connes fusion to composition of homomorphism (i). classical tensor product O-X adds the changes,(ii). Relative tensor product H-X preserve the changes. For photonGluonFusion/PGF defined:''photon is the gauge boson of QED, the simplest of all boson'' devotes to CFT as ``quantum field theory which are invariant under conformal transformation & in 2D there are infinite dimensional algebra. Alain Connes states theirselves Connes fusion as ``associative tensor operation'' to be in coincidences with ``their dynamic behavior driven by the balance in mitochondrial fusion & fission (Carveney, 2007) from Peter Alexander Williams: ``Retinal neuronal remodeling in a model of Optic Atrophy'', Dec, 2011. Great acknowledged to the VicePresident of the R.I, HE.Mr. Drs. M. JUSUF KALLA.
Interpretation of the Weyl tensor
NASA Astrophysics Data System (ADS)
Hofmann, Stefan; Niedermann, Florian; Schneider, Robert
2013-09-01
According to folklore in general relativity, the Weyl tensor can be decomposed into parts corresponding to Newton-like, incoming and outgoing wavelike field components. It is shown here that this one-to-one correspondence does not hold for space-time geometries with cylindrical isometries. This is done by investigating some well-known exact solutions of Einstein’s field equations with whole-cylindrical symmetry, for which the physical interpretation is very clear, but for which the standard Weyl interpretation would give contradictory results. For planar or spherical geometries, however, the standard interpretation works for both static and dynamical space-times. It is argued that one reason for the failure in the cylindrical case is that for waves spreading in two spatial dimensions there is no local criterion to distinguish incoming and outgoing waves already at the linear level. It turns out that Thorne’s local energy notion, subject to certain qualifications, provides an efficient diagnostic tool to extract the proper physical interpretation of the space-time geometry in the case of cylindrical configurations.
Diffusion Tensor Imaging of Pedophilia.
Cantor, James M; Lafaille, Sophie; Soh, Debra W; Moayedi, Massieh; Mikulis, David J; Girard, Todd A
2015-11-01
Pedophilia is a principal motivator of child molestation, incurring great emotional and financial burdens on victims and society. Even among pedophiles who never commit any offense,the condition requires lifelong suppression and control. Previous comparison using voxel-based morphometry (VBM)of MR images from a large sample of pedophiles and controls revealed group differences in white matter. The present study therefore sought to verify and characterize white matter involvement using diffusion tensor imaging (DTI), which better captures the microstructure of white matter than does VBM. Pedophilics ex offenders (n=24) were compared with healthy, age-matched controls with no criminal record and no indication of pedophilia (n=32). White matter microstructure was analyzed with Tract-Based Spatial Statistics, and the trajectories of implicated fiber bundles were identified by probabilistic tractography. Groups showed significant, highly focused differences in DTI parameters which related to participants’ genital responses to sexual depictions of children, but not to measures of psychopathy or to childhood histories of physical abuse, sexual abuse, or neglect. Some previously reported gray matter differences were suggested under highly liberal statistical conditions (p(uncorrected)<.005), but did not survive ordinary statistical correction (whole brain per voxel false discovery rate of 5%). These results confirm that pedophilia is characterized by neuroanatomical differences in white matter microstructure, over and above any neural characteristics attributable to psychopathy and childhood adversity, which show neuroanatomic footprints of their own. Although some gray matter structures were implicated previously, only few have emerged reliably. PMID:26494360
Adaptive Multilinear Tensor Product Wavelets.
Weiss, Kenneth; Lindstrom, Peter
2016-01-01
Many foundational visualization techniques including isosurfacing, direct volume rendering and texture mapping rely on piecewise multilinear interpolation over the cells of a mesh. However, there has not been much focus within the visualization community on techniques that efficiently generate and encode globally continuous functions defined by the union of multilinear cells. Wavelets provide a rich context for analyzing and processing complicated datasets. In this paper, we exploit adaptive regular refinement as a means of representing and evaluating functions described by a subset of their nonzero wavelet coefficients. We analyze the dependencies involved in the wavelet transform and describe how to generate and represent the coarsest adaptive mesh with nodal function values such that the inverse wavelet transform is exactly reproduced via simple interpolation (subdivision) over the mesh elements. This allows for an adaptive, sparse representation of the function with on-demand evaluation at any point in the domain. We focus on the popular wavelets formed by tensor products of linear B-splines, resulting in an adaptive, nonconforming but crack-free quadtree (2D) or octree (3D) mesh that allows reproducing globally continuous functions via multilinear interpolation over its cells. PMID:26529742
Vacuum for a massless quantum scalar field outside a collapsing shell in anti-de Sitter space-time
NASA Astrophysics Data System (ADS)
Abel, Paul G.; Winstanley, Elizabeth
2016-08-01
We consider a massless quantum scalar field on a two-dimensional space-time describing a thin shell of matter collapsing to form a Schwarzschild-anti-de Sitter black hole. At early times, before the shell starts to collapse, the quantum field is in the vacuum state, corresponding to the Boulware vacuum on an eternal black hole space-time. The scalar field satisfies reflecting boundary conditions on the anti-de Sitter boundary. Using the Davies-Fulling-Unruh prescription for computing the renormalized expectation value of the stress-energy tensor, we find that at late times the black hole is in thermal equilibrium with a heat bath at the Hawking temperature, so the quantum field is in a state analogous to the Hartle-Hawking vacuum on an eternal black hole space-time.
Potentials for transverse trace-free tensors
NASA Astrophysics Data System (ADS)
Conboye, Rory; Murchadha, Niall Ó.
2014-04-01
In constructing and understanding initial conditions in the 3 + 1 formalism for numerical relativity, the transverse and trace-free (TT) part of the extrinsic curvature plays a key role. We know that TT tensors possess two degrees of freedom per space point. However, finding an expression for a TT tensor depending on only two scalar functions is a non-trivial task. Assuming either axial or translational symmetry, expressions depending on two scalar potentials alone are derived here for all TT tensors in flat 3-space. In a more general spatial slice, only one of these potentials is found, the same potential given in (Baker and Puzio 1999 Phys. Rev. D 59 044030) and (Dain 2001 Phys. Rev. D 64 124002), with the remaining equations reduced to a partial differential equation, depending on boundary conditions for a solution. As an exercise, we also derive the potentials which give the Bowen-York curvature tensor in flat space.
Shifted power method for computing tensor eigenvalues.
Mayo, Jackson R.; Kolda, Tamara Gibson
2010-07-01
Recent work on eigenvalues and eigenvectors for tensors of order m >= 3 has been motivated by applications in blind source separation, magnetic resonance imaging, molecular conformation, and more. In this paper, we consider methods for computing real symmetric-tensor eigenpairs of the form Ax{sup m-1} = lambda x subject to ||x||=1, which is closely related to optimal rank-1 approximation of a symmetric tensor. Our contribution is a shifted symmetric higher-order power method (SS-HOPM), which we show is guaranteed to converge to a tensor eigenpair. SS-HOPM can be viewed as a generalization of the power iteration method for matrices or of the symmetric higher-order power method. Additionally, using fixed point analysis, we can characterize exactly which eigenpairs can and cannot be found by the method. Numerical examples are presented, including examples from an extension of the method to finding complex eigenpairs.
The Weyl tensor correlator in cosmological spacetimes
Fröb, Markus B.
2014-12-01
We give a general expression for the Weyl tensor two-point function in a general Friedmann-Lemaître-Robertson-Walker spacetime. We work in reduced phase space for the perturbations, i.e., quantize only the dynamical degrees of freedom without adding any gauge-fixing term. The general formula is illustrated by a calculation in slow-roll single-field inflation to first order in the slow-roll parameters ε and δ, and the result is shown to have the correct de Sitter limit as ε, δ → 0. Furthermore, it is seen that the Weyl tensor correlation function in slow-roll does not suffer from infrared divergences, unlike the two-point functions of the metric and scalar field perturbations. Lastly, we show how to recover the usual tensor power spectrum from the Weyl tensor correlation function.
The Weyl tensor correlator in cosmological spacetimes
Fröb, Markus B.
2014-12-05
We give a general expression for the Weyl tensor two-point function in a general Friedmann-Lemaître-Robertson-Walker spacetime. We work in reduced phase space for the perturbations, i.e., quantize only the dynamical degrees of freedom without adding any gauge-fixing term. The general formula is illustrated by a calculation in slow-roll single-field inflation to first order in the slow-roll parameters ϵ and δ, and the result is shown to have the correct de Sitter limit as ϵ,δ→0. Furthermore, it is seen that the Weyl tensor correlation function in slow-roll does not suffer from infrared divergences, unlike the two-point functions of the metric and scalar field perturbations. Lastly, we show how to recover the usual tensor power spectrum from the Weyl tensor correlation function.
Shifted power method for computing tensor eigenpairs.
Mayo, Jackson R.; Kolda, Tamara Gibson
2010-10-01
Recent work on eigenvalues and eigenvectors for tensors of order m {>=} 3 has been motivated by applications in blind source separation, magnetic resonance imaging, molecular conformation, and more. In this paper, we consider methods for computing real symmetric-tensor eigenpairs of the form Ax{sup m-1} = {lambda}x subject to {parallel}x{parallel} = 1, which is closely related to optimal rank-1 approximation of a symmetric tensor. Our contribution is a novel shifted symmetric higher-order power method (SS-HOPM), which we showis guaranteed to converge to a tensor eigenpair. SS-HOPM can be viewed as a generalization of the power iteration method for matrices or of the symmetric higher-order power method. Additionally, using fixed point analysis, we can characterize exactly which eigenpairs can and cannot be found by the method. Numerical examples are presented, including examples from an extension of the method to fnding complex eigenpairs.
NASA Astrophysics Data System (ADS)
Babatunde, J. Falaye; Sameer, M. Ikhdair
2013-06-01
The Dirac equation is solved to obtain its approximate bound states for a spin-1/2 particle in the presence of trigonometric Pöschl—Teller (tPT) potential including a Coulomb-like tensor interaction with arbitrary spin—orbit quantum number κ using an approximation scheme to substitute the centrifugal terms κ(κ ± 1)r-2. In view of spin and pseudo-spin (p-spin) symmetries, the relativistic energy eigenvalues and the corresponding two-component wave functions of a particle moving in the field of attractive and repulsive tPT potentials are obtained using the asymptotic iteration method (AIM). We present numerical results in the absence and presence of tensor coupling A and for various values of spin and p-spin constants and quantum numbers n and κ. The non-relativistic limit is also obtained.
The energy-momentum tensor(s) in classical gauge theories
Gieres, Francois; Blaschke, Daniel N.; Reboud, Meril; Schweda, Manfred
2016-07-12
We give an introduction to, and review of, the energy–momentum tensors in classical gauge field theories in Minkowski space, and to some extent also in curved space–time. For the canonical energy–momentum tensor of non-Abelian gauge fields and of matter fields coupled to such fields, we present a new and simple improvement procedure based on gauge invariance for constructing a gauge invariant, symmetric energy–momentum tensor. Here, the relationship with the Einstein–Hilbert tensor following from the coupling to a gravitational field is also discussed.
Novel Physics with Tensor Polarized Deuteron Targets
Slifer, Karl J.; Long, Elena A.
2013-09-01
Development of solid spin-1 polarized targets will open the study of tensor structure functions to precise measurement, and holds the promise to enable a new generation of polarized scattering experiments. In this talk we will discuss a measurement of the leading twist tensor structure function b1, along with prospects for future experiments with a solid tensor polarized target. The recently approved JLab experiment E12-13-011 will measure the lead- ing twist tensor structure function b1, which provides a unique tool to study partonic effects, while also being sensitive to coherent nuclear properties in the simplest nuclear system. At low x, shadowing effects are expected to dominate b1, while at larger values, b1 provides a clean probe of exotic QCD effects, such as hidden color due to 6-quark configuration. Since the deuteron wave function is relatively well known, any non-standard effects are expected to be readily observable. All available models predict a small or vanishing value of b1 at moderate x. However, the first pioneer measurement of b1 at HERMES revealed a crossover to an anomalously large negative value in the region 0.2 < x < 0.5, albeit with relatively large experimental uncertainty. E12-13-011 will perform an inclusive measurement of the deuteron tensor asymmetry in the region 0.16 < x < 0.49, for 0.8 < Q2 < 5.0 GeV2. The UVa solid polarized ND3 target will be used, along with the Hall C spectrometers, and an unpolarized 115 nA beam. This measurement will provide access to the tensor quark polarization, and allow a test of the Close-Kumano sum rule, which vanishes in the absence of tensor polarization in the quark sea. Until now, tensor structure has been largely unexplored, so the study of these quantities holds the potential of initiating a new field of spin physics at Jefferson Lab.
Temperature-polarization correlations from tensor fluctuations
Crittenden, R.G.; Coulson, D.; Turok, N.G. |
1995-11-15
We study the polarization-temperature correlations on the cosmic microwave sky resulting from an initial scale-invariant spectrum of tensor (gravity wave) fluctuations, such as those which might arise during inflation. The correlation function has the opposite sign to that for scalar fluctuations on large scales, raising the possibility of a direct determination of whether the microwave anisotropies have a significant tensor component. We briefly discuss the important problem of estimating the expected foreground contamination.
Visualization of 3-D tensor fields
NASA Technical Reports Server (NTRS)
Hesselink, L.
1996-01-01
Second-order tensor fields have applications in many different areas of physics, such as general relativity and fluid mechanics. The wealth of multivariate information in tensor fields makes them more complex and abstract than scalar and vector fields. Visualization is a good technique for scientists to gain new insights from them. Visualizing a 3-D continuous tensor field is equivalent to simultaneously visualizing its three eigenvector fields. In the past, research has been conducted in the area of two-dimensional tensor fields. It was shown that degenerate points, defined as points where eigenvalues are equal to each other, are the basic singularities underlying the topology of tensor fields. Moreover, it was shown that eigenvectors never cross each other except at degenerate points. Since we live in a three-dimensional world, it is important for us to understand the underlying physics of this world. In this report, we describe a new method for locating degenerate points along with the conditions for classifying them in three-dimensional space. Finally, we discuss some topological features of three-dimensional tensor fields, and interpret topological patterns in terms of physical properties.
Visualization of tensor fields using superquadric glyphs.
Ennis, Daniel B; Kindlman, Gordon; Rodriguez, Ignacio; Helm, Patrick A; McVeigh, Elliot R
2005-01-01
The spatially varying tensor fields that arise in magnetic resonance imaging are difficult to visualize due to the multivariate nature of the data. To improve the understanding of myocardial structure and function a family of objects called glyphs, derived from superquadric parametric functions, are used to create informative and intuitive visualizations of the tensor fields. The superquadric glyphs are used to visualize both diffusion and strain tensors obtained in canine myocardium. The eigensystem of each tensor defines the glyph shape and orientation. Superquadric functions provide a continuum of shapes across four distinct eigensystems (lambda(i), sorted eigenvalues), lambda(1) = lambda(2) = lambda(3) (spherical), lambda(1) < lambda(2) = lambda(3) (oblate), lambda(1) > lambda(2) = lambda(3) (prolate), and lambda(1) > lambda(2) > lambda(3) (cuboid). The superquadric glyphs are especially useful for identifying regions of anisotropic structure and function. Diffusion tensor renderings exhibit fiber angle trends and orthotropy (three distinct eigenvalues). Visualization of strain tensors with superquadric glyphs compactly exhibits radial thickening gradients, circumferential and longitudinal shortening, and torsion combined. The orthotropic nature of many biologic tissues and their DTMRI and strain data require visualization strategies that clearly exhibit the anisotropy of the data if it is to be interpreted properly. Superquadric glyphs improve the ability to distinguish fiber orientation and tissue orthotropy compared to ellipsoids. PMID:15690516
Measuring Nematic Susceptibilities from the Elastoresistivity Tensor
NASA Astrophysics Data System (ADS)
Hristov, A. T.; Shapiro, M. C.; Hlobil, Patrick; Maharaj, Akash; Chu, Jiun-Haw; Fisher, Ian
The elastoresistivity tensor mijkl relates changes in resistivity to the strain on a material. As a fourth-rank tensor, it contains considerably more information about the material than the simpler (second-rank) resistivity tensor; in particular, certain elastoresistivity coefficients can be related to thermodynamic susceptibilities and serve as a direct probe of symmetry breaking at a phase transition. The aim of this talk is twofold. First, we enumerate how symmetry both constrains the structure of the elastoresistivity tensor into an easy-to-understand form and connects tensor elements to thermodynamic susceptibilities. In the process, we generalize previous studies of elastoresistivity to include the effects of magnetic field. Second, we describe an approach to measuring quantities in the elastoresistivity tensor with a novel transverse measurement, which is immune to relative strain offsets. These techniques are then applied to BaFe2As2 in a proof of principle measurement. This work is supported by the Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division, under Contract DE-AC02-76SF00515.
C%2B%2B tensor toolbox user manual.
Plantenga, Todd D.; Kolda, Tamara Gibson
2012-04-01
The C++ Tensor Toolbox is a software package for computing tensor decompositions. It is based on the Matlab Tensor Toolbox, and is particularly optimized for sparse data sets. This user manual briefly overviews tensor decomposition mathematics, software capabilities, and installation of the package. Tensors (also known as multidimensional arrays or N-way arrays) are used in a variety of applications ranging from chemometrics to network analysis. The Tensor Toolbox provides classes for manipulating dense, sparse, and structured tensors in C++. The Toolbox compiles into libraries and is intended for use with custom applications written by users.
Tensor Networks for Lattice Gauge Theories with Continuous Groups
NASA Astrophysics Data System (ADS)
Tagliacozzo, L.; Celi, A.; Lewenstein, M.
2014-10-01
We discuss how to formulate lattice gauge theories in the tensor-network language. In this way, we obtain both a consistent-truncation scheme of the Kogut-Susskind lattice gauge theories and a tensor-network variational ansatz for gauge-invariant states that can be used in actual numerical computations. Our construction is also applied to the simplest realization of the quantum link models or gauge magnets and provides a clear way to understand their microscopic relation with the Kogut-Susskind lattice gauge theories. We also introduce a new set of gauge-invariant operators that modify continuously Rokhsar-Kivelson wave functions and can be used to extend the phase diagrams of known models. As an example, we characterize the transition between the deconfined phase of the Z2 lattice gauge theory and the Rokhsar-Kivelson point of the U (1 ) gauge magnet in 2D in terms of entanglement entropy. The topological entropy serves as an order parameter for the transition but not the Schmidt gap.
Non-monotonicity of Trace Distance Under Tensor Products
NASA Astrophysics Data System (ADS)
Maziero, Jonas
2015-10-01
The trace distance (TD) possesses several of the good properties required for a faithful distance measure in the quantum state space. Despite its importance and ubiquitous use in quantum information science, one of its questionable features, its possible non-monotonicity under taking tensor products of its arguments (NMuTP), has been hitherto unexplored. In this article, we advance analytical and numerical investigations of this issue considering different classes of states living in a discrete and finite dimensional Hilbert space. Our results reveal that although this property of TD does not show up for pure states and for some particular classes of mixed states, it is present in a non-negligible fraction of the regarded density operators. Hence, even though the percentage of quartets of states leading to the NMuTP drawback of TD and its strength decrease as the system's dimension grows, this property of TD must be taken into account before using it as a figure of merit for distinguishing mixed quantum states.
Local Scale Transformations on the Lattice with Tensor Network Renormalization
NASA Astrophysics Data System (ADS)
Evenbly, G.; Vidal, G.
2016-01-01
Consider the partition function of a classical system in two spatial dimensions, or the Euclidean path integral of a quantum system in two space-time dimensions, both on a lattice. We show that the tensor network renormalization algorithm [G. Evenbly and G. Vidal Phys. Rev. Lett. 115, 180405 (2015)] can be used to implement local scale transformations on these objects, namely, a lattice version of conformal maps. Specifically, we explain how to implement the lattice equivalent of the logarithmic conformal map that transforms the Euclidean plane into a cylinder. As an application, and with the 2D critical Ising model as a concrete example, we use this map to build a lattice version of the scaling operators of the underlying conformal field theory, from which one can extract their scaling dimensions and operator product expansion coefficients.
Symmetry-enriched topological invariants from tensor network representations
NASA Astrophysics Data System (ADS)
Ware, Brayden; Cheng, Meng; Bauer, Bela
We examine topologically ordered quantum phases in 2+1 dimensions where in the presence of symmetries the topological phase splits into multiple symmetry enriched topological (SET) phases. These SET phases become adiabatically connected when the symmetry is broken, but are separated by phase transitions when symmetry is enforced. Using tensor network representations of representative wavefunctions for certain SET phases, we demonstrate the calculation of the extended modular matrices, a generalization of the well-known modular matrices that have been used to robustly characterize topological phases in numerical calculations. Here, the crucial extension is to systems with symmetry defects. The extended modular matrices are used to form symmetry-enriched topological invariants which distinguish different SET phases.
Local Scale Transformations on the Lattice with Tensor Network Renormalization.
Evenbly, G; Vidal, G
2016-01-29
Consider the partition function of a classical system in two spatial dimensions, or the Euclidean path integral of a quantum system in two space-time dimensions, both on a lattice. We show that the tensor network renormalization algorithm [G. Evenbly and G. Vidal Phys. Rev. Lett. 115, 180405 (2015)] can be used to implement local scale transformations on these objects, namely, a lattice version of conformal maps. Specifically, we explain how to implement the lattice equivalent of the logarithmic conformal map that transforms the Euclidean plane into a cylinder. As an application, and with the 2D critical Ising model as a concrete example, we use this map to build a lattice version of the scaling operators of the underlying conformal field theory, from which one can extract their scaling dimensions and operator product expansion coefficients. PMID:26871313
Moment tensors of a dislocation in a porous medium
NASA Astrophysics Data System (ADS)
Wang, Zhi; Hu, Hengshan
2016-06-01
A dislocation can be represented by a moment tensor for calculating seismic waves. However, the moment tensor expression was derived in an elastic medium and cannot completely describe a dislocation in a porous medium. In this paper, effective moment tensors of a dislocation in a porous medium are derived. It is found that the dislocation is equivalent to two independent moment tensors, i.e., the bulk moment tensor acting on the bulk of the porous medium and the isotropic fluid moment tensor acting on the pore fluid. Both of them are caused by the solid dislocation as well as the fluid-solid relative motion corresponding to fluid injection towards the surrounding rocks (or fluid outflow) through the fault plane. For a shear dislocation, the fluid moment tensor is zero, and the dislocation is equivalent to a double couple acting on the bulk; for an opening dislocation or fluid injection, the two moment tensors are needed to describe the source. The fluid moment tensor only affects the radiated compressional waves. By calculating the ratio of the radiation fields generated by unit fluid moment tensor and bulk moment tensor, it is found that the fast compressional wave radiated by the bulk moment tensor is much stronger than that radiated by the fluid moment tensor, while the slow compressional wave radiated by the fluid moment tensor is several times stronger than that radiated by the bulk moment tensor.
Non-standard symmetries and quantum anomalies
Visinescu, Anca; Visinescu, Mihai
2008-08-31
Quantum anomalies are investigated on curved spacetimes. The intimate relation between Killing-Yano tensors and non-standard symmetries is pointed out. The gravitational anomalies are absent if the hidden symmetry is associated to a Killing-Yano tensor. The axial anomaly in a background gravitational field is directly related with the index of the Dirac operator. In the Dirac theory on curved spaces, Killing-Yano tensors generate Dirac-type operators involved in interesting algebraic structures. The general results are applied to the 4-dimensional Euclidean Taub-NUT space.
NASA Astrophysics Data System (ADS)
Liu, Ming-Gang; Yang, Yi-Bin; Xiang, Peng; Chen, Wei-Jie; Han, Xiao-Biao; Lin, Xiu-Qi; Lin, Jia-Li; Luo, Hui; Liao, Qiang; Zang, Wen-Jie; Wu, Zhi-Sheng; Liu, Yang; Zhang, Bai-Jun
2015-06-01
The influences of stress on the properties of InGaN/GaN multiple quantum wells (MQWs) grown on silicon substrate were investigated. The different stresses were induced by growing InGaN and AlGaN insertion layers (IL) respectively before the growth of MQWs in metal-organic chemical vapor deposition (MOCVD) system. High resolution x-ray diffraction (HRXRD) and photoluminescence (PL) measurements demonstrated that the InGaN IL introduced an additional tensile stress in n-GaN, which released the strain in MQWs. It is helpful to increase the indium incorporation in MQWs. In comparison with MQWs without the IL, the wavelength shows a red-shift. AlGaN IL introduced a compressive stress to compensate the tensile stress, which reduces the indium composition in MQWs. PL measurement shows a blue-shift of wavelength. The two kinds of ILs were adopted to InGaN/GaN MQWs LED structures. The same wavelength shifts were also observed in the electroluminescence (EL) measurements of the LEDs. Improved indium homogeneity with InGaN IL, and phase separation with AlGaN IL were observed in the light images of the LEDs. Project supported by the National Natural Science Foundation of China (Grant Nos. 61274039 and 51177175), the National Basic Research Program of China (Grant Nos. 2010CB923201 and 2011CB301903), the Ph. D. Program Foundation of the Ministry of Education of China (Grant No. 20110171110021), the International Science and Technology Collaboration Program of China (Grant No. 2012DFG52260), the National High Technology Research and Development Program of China (Grant No. 2014AA032606), the International Science and Technology Collaboration Program of Guangdong Province, China (Grant No. 2013B051000041), and the Opened Fund of the State Key Laboratory on Integrated Optoelectronics (Grant No. IOSKL2014KF17).
Diffusion tensor smoothing through weighted Karcher means.
Carmichael, Owen; Chen, Jun; Paul, Debashis; Peng, Jie
2013-01-01
Diffusion tensor magnetic resonance imaging (MRI) quantifies the spatial distribution of water Diffusion at each voxel on a regular grid of locations in a biological specimen by Diffusion tensors- 3 × 3 positive definite matrices. Removal of noise from DTI is an important problem due to the high scientific relevance of DTI and relatively low signal to noise ratio it provides. Leading approaches to this problem amount to estimation of weighted Karcher means of Diffusion tensors within spatial neighborhoods, under various metrics imposed on the space of tensors. However, it is unclear how the behavior of these estimators varies with the magnitude of DTI sensor noise (the noise resulting from the thermal e!ects of MRI scanning) as well as the geometric structure of the underlying Diffusion tensor neighborhoods. In this paper, we combine theoretical analysis, empirical analysis of simulated DTI data, and empirical analysis of real DTI scans to compare the noise removal performance of three kernel-based DTI smoothers that are based on Euclidean, log-Euclidean, and affine-invariant metrics. The results suggest, contrary to conventional wisdom, that imposing a simplistic Euclidean metric may in fact provide comparable or superior noise removal, especially in relatively unstructured regions and/or in the presence of moderate to high levels of sensor noise. On the contrary, log-Euclidean and affine-invariant metrics may lead to better noise removal in highly structured anatomical regions, especially when the sensor noise is of low magnitude. These findings emphasize the importance of considering the interplay of sensor noise magnitude and tensor field geometric structure when assessing Diffusion tensor smoothing options. They also point to the necessity for continued development of smoothing methods that perform well across a large range of scenarios. PMID:25419264
Lepore, Natasha; Brun, Caroline; Chou, Yi-Yu; Chiang, Ming-Chang; Dutton, Rebecca A.; Hayashi, Kiralee M.; Luders, Eileen; Lopez, Oscar L.; Aizenstein, Howard J.; Toga, Arthur W.; Becker, James T.; Thompson, Paul M.
2009-01-01
This paper investigates the performance of a new multivariate method for tensor-based morphometry (TBM). Statistics on Riemannian manifolds are developed that exploit the full information in deformation tensor fields. In TBM, multiple brain images are warped to a common neuroanatomical template via 3-D nonlinear registration; the resulting deformation fields are analyzed statistically to identify group differences in anatomy. Rather than study the Jacobian determinant (volume expansion factor) of these deformations, as is common, we retain the full deformation tensors and apply a manifold version of Hotelling’s T 2 test to them, in a Log-Euclidean domain. In 2-D and 3-D magnetic resonance imaging (MRI) data from 26 HIV/AIDS patients and 14 matched healthy subjects, we compared multivariate tensor analysis versus univariate tests of simpler tensor-derived indices: the Jacobian determinant, the trace, geodesic anisotropy, and eigenvalues of the deformation tensor, and the angle of rotation of its eigenvectors. We detected consistent, but more extensive patterns of structural abnormalities, with multivariate tests on the full tensor manifold. Their improved power was established by analyzing cumulative p-value plots using false discovery rate (FDR) methods, appropriately controlling for false positives. This increased detection sensitivity may empower drug trials and large-scale studies of disease that use tensor-based morphometry. PMID:18270068
Lepore, N; Brun, C; Chou, Y Y; Chiang, M C; Dutton, R A; Hayashi, K M; Luders, E; Lopez, O L; Aizenstein, H J; Toga, A W; Becker, J T; Thompson, P M
2008-01-01
This paper investigates the performance of a new multivariate method for tensor-based morphometry (TBM). Statistics on Riemannian manifolds are developed that exploit the full information in deformation tensor fields. In TBM, multiple brain images are warped to a common neuroanatomical template via 3-D nonlinear registration; the resulting deformation fields are analyzed statistically to identify group differences in anatomy. Rather than study the Jacobian determinant (volume expansion factor) of these deformations, as is common, we retain the full deformation tensors and apply a manifold version of Hotelling's $T(2) test to them, in a Log-Euclidean domain. In 2-D and 3-D magnetic resonance imaging (MRI) data from 26 HIV/AIDS patients and 14 matched healthy subjects, we compared multivariate tensor analysis versus univariate tests of simpler tensor-derived indices: the Jacobian determinant, the trace, geodesic anisotropy, and eigenvalues of the deformation tensor, and the angle of rotation of its eigenvectors. We detected consistent, but more extensive patterns of structural abnormalities, with multivariate tests on the full tensor manifold. Their improved power was established by analyzing cumulative p-value plots using false discovery rate (FDR) methods, appropriately controlling for false positives. This increased detection sensitivity may empower drug trials and large-scale studies of disease that use tensor-based morphometry. PMID:18270068
ERIC Educational Resources Information Center
Marin Quintero, Maider J.
2013-01-01
The structure tensor for vector valued images is most often defined as the average of the scalar structure tensors in each band. The problem with this definition is the assumption that all bands provide the same amount of edge information giving them the same weights. As a result non-edge pixels can be reinforced and edges can be weakened…
Experimental measurement and modeling analysis on mechanical properties of tensor tympani tendon.
Cheng, Tao; Gan, Rong Z
2008-04-01
In this paper, we report mechanical properties of the tensor tympani tendon of human ear measured from uniaxial tensile, stress relaxation and failure tests. The hyperelastic Ogden model and digital image correlation method were employed to analyze experimental data. The constitutive equation of the tendon was derived through data iteration processes, and Young's modulus was presented as a function of stress. The viscoelastic property of the tendon was described by stress relaxation function and hysteresis. Furthermore, three-dimensional finite element analysis was carried out on five tendon models to investigate relationship between the structure and properties. The dimensions of the tendon were also measured by image processing techniques and presented with statistic significance. The structure and properties of the tensor tympani tendon reported in this study add new data into the study of ear tissue biomechanics. PMID:17553724
Killing-Yano tensors, rank-2 Killing tensors, and conserved quantities in higher dimensions
NASA Astrophysics Data System (ADS)
Krtous, Pavel; Kubiznák, David; Page, Don N.; Frolov, Valeri P.
2007-02-01
From the metric and one Killing-Yano tensor of rank D-2 in any D-dimensional spacetime with such a principal Killing-Yano tensor, we show how to generate k = [(D+1)/2] Killing-Yano tensors, of rank D-2j for all 0 <= j <= k-1, and k rank-2 Killing tensors, giving k constants of geodesic motion that are in involution. For the example of the Kerr-NUT-AdS spacetime (hep-th/0604125) with its principal Killing-Yano tensor (gr-qc/0610144), these constants and the constants from the k Killing vectors give D independent constants in involution, making the geodesic motion completely integrable (hep-th/0611083). The constants of motion are also related to the constants recently obtained in the separation of the Hamilton-Jacobi and Klein-Gordon equations (hep-th/0611245).
Tensor network algorithm by coarse-graining tensor renormalization on finite periodic lattices
NASA Astrophysics Data System (ADS)
Zhao, Hui-Hai; Xie, Zhi-Yuan; Xiang, Tao; Imada, Masatoshi
2016-03-01
We develop coarse-graining tensor renormalization group algorithms to compute physical properties of two-dimensional lattice models on finite periodic lattices. Two different coarse-graining strategies, one based on the tensor renormalization group and the other based on the higher-order tensor renormalization group, are introduced. In order to optimize the tensor network model globally, a sweeping scheme is proposed to account for the renormalization effect from the environment tensors under the framework of second renormalization group. We demonstrate the algorithms by the classical Ising model on the square lattice and the Kitaev model on the honeycomb lattice, and show that the finite-size algorithms achieve substantially more accurate results than the corresponding infinite-size ones.
NASA Astrophysics Data System (ADS)
Magnoni, F.; Scognamiglio, L.; Tinti, E.; Casarotti, E.
2014-12-01
Seismic moment tensor is one of the most important source parameters defining the earthquake dimension and style of the activated fault. Moment tensor catalogues are ordinarily used by geoscientists, however, few attempts have been done to assess possible impacts of moment magnitude uncertainties upon their own analysis. The 2012 May 20 Emilia mainshock is a representative event since it is defined in literature with a moment magnitude value (Mw) spanning between 5.63 and 6.12. An uncertainty of ~0.5 units in magnitude leads to a controversial knowledge of the real size of the event. The possible uncertainty associated to this estimate could be critical for the inference of other seismological parameters, suggesting caution for seismic hazard assessment, coulomb stress transfer determination and other analyses where self-consistency is important. In this work, we focus on the variability of the moment tensor solution, highlighting the effect of four different velocity models, different types and ranges of filtering, and two different methodologies. Using a larger dataset, to better quantify the source parameter uncertainty, we also analyze the variability of the moment tensor solutions depending on the number, the epicentral distance and the azimuth of used stations. We endorse that the estimate of seismic moment from moment tensor solutions, as well as the estimate of the other kinematic source parameters, cannot be considered an absolute value and requires to come out with the related uncertainties and in a reproducible framework characterized by disclosed assumptions and explicit processing workflows.
A confidence parameter for seismic moment tensors
NASA Astrophysics Data System (ADS)
Tape, Walter; Tape, Carl
2016-02-01
Given a moment tensor m inferred from seismic data for an earthquake, we define P(V) to be the probability that the true moment tensor for the earthquake lies in the neighborhood of m that has fractional volume V. The average value of P(V) is then a measure of our confidence in m. The calculation of P(V) requires knowing both the probability hat{P}(ω ) and the fractional volume hat{V}(ω ) of the set of moment tensors within a given angular radius ω of m. We explain how to construct hat{P}(ω ) from a misfit function derived from seismic data, and we show how to calculate hat{V}(ω ), which depends on the set M of moment tensors under consideration. The two most important instances of M are where M is the set of all moment tensors of fixed norm, and where M is the set of all double couples of fixed norm.
A confidence parameter for seismic moment tensors
NASA Astrophysics Data System (ADS)
Tape, Walter; Tape, Carl
2016-05-01
Given a moment tensor m inferred from seismic data for an earthquake, we define P(V) to be the probability that the true moment tensor for the earthquake lies in the neighbourhood of m that has fractional volume V. The average value of P(V) is then a measure of our confidence in m. The calculation of P(V) requires knowing both the probability hat{P}(ω) and the fractional volume hat{V}(ω) of the set of moment tensors within a given angular radius ω of m. We explain how to construct hat{P}(ω) from a misfit function derived from seismic data, and we show how to calculate hat{V}(ω), which depends on the set M of moment tensors under consideration. The two most important instances of M are where M is the set of all moment tensors of fixed norm, and where M is the set of all double couples of fixed norm.
Robust Face Clustering Via Tensor Decomposition.
Cao, Xiaochun; Wei, Xingxing; Han, Yahong; Lin, Dongdai
2015-11-01
Face clustering is a key component either in image managements or video analysis. Wild human faces vary with the poses, expressions, and illumination changes. All kinds of noises, like block occlusions, random pixel corruptions, and various disguises may also destroy the consistency of faces referring to the same person. This motivates us to develop a robust face clustering algorithm that is less sensitive to these noises. To retain the underlying structured information within facial images, we use tensors to represent faces, and then accomplish the clustering task based on the tensor data. The proposed algorithm is called robust tensor clustering (RTC), which firstly finds a lower-rank approximation of the original tensor data using a L1 norm optimization function. Because L1 norm does not exaggerate the effect of noises compared with L2 norm, the minimization of the L1 norm approximation function makes RTC robust. Then, we compute high-order singular value decomposition of this approximate tensor to obtain the final clustering results. Different from traditional algorithms solving the approximation function with a greedy strategy, we utilize a nongreedy strategy to obtain a better solution. Experiments conducted on the benchmark facial datasets and gait sequences demonstrate that RTC has better performance than the state-of-the-art clustering algorithms and is more robust to noises. PMID:25546869
Non-standard symmetries and Killing tensors
NASA Astrophysics Data System (ADS)
Visinescu, Mihai
2009-10-01
Higher order symmetries corresponding to Killing tensors are investigated. The intimate relation between Killing-Yano tensors and non-standard supersymmetries is pointed out. The gravitational anomalies are absent if the hidden symmetry is associated with a Killing-Yano tensor. In the Dirac theory on curved spaces, Killing-Yano tensors generate Dirac type operators involved in interesting algebraic structures as dynamical algebras or even infinite dimensional algebras or superalgebras. The general results are applied to space-times which appear in modern studies. The 4-dimensional Euclidean Taub-NUT space and its generalizations introduced by Iwai and Katayama are analyzed from the point of view of hidden symmetries. One presents the infinite dimensional superalgebra of Dirac type operators on Taub-NUT space that can be seen as a twisted loop algebra. The axial anomaly, interpreted as the index of the Dirac operator, is computed for the generalized Taub-NUT metrics. The existence of the conformal Killing-Yano tensors is investigated for some spaces with mixed Sasakian structures.
Adding stress plot function to NASTRAN
NASA Technical Reports Server (NTRS)
Katoh, S.
1978-01-01
Stress plot function was developed and added to the NASTRAN level 15.5. Computed stress distribution can be displayed by this function, with vectors showing the principal stresses of the finite elements over the specified portions of the structure. NASTRAN is reviewed in the aspect of plotting capabilities. Stress tensor field is examined in preparation of stress display. Then the stress plot function as added to the NASTRAN is described. A sample plotout by this function is shown.
Information Thermodynamics applied to the MERA quantum circuit
NASA Astrophysics Data System (ADS)
Passias, Vasilios; Chua, Victor; Tiwari, Apoorv; Ryu, Shinsei
We interpret the MERA (Multiscale Entanglement Renormalization Ansatz) tensor network as a unitary quantum circuit to study excited states of quantum spin-chains. Contrary to the common use of MERA as a variational ground state ansatz, the quantum circuit defined by MERA - adapted to a fixed ground state - is employed as a diagnostic tool to study dynamically evolving excited state wavefunctions. Outputs of the quantum computation emanating from the isometry tensors, which are normally approximate tensor product states, now fluctuate strongly. These ``bulk'' degrees of freedom in the MERA which act as logical qubits are studied using tools from quantum information theory and information thermodynamics. A local temperature scale based on Landauer's information erasure principle is defined to measure their degree of fluctuation. We investigate properties of this temperature against the expectations of Luttinger's theorem which relates weak field gravity to heat flow. This work was supported by the Gordon and Betty Moore Foundation.
Local anisotropy of fluids using Minkowski tensors
NASA Astrophysics Data System (ADS)
Kapfer, S. C.; Mickel, W.; Schaller, F. M.; Spanner, M.; Goll, C.; Nogawa, T.; Ito, N.; Mecke, K.; Schröder-Turk, G. E.
2010-11-01
Statistics of the free volume available to individual particles have previously been studied for simple and complex fluids, granular matter, amorphous solids, and structural glasses. Minkowski tensors provide a set of shape measures that are based on strong mathematical theorems and easily computed for polygonal and polyhedral bodies such as free volume cells (Voronoi cells). They characterize the local structure beyond the two-point correlation function and are suitable to define indices 0 <= βνa, b <= 1 of local anisotropy. Here, we analyze the statistics of Minkowski tensors for configurations of simple liquid models, including the ideal gas (Poisson point process), the hard disks and hard spheres ensemble, and the Lennard-Jones fluid. We show that Minkowski tensors provide a robust characterization of local anisotropy, which ranges from βνa, b≈0.3 for vapor phases to \\beta_\
NASA Astrophysics Data System (ADS)
Huf, P. A.; Carminati, J.
2015-09-01
In this paper we: (1) introduce TensorPack, a software package for the algebraic manipulation of tensors in covariant index format in Maple; (2) briefly demonstrate the use of the package with an orthonormal tensor proof of the shearfree conjecture for dust. TensorPack is based on the Riemann and Canon tensor software packages and uses their functions to express tensors in an indexed covariant format. TensorPack uses a string representation as input and provides functions for output in index form. It extends the functionality to basic algebra of tensors, substitution, covariant differentiation, contraction, raising/lowering indices, symmetry functions and other accessory functions. The output can be merged with text in the Maple environment to create a full working document with embedded dynamic functionality. The package offers potential for manipulation of indexed algebraic tensor expressions in a flexible software environment.
Limitations of the Concept of Stress in Structural Analysis.
ERIC Educational Resources Information Center
Edelman, Steven Harold
1989-01-01
Provides an introduction and explanations of stress-strain relationships, measuring stress, a goal of structural analysis, and legitimate applications of the concept of stress. Diagrams include a derivation of the stress tensor, graphical representations of stress-strain relations, and related problems. (RT)
Scale Dependence of Equivalent Permeability Tensor in Naturally Fractured Reservoirs
NASA Astrophysics Data System (ADS)
Azizmohammadi, S.; Matthäi, S. K.; Paul, J. D.
2012-04-01
Fracture geometries in naturally fractured reservoirs are usually inferred from sparse subsurface observations from well logs or cores. Since the largest fractures tend to be the least frequent, they are often undersampled. Therefore, interpretations based on samples taken at any scale smaller than that of interest contain a bias, misrepresenting the true characteristics of the fracture system. This bias may lead to the incorrect characterisation of the reservoir, upscaling and gridding. In this work, we investigate the variation of the equivalent permeability and its anisotropy in naturally fractured rocks as a function of sample size. We use a two dimensional linear elastic model of fracture aperture, taking into account the far-field stresses in conjunction with the parallel plate model, to determine fracture permeability. These apertures are applied to fractured reservoir analogues mapped in the field to numerically estimate permeability. We then employ a finite element scheme to compute equivalent permeability tensors for random samples of the fractured porous medium at specific length scales. We find that the distribution of the principle component of equivalent permeability tensor computed at each scale size appears to be dependent upon the underlying attributes of the fracture networks. We notice a clear trend between the mean equivalent permeability and sample size. Our findings suggest that fracture geometries in naturally fractured reservoirs should be sampled at the scales of interest; if not, the equivalent permeability of such reservoirs might be significantly underestimated.
Seismic moment tensor for anisotropic media: implication for Non-double-couple earthquakes
NASA Astrophysics Data System (ADS)
Cai, X.; Chen, X.; Chen, Y.; Cai, M.
2008-12-01
It is often found that the inversion results of seismic moment tensor from real seismic recorded data show the trace of seismic moment tensor M is not zero, a phenomenon called non-double-couple earthquake sources mechanism. Recently we have derived the analytical expressions of M in transversely isotropic media with the titled axis of symmetry and the results shows even only pure shear-motion of fault can lead to the implosive components determined by several combined anisotropic elastic constants. Many non-double-couple earthquakes from observations often appear in volcanic and geothermal areas (Julian, 1998), where there exist a mount of stress-aligned fluid-saturated parallel vertical micro-cracks identical to transversely isotropic media (Crampin, 2008), this stress-aligned crack will modify the seismic moment tensor. In another word, non-double-couple earthquakes don't mean to have a seismic failure movement perpendicular to the fault plane, while traditional research of seismic moment tensor focus on the case of isotropy, which cannot provide correct interpretation of seismic source mechanism. Reference: Julian, B.R., Miller, A.D. and Foulger, G.R., 1998. Non-double-couple earthquakes,1. Theory, Rev. Geophys., 36, 525¨C549. Crampin,S., Peacock,S., 2008, A review of the current understanding of seismic shear-wave splitting in the Earth's crust and common fallacies in interpretation, wave motion, 45,675-722
A q-Analogue of Derivations on the Tensor Algebra and the q-Schur-Weyl Duality
NASA Astrophysics Data System (ADS)
Itoh, Minoru
2015-10-01
This paper presents a q-analogue of an extension of the tensor algebra given by the same author. This new algebra naturally contains the ordinary tensor algebra and the Iwahori-Hecke algebra type A of infinite degree. Namely, this algebra can be regarded as a natural mix of these two algebras. Moreover, we can consider natural "derivations" on this algebra. Using these derivations, we can easily prove the q-Schur-Weyl duality (the duality between the quantum enveloping algebra of the general linear Lie algebra and the Iwahori-Hecke algebra of type A).
Tensor representation techniques in post-Hartree-Fock methods: matrix product state tensor format
NASA Astrophysics Data System (ADS)
Benedikt, Udo; Auer, Henry; Espig, Mike; Hackbusch, Wolfgang; Auer, Alexander A.
2013-09-01
In this proof-of-principle study, we discuss the application of various tensor representation formats and their implications on memory requirements and computational effort for tensor manipulations as they occur in typical post-Hartree-Fock (post-HF) methods. A successive tensor decomposition/rank reduction scheme in the matrix product state (MPS) format for the two-electron integrals in the AO and MO bases and an estimate of the t 2 amplitudes as obtained from second-order many-body perturbation theory (MP2) are described. Furthermore, the AO-MO integral transformation, the calculation of the MP2 energy and the potential usage of tensors in low-rank MPS representation for the tensor contractions in coupled cluster theory are discussed in detail. We are able to show that the overall scaling of the memory requirements is reduced from the conventional N 4 scaling to approximately N 3 and the scaling of computational effort for tensor contractions in post-HF methods can be reduced to roughly N 4 while the decomposition itself scales as N 5. While efficient algorithms with low prefactor for the tensor decomposition have yet to be devised, this ansatz offers the possibility to find a robust approximation with low-scaling behaviour with system and basis-set size for post-HF ab initio methods.
Role of the tensor interaction in He isotopes with a tensor-optimized shell model
Myo, Takayuki; Umeya, Atsushi; Toki, Hiroshi; Ikeda, Kiyomi
2011-09-15
We studied the role of the tensor interaction in He isotopes systematically on the basis of the tensor-optimized shell model (TOSM). We use a bare nucleon-nucleon interaction AV8{sup '} obtained from nucleon-nucleon scattering data. The short-range correlation is treated in the unitary correlation operator method (UCOM). Using the TOSM + UCOM approach, we investigate the role of tensor interaction on each spectrum in He isotopes. It is found that the tensor interaction enhances the LS splitting energy observed in {sup 5}He, in which the p{sub 1/2} and p{sub 3/2} orbits play different roles on the tensor correlation. In {sup 6,7,8}He, the low-lying states containing extra neutrons in the p{sub 3/2} orbit gain the tensor contribution. On the other hand, the excited states containing extra neutrons in the p{sub 1/2} orbit lose the tensor contribution due to the Pauli-blocking effect with the 2p2h states in the {sup 4}He core configuration.
Blue running of the primordial tensor spectrum
Gong, Jinn-Ouk
2014-07-01
We examine the possibility of positive spectral index of the power spectrum of the primordial tensor perturbation produced during inflation in the light of the detection of the B-mode polarization by the BICEP2 collaboration. We find a blue tilt is in general possible when the slow-roll parameter decays rapidly. We present two known examples in which a positive spectral index for the tensor power spectrum can be obtained. We also briefly discuss other consistency tests for further studies on inflationary dynamics.
Tensor distinction of domains in ferroic crystals
NASA Astrophysics Data System (ADS)
Litvin, D. B.
2009-10-01
Ferroic crystals contain two or more domains and may be distinguished by the values of components of tensorial physical properties of the domains. We have extended Aizu’s global tensor distinction by magnetization, polarization, and strain of all domains which arise in a ferroic phase transition to include distinction by toroidal moment, and from phases invariant under time reversal to domains which arise in transitions from all magnetic and non-magnetic phases. For determining possible switching of domains, a domain pair tensor distinction is also considered for all pairs of domains which arise in each ferroic phase transition.
Tensor mesons produced in tau lepton decays
Lopez Castro, G.; Munoz, J. H.
2011-05-01
Light tensor mesons (T=a{sub 2}, f{sub 2} and K{sub 2}*) can be produced in decays of {tau} leptons. In this paper we compute the branching ratios of {tau}{yields}T{pi}{nu} decays by assuming the dominance of intermediate virtual states to model the form factors involved in the relevant hadronic matrix elements. The exclusive f{sub 2}(1270){pi}{sup -} decay mode turns out to have the largest branching ratio, of O(10{sup -4}). Our results indicate that the contribution of tensor meson intermediate states to the three-pseudoscalar channels of {tau} decays are rather small.
Quantum fields near phantom-energy ''sudden'' singularities
Calderon, Hector H.
2008-08-15
This paper is committed to calculations near a type of future singularity driven by phantom energy. At the singularities considered, the scale factor remains finite but its derivative diverges. The general behavior of barotropic phantom energy producing this singularity is calculated under the assumption that near the singularity such fluid is the dominant contributor. We use the semiclassical formula for renormalized stress tensors of conformally invariant fields in conformally flat spacetimes and analyze the softening/enhancing of the singularity due to quantum vacuum contributions. This dynamical analysis is then compared to results from thermodynamical considerations. In both cases, the vacuum states of quantized scalar and spinor fields strengthen the accelerating expansion near the singularity whereas the vacuum states of vector fields weaken it.
Quantum corrected spherical collapse: A phenomenological framework
Ziprick, Jonathan; Kunstatter, Gabor
2010-08-15
A phenomenological framework is presented for incorporating quantum gravity motivated corrections into the dynamics of spherically symmetric collapse. The effective equations are derived from a variational principle that guarantees energy conservation and the existence of a Birkhoff theorem. The gravitational potential can be chosen as a function of the areal radius to yield specific nonsingular static spherically symmetric solutions that generically have two horizons. For a specific choice of potential, the effective stress energy tensor violates only the dominant energy condition. The violations are maximum near the inner horizon and die off rapidly. A numerical study of the quantum corrected collapse of a spherically symmetric scalar field in this case reveals that the modified gravitational potential prevents the formation of a central singularity and ultimately yields a static, mostly vacuum, spacetime with two horizons. The matter 'piles up' on the inner horizon giving rise to mass inflation at late times. The Cauchy horizon is transformed into a null, weak singularity, but in contrast to Einstein gravity, the absence of a central singularity renders this null singularity stable.
Second order tensor finite element
NASA Technical Reports Server (NTRS)
Oden, J. Tinsley; Fly, J.; Berry, C.; Tworzydlo, W.; Vadaketh, S.; Bass, J.
1990-01-01
The results of a research and software development effort are presented for the finite element modeling of the static and dynamic behavior of anisotropic materials, with emphasis on single crystal alloys. Various versions of two dimensional and three dimensional hybrid finite elements were implemented and compared with displacement-based elements. Both static and dynamic cases are considered. The hybrid elements developed in the project were incorporated into the SPAR finite element code. In an extension of the first phase of the project, optimization of experimental tests for anisotropic materials was addressed. In particular, the problem of calculating material properties from tensile tests and of calculating stresses from strain measurements were considered. For both cases, numerical procedures and software for the optimization of strain gauge and material axes orientation were developed.
Stress and Deformation: A Handbook on Tensors in Geology
NASA Astrophysics Data System (ADS)
Allmendinger, Rick
Okay, everyone who thinks that continuum mechanics makes inherently fascinating, light reading, raise your hands. Hmm, I thought so. Most geologists and not a few geophysicists view continuum mechanics almost as a necessary evil, somewhat akin to a bad tasting medicine, which will make us better scientists even though the process of acquiring that knowledge may be unpleasant. Nonetheless, there is something appealing about the common mechanical underpinnings of such diverse topics as structuralgeology, crystallography, glacial physics, and seismology, to name a few. The question is, how can we teach continuum mechanics to students so that they not only “get it” but appreciate it?
Cosmic Ray Diffusion Tensor Throughout the Heliosphere
NASA Astrophysics Data System (ADS)
Pei, C.; Bieber, J. W.; Breech, B.; Burger, R. A.; Clem, J.; Matthaeus, W. H.
2008-12-01
We calculate the cosmic ray diffusion tensor based on a recently developed model of magnetohydrodynamic (MHD) turbulence in the expanding solar wind [Breech et al., 2008.]. Parameters of this MHD model are tuned by using published observations from Helios, Voyager 2, and Ulysses. We present solutions of two turbulence parameter sets and derive the characteristics of the cosmic ray diffusion tensor for each. We determine the parallel diffusion coefficient of the cosmic ray following the method presented in Bieber et al. [1995]. We use the nonlinear guiding center (NLGC) theory to obtain the perpendicular diffusion coefficient of the cosmic ray [Matthaeus et al. 2003]. We find that (1) the radial mean free path decreases from 1 AU to 20 AU for both turbulence scenarios; (2) after 40 AU the radial mean free path is nearly constant; (3) the radial mean free path is dominated by the parallel component before 20 AU, after which the perpendicular component becomes important; (4) the rigidity P dependence of the parallel component of the diffusion tensor is proportional to P.404 for one turbulence scenario and P.374 for the other at 1 AU from 0.1 GVto 10 GV, but in the outer heliosphere its dependence becomes stronger above 4 GV; (5) the rigidity P dependence of the perpendicular component of the diffusion tensor is very weak. Supported by NASA Heliophysics Guest Investigator grant NNX07AH73G and by NASA Heliophysics Theory grant NNX08AI47G.
Spacetime encodings. III. Second order Killing tensors
Brink, Jeandrew
2010-01-15
This paper explores the Petrov type D, stationary axisymmetric vacuum (SAV) spacetimes that were found by Carter to have separable Hamilton-Jacobi equations, and thus admit a second-order Killing tensor. The derivation of the spacetimes presented in this paper borrows from ideas about dynamical systems, and illustrates concepts that can be generalized to higher-order Killing tensors. The relationship between the components of the Killing equations and metric functions are given explicitly. The origin of the four separable coordinate systems found by Carter is explained and classified in terms of the analytic structure associated with the Killing equations. A geometric picture of what the orbital invariants may represent is built. Requiring that a SAV spacetime admits a second-order Killing tensor is very restrictive, selecting very few candidates from the group of all possible SAV spacetimes. This restriction arises due to the fact that the consistency conditions associated with the Killing equations require that the field variables obey a second-order differential equation, as opposed to a fourth-order differential equation that imposes the weaker condition that the spacetime be SAV. This paper introduces ideas that could lead to the explicit computation of more general orbital invariants in the form of higher-order Killing tensors.
Nonlinear symmetries on spaces admitting Killing tensors
NASA Astrophysics Data System (ADS)
Visinescu, Mihai
2010-04-01
Nonlinear symmetries corresponding to Killing tensors are investigated. The intimate relation between Killing-Yano tensors and non-standard supersymmetries is pointed out. The gravitational anomalies are absent if the hidden symmetry is associated with a Killing-Yano tensor. In the case of the nonlinear symmetries the dynamical algebras of the Dirac-type operators is more involved and could be organized as infinite dimensional algebras or superalgebras. The general results are applied to some concrete spaces involved in theories of modern physics. As a first example it is considered the 4-dimensional Euclidean Taub-NUT space and its generalizations introduced by Iwai and Katayama. One presents the infinite dimensional superalgebra of Dirac type operators on Taub-NUT space that could be seen as a graded loop superalgebra of the Kac-Moody type. The axial anomaly, interpreted as the index of the Dirac operator, is computed for the generalized Taub-NUT metrics. Finally the existence of the conformal Killing-Yano tensors is investigated for some spaces with mixed Sasakian structures.
Efficient Anisotropic Filtering of Diffusion Tensor Images
Xu, Qing; Anderson, Adam W.; Gore, John C.; Ding, Zhaohua
2009-01-01
To improve the accuracy of structural and architectural characterization of living tissue with diffusion tensor imaging, an efficient smoothing algorithm is presented for reducing noise in diffusion tensor images. The algorithm is based on anisotropic diffusion filtering, which allows both image detail preservation and noise reduction. However, traditional numerical schemes for anisotropic filtering have the drawback of inefficiency and inaccuracy due to their poor stability and first order time accuracy. To address this, an unconditionally stable and second order time accuracy semi-implicit Craig-Sneyd scheme is adapted in our anisotropic filtering. By using large step size, unconditional stability allows this scheme to take much fewer iterations and thus less computation time than the explicit scheme to achieve a certain degree of smoothing. Second order time accuracy makes the algorithm reduce noise more effectively than a first order scheme with the same total iteration time. Both the efficiency and effectiveness are quantitatively evaluated based on synthetic and in vivo human brain diffusion tensor images, and these tests demonstrate that our algorithm is an efficient and effective tool for denoising diffusion tensor images. PMID:20061113
Role of Tensor Force in Light Nuclei Based on the Tensor Optimized Shell Model
Myo, Takayuki; Umeya, Atsushi; Ikeda, Kiyomi; Valverde, Manuel; Toki, Hiroshi
2011-10-21
We propose a new theoretical approach to describe nucleus using bare nuclear interaction, in which the tensor and short-range correlations are described with the tensor optimized shell model (TOSM) and the unitary correlation operator method (UCOM), respectively. We show the obtained results of He isotopes using TOSM+UCOM, such as the importance of the pn-pair correlated by the tensor force, and the structure differences in the LS partners of 3/2{sup -} and 1/2{sup -} states of {sup 5}He. We also apply TOSM to the analysis of two-neutron halo nucleus {sup 11}Li, on the basis of the ''core described in TOSM''+n+n model. The halo formation of {sup 11}Li is naturally explained, in which the tensor correlation in the {sup 9}Li core is Pauli-blocked on the p-wave neutrons in {sup 11}Li and the s-wave component of halo structure is enhanced.
Vector and tensor contributions to the curvature perturbation at second order
NASA Astrophysics Data System (ADS)
Carrilho, Pedro; Malik, Karim A.
2016-02-01
We derive the evolution equation for the second order curvature perturbation using standard techniques of cosmological perturbation theory. We do this for different definitions of the gauge invariant curvature perturbation, arising from different splits of the spatial metric, and compare the expressions. The results are valid at all scales and include all contributions from scalar, vector and tensor perturbations, as well as anisotropic stress, with all our results written purely in terms of gauge invariant quantities. Taking the large-scale approximation, we find that a conserved quantity exists only if, in addition to the non-adiabatic pressure, the transverse traceless part of the anisotropic stress tensor is also negligible. We also find that the version of the gauge invariant curvature perturbation which is exactly conserved is the one defined with the determinant of the spatial part of the inverse metric.
Skyrme tensor force in heavy ion collisions
NASA Astrophysics Data System (ADS)
Stevenson, P. D.; Suckling, E. B.; Fracasso, S.; Barton, M. C.; Umar, A. S.
2016-05-01
Background: It is generally acknowledged that the time-dependent Hartree-Fock (TDHF) method provides a useful foundation for a fully microscopic many-body theory of low-energy heavy ion reactions. The TDHF method is also known in nuclear physics in the small-amplitude domain, where it provides a useful description of collective states, and is based on the mean-field formalism, which has been a relatively successful approximation to the nuclear many-body problem. Currently, the TDHF theory is being widely used in the study of fusion excitation functions, fission, and deep-inelastic scattering of heavy mass systems, while providing a natural foundation for many other studies. Purpose: With the advancement of computational power it is now possible to undertake TDHF calculations without any symmetry assumptions and incorporate the major strides made by the nuclear structure community in improving the energy density functionals used in these calculations. In particular, time-odd and tensor terms in these functionals are naturally present during the dynamical evolution, while being absent or minimally important for most static calculations. The parameters of these terms are determined by the requirement of Galilean invariance or local gauge invariance but their significance for the reaction dynamics have not been fully studied. This work addresses this question with emphasis on the tensor force. Method: The full version of the Skyrme force, including terms arising only from the Skyrme tensor force, is applied to the study of collisions within a completely symmetry-unrestricted TDHF implementation. Results: We examine the effect on upper fusion thresholds with and without the tensor force terms and find an effect on the fusion threshold energy of the order several MeV. Details of the distribution of the energy within terms in the energy density functional are also discussed. Conclusions: Terms in the energy density functional linked to the tensor force can play a non
3-D inversion of magnetotelluric Phase Tensor
NASA Astrophysics Data System (ADS)
Patro, Prasanta; Uyeshima, Makoto
2010-05-01
Three-dimensional (3-D) inversion of the magnetotelluric (MT) has become a routine practice among the MT community due to progress of algorithms for 3-D inverse problems (e.g. Mackie and Madden, 1993; Siripunvaraporn et al., 2005). While availability of such 3-D inversion codes have increased the resolving power of the MT data and improved the interpretation, on the other hand, still the galvanic effects poses difficulties in interpretation of resistivity structure obtained from the MT data. In order to tackle the galvanic distortion of MT data, Caldwell et al., (2004) introduced the concept of phase tensor. They demonstrated how the regional phase information can be retrieved from the observed impedance tensor without any assumptions for structural dimension, where both the near surface inhomogeneity and the regional conductivity structures can be 3-D. We made an attempt to modify a 3-D inversion code (Siripunvaraporn et al., 2005) to directly invert the phase tensor elements. We present here the main modification done in the sensitivity calculation and then show a few synthetic studies and its application to the real data. The synthetic model study suggests that the prior model (m_0) setting is important in retrieving the true model. This is because estimation of correct induction scale length lacks in the phase tensor inversion process. Comparison between results from conventional impedance inversion and new phase tensor inversion suggests that, in spite of presence of the galvanic distortion (due to near surface checkerboard anomalies in our case), the new inverion algorithm retrieves the regional conductivitity structure reliably. We applied the new inversion to the real data from the Indian sub continent and compared with the results from conventional impedance inversion.
Bremner, S. P.; Ban, K.-Y.; Faleev, N. N.; Honsberg, C. B.; Smith, D. J.
2013-09-14
We describe InAs quantum dot creation in InAs/GaAsSb barrier structures grown on GaAs (001) wafers by molecular beam epitaxy. The structures consist of 20-nm-thick GaAsSb barrier layers with Sb content of 8%, 13%, 15%, 16%, and 37% enclosing 2 monolayers of self-assembled InAs quantum dots. Transmission electron microscopy and X-ray diffraction results indicate the onset of relaxation of the GaAsSb layers at around 15% Sb content with intersected 60° dislocation semi-loops, and edge segments created within the volume of the epitaxial structures. 38% relaxation of initial elastic stress is seen for 37% Sb content, accompanied by the creation of a dense net of dislocations. The degradation of In surface migration by these dislocation trenches is so severe that quantum dot formation is completely suppressed. The results highlight the importance of understanding defect formation during stress relaxation for quantum dot structures particularly those with larger numbers of InAs quantum-dot layers, such as those proposed for realizing an intermediate band material.
Three-dimensional manifolds with special Cotton tensor
NASA Astrophysics Data System (ADS)
Calviño-Louzao, E.; García-Río, E.; Seoane-Bascoy, J.; Vázquez-Lorenzo, R.
2015-10-01
The Cotton tensor of three-dimensional Walker manifolds is investigated. A complete description of all locally conformally flat Walker three-manifolds is given, as well as that of Walker manifolds whose Cotton tensor is either a Codazzi or a Killing tensor.
Efficient MATLAB computations with sparse and factored tensors.
Bader, Brett William; Kolda, Tamara Gibson (Sandia National Lab, Livermore, CA)
2006-12-01
In this paper, the term tensor refers simply to a multidimensional or N-way array, and we consider how specially structured tensors allow for efficient storage and computation. First, we study sparse tensors, which have the property that the vast majority of the elements are zero. We propose storing sparse tensors using coordinate format and describe the computational efficiency of this scheme for various mathematical operations, including those typical to tensor decomposition algorithms. Second, we study factored tensors, which have the property that they can be assembled from more basic components. We consider two specific types: a Tucker tensor can be expressed as the product of a core tensor (which itself may be dense, sparse, or factored) and a matrix along each mode, and a Kruskal tensor can be expressed as the sum of rank-1 tensors. We are interested in the case where the storage of the components is less than the storage of the full tensor, and we demonstrate that many elementary operations can be computed using only the components. All of the efficiencies described in this paper are implemented in the Tensor Toolbox for MATLAB.
Inflation without quantum gravity
NASA Astrophysics Data System (ADS)
Markkanen, Tommi; Räsänen, Syksy; Wahlman, Pyry
2015-04-01
It is sometimes argued that observation of tensor modes from inflation would provide the first evidence for quantum gravity. However, in the usual inflationary formalism, also the scalar modes involve quantized metric perturbations. We consider the issue in a semiclassical setup in which only matter is quantized, and spacetime is classical. We assume that the state collapses on a spacelike hypersurface and find that the spectrum of scalar perturbations depends on the hypersurface. For reasonable choices, we can recover the usual inflationary predictions for scalar perturbations in minimally coupled single-field models. In models where nonminimal coupling to gravity is important and the field value is sub-Planckian, we do not get a nearly scale-invariant spectrum of scalar perturbations. As gravitational waves are only produced at second order, the tensor-to-scalar ratio is negligible. We conclude that detection of inflationary gravitational waves would indeed be needed to have observational evidence of quantization of gravity.
BOOK REVIEW: The Scalar-Tensor Theory of Gravitation
NASA Astrophysics Data System (ADS)
Fujii, Yasunori; Maeda, Kei-ichi
2003-10-01
Since the scalar-tensor theory of gravitation was proposed almost 50 years ago, it has recently become a robust alternative theory to Einstein's general relativity due to the fact that it appears to represent the lower level of a more fundamental theory and can serve both as a phenomenological theory to explain the recently observed acceleration of the universe, and to solve the cosmological constant problem. To my knowledge The Scalar-Tensor Theory of Gravitation by Y Fujii and K Maeda is the first book to develop a modern view on this topic and is one of the latest titles in the well-presented Cambridge Monographs on Mathematical Physics series. This book is an excellent readable introduction and up-to-date review of the subject. The discussion is well organized; after a comprehensible introduction to the Brans-Dicke theory and the important role played by conformal transformations, the authors review cosmologies with the cosmological constant and how the scalar-tensor theory can serve to explain the accelerating universe, including discussions on dark energy, quintessence and braneworld cosmologies. The book ends with a chapter devoted to quantum effects. To make easy the lectures of the book, each chapter starts with a summary of the subject to be dealt with. As the book proceeds, important issues like conformal frames and the weak equivalence principle are fully discussed. As the authors warn in the preface, the book is not encyclopedic (from my point of view the list of references is fairly short, for example, but this is a minor drawback) and the choice of included topics corresponds to the authors' interests. Nevertheless, the book seems to cover a broad range of the most essential aspects of the subject. Long and 'boring' mathematical derivations are left to appendices so as not to interrupt the flow of the reasoning, allowing the reader to focus on the physical aspects of each subject. These appendices are a valuable help in entering into the mathematical
A preliminary report on the development of MATLAB tensor classes for fast algorithm prototyping.
Bader, Brett William; Kolda, Tamara Gibson
2004-07-01
We describe three MATLAB classes for manipulating tensors in order to allow fast algorithm prototyping. A tensor is a multidimensional or N-way array. We present a tensor class for manipulating tensors which allows for tensor multiplication and 'matricization.' We have further added two classes for representing tensors in decomposed format: cp{_}tensor and tucker{_}tensor. We demonstrate the use of these classes by implementing several algorithms that have appeared in the literature.
Generalization of the Bollobás-Riordan polynomial for tensor graphs
NASA Astrophysics Data System (ADS)
Tanasa, Adrian
2011-07-01
Tensor models are used nowadays for implementing a fundamental theory of quantum gravity. We define here a polynomial T encoding the supplementary topological information. This polynomial is a natural generalization of the Bollobás-Riordan polynomial (used to characterize matrix graphs) and is different from the Gurău polynomial [R. Gurău, Ann. Henri Poincare 11, 565 (2010)], 10.1007/s00023-010-0035-6, defined for a particular class of tensor graphs, the colorable ones. The polynomial T is defined for both colorable and non-colorable graphs and it is proved to satisfy the deletion/contraction relation. A non-trivial example of a non-colorable graphs is analyzed.
Large tensor mode, field range bound and consistency in generalized G-inflation
NASA Astrophysics Data System (ADS)
Kunimitsu, Taro; Suyama, Teruaki; Watanabe, Yuki; Yokoyama, Jun'ichi
2015-08-01
We systematically show that in potential driven generalized G-inflation models, quantum corrections coming from new physics at the strong coupling scale can be avoided, while producing observable tensor modes. The effective action can be approximated by the tree level action, and as a result, these models are internally consistent, despite the fact that we introduced new mass scales below the energy scale of inflation. Although observable tensor modes are produced with sub-strong coupling scale field excursions, this is not an evasion of the Lyth bound, since the models include higher-derivative non-canonical kinetic terms, and effective rescaling of the field would result in super-Planckian field excursions. We argue that the enhanced kinetic term of the inflaton screens the interactions with other fields, keeping the system weakly coupled during inflation.
Benzi, Caterina; Cossi, Maurizio; Barone, Vincenzo
2005-11-15
High-level ab initio g and A tensor components have been calculated for PD-tempone and tempo-palmitate (TP) radical spin probes dissolved in n-pentyl and n-hexyl cyanobiphenyl liquid crystals. Solvent effects have been included in the proposed approach by means of the polarizable continuum model, allowing for solvent anisotropy. An in-depth analysis of the electronic structure of probes was performed to choose a suitable model for TP and make the calculations more accessible. Computed magnetic tensor components have been compared with corresponding values measured in the rigid limit. The quality of the results suggests the use of quantum-mechanical data to determine the order parameter of the nematic from experimental electron-spin resonance measurements. PMID:16321115
Quantum Vacuum Instability of ``Eternal'' de Sitter Space
NASA Astrophysics Data System (ADS)
Mottola, Emil
2015-04-01
The Euclidean or Bunch-Davies state of quantum fields in global de Sitter space is shown to be unstable to small perturbations, even for a massive free field with no self-interactions. There are perturbations of this state with arbitrarily small energy density at early times that is exponentially blueshifted in the contracting phase of ``eternal'' de Sitter space, and becomes large enough to disturb the classical geometry through the semiclassical Einstein eqs. at later times. In the closely analogous case of a constant, uniform electric field, a time symmetric state equivalent to the de Sitter invariant one is constructed, which is also not a stable vacuum state under perturbations. The role of a quantum anomaly in the growth of perturbations and symmetry breaking is emphasized in both cases. The anomaly stress tensor shows that states invariant under the O(4) subgroup of the de Sitter group are also unstable to perturbations of lower spatial symmetry, implying that both the O(4) subgroup are broken by quantum fluctuations. Consequences of this result for cosmology and the problem of vacuum energy will be discussed.
Bures metric over thermal state manifolds and quantum criticality
Zanardi, Paolo; Campos Venuti, Lorenzo; Giorda, Paolo
2007-12-15
We analyze the Bures metric over the manifold of thermal density matrices for systems featuring a zero temperature quantum phase transition. We show that the quantum critical region can be characterized in terms of the temperature scaling behavior of the metric tensor itself. Furthermore, the analysis of the metric tensor when both temperature and an external field are varied, allows one to complement the understanding of the phase diagram including crossover regions which are not characterized by any singular behavior. These results provide a further extension of the scope of the metric approach to quantum criticality.
Quantum Computation and Quantum Information
NASA Astrophysics Data System (ADS)
Nielsen, Michael A.; Chuang, Isaac L.
2010-12-01
Part I. Fundamental Concepts: 1. Introduction and overview; 2. Introduction to quantum mechanics; 3. Introduction to computer science; Part II. Quantum Computation: 4. Quantum circuits; 5. The quantum Fourier transform and its application; 6. Quantum search algorithms; 7. Quantum computers: physical realization; Part III. Quantum Information: 8. Quantum noise and quantum operations; 9. Distance measures for quantum information; 10. Quantum error-correction; 11. Entropy and information; 12. Quantum information theory; Appendices; References; Index.
NASA Astrophysics Data System (ADS)
Stierle, Eva; Vavryčuk, Václav; Kwiatek, Grzegorz; Charalampidou, Elli-Maria; Bohnhoff, Marco
2016-04-01
Seismic moment tensors can provide information on the size and orientation of fractures producing acoustic emissions (AEs) and on the stress conditions in the sample. The moment tensor inversion of AEs is, however, a demanding procedure requiring carefully calibrated sensors and accurate knowledge of the velocity model. In field observations, the velocity model is usually isotropic and time independent. In laboratory experiments, the velocity is often anisotropic and time dependent and attenuation might be significant due to opening or closure of microcracks in the sample during loading. In this paper, we study the sensitivity of the moment tensor inversion to anisotropy of P-wave velocities and attenuation. We show that retrieved moment tensors critically depend on anisotropy and attenuation and their neglect can lead to misinterpretations of the source mechanisms. The accuracy of the inversion also depends on the fracturing mode of AEs: tensile events are more sensitive to P-wave anisotropy and attenuation than shear events. We show that geometry of faulting in anisotropic rocks should be studied using the source tensors, since the P- and T-axes of the moment tensors are affected by velocity anisotropy and deviate from the true orientation of faulting. The stronger the anisotropy is, the larger the deviations are. Finally, we prove that the moment tensor inversion applied to a large dataset of AEs can be utilized to provide information on the attenuation parameters of the rock sample. The method is capable of measuring anisotropic attenuation in the sample and allows for detection of dilatant cracking according to the stress regime.
Global moment tensor computation at GFZ Potsdam
NASA Astrophysics Data System (ADS)
Saul, J.; Becker, J.; Hanka, W.
2011-12-01
As part of its earthquake information service, GFZ Potsdam has started to provide seismic moment tensor solutions for significant earthquakes world-wide. The software used to compute the moment tensors is a GFZ-Potsdam in-house development, which uses the framework of the software SeisComP 3 (Hanka et al., 2010). SeisComP 3 (SC3) is a software package for seismological data acquisition, archival, quality control and analysis. SC3 is developed by GFZ Potsdam with significant contributions from its user community. The moment tensor inversion technique uses a combination of several wave types, time windows and frequency bands depending on magnitude and station distance. Wave types include body, surface and mantle waves as well as the so-called 'W-Phase' (Kanamori and Rivera, 2008). The inversion is currently performed in the time domain only. An iterative centroid search can be performed independently both horizontally and in depth. Moment tensors are currently computed in a semi-automatic fashion. This involves inversions that are performed automatically in near-real time, followed by analyst review prior to publication. The automatic results are quite often good enough to be published without further improvements, sometimes in less than 30 minutes from origin time. In those cases where a manual interaction is still required, the automatic inversion usually does a good job at pre-selecting those traces that are the most relevant for the inversion, keeping the work required for the analyst at a minimum. Our published moment tensors are generally in good agreement with those published by the Global Centroid-Moment-Tensor (GCMT) project for earthquakes above a magnitude of about Mw 5. Additionally we provide solutions for smaller earthquakes above about Mw 4 in Europe, which are normally not analyzed by the GCMT project. We find that for earthquakes above Mw 6, the most robust automatic inversions can usually be obtained using the W-Phase time window. The GFZ earthquake
Yan, Ming; Zhang, Yun; Qin, Haiyan; Liu, Kezhou; Guo, Miao; Ge, Yakun; Xu, Mingen; Sun, Yonghong; Zheng, Xiaoxiang
2016-01-01
Cadmium telluride quantum dots (CdTe QDs) have been proposed to induce oxidative stress, which plays a crucial role in CdTe QDs-mediated mitochondrial-dependent apoptosis in human umbilical vein endothelial cells (HUVECs). However, the direct interactions of CdTe QDs with HUVECs and their potential impairment of other organelles like endoplasmic reticulum (ER) in HUVECs are poorly understood. In this study, we reported that the negatively charged CdTe QDs (−21.63±0.91 mV), with good dispersity and fluorescence stability, were rapidly internalized via endocytosis by HUVECs, as the notable internalization could be inhibited up to 95.52% by energy depletion (NaN3/deoxyglucose or low temperature). The endocytosis inhibitors (methyl-β-cyclodextrin, genistein, sucrose, chlorpromazine, and colchicine) dramatically decreased the uptake of CdTe QDs by HUVECs, suggesting that both caveolae/raft- and clathrin-mediated endocytosis were involved in the endothelial uptake of CdTe QDs. Using immunocytochemistry, a striking overlap of the internalized CdTe QDs and ER marker was observed, which indicates that QDs may be transported to ER. The CdTe QDs also caused remarkable ER stress responses in HUVECs, confirmed by significant dilatation of ER cisternae, upregulation of ER stress markers GRP78/GRP94, and activation of protein kinase RNA-like ER kinase-eIF2α-activating transcription factor 4 pathway (including phosphorylation of both protein kinase RNA-like ER kinase and eIF2α and elevated level of activating transcription factor 4). CdTe QDs further promoted an increased C/EBP homologous protein expression, phosphorylation of c-JUN NH2-terminal kinase, and cleavage of ER-resident caspase-4, while the specific inhibitor (SP600125, Z-LEVD-fmk, or salubrinal) significantly attenuated QDs-triggered apoptosis, indicating that all three ER stress-mediated apoptosis pathways were activated and the direct participation of ER in the CdTe QDs-caused apoptotic cell death in HUVECs
Yan, Ming; Zhang, Yun; Qin, Haiyan; Liu, Kezhou; Guo, Miao; Ge, Yakun; Xu, Mingen; Sun, Yonghong; Zheng, Xiaoxiang
2016-01-01
Cadmium telluride quantum dots (CdTe QDs) have been proposed to induce oxidative stress, which plays a crucial role in CdTe QDs-mediated mitochondrial-dependent apoptosis in human umbilical vein endothelial cells (HUVECs). However, the direct interactions of CdTe QDs with HUVECs and their potential impairment of other organelles like endoplasmic reticulum (ER) in HUVECs are poorly understood. In this study, we reported that the negatively charged CdTe QDs (-21.63±0.91 mV), with good dispersity and fluorescence stability, were rapidly internalized via endocytosis by HUVECs, as the notable internalization could be inhibited up to 95.52% by energy depletion (NaN3/deoxyglucose or low temperature). The endocytosis inhibitors (methyl-β-cyclodextrin, genistein, sucrose, chlorpromazine, and colchicine) dramatically decreased the uptake of CdTe QDs by HUVECs, suggesting that both caveolae/raft- and clathrin-mediated endocytosis were involved in the endothelial uptake of CdTe QDs. Using immunocytochemistry, a striking overlap of the internalized CdTe QDs and ER marker was observed, which indicates that QDs may be transported to ER. The CdTe QDs also caused remarkable ER stress responses in HUVECs, confirmed by significant dilatation of ER cisternae, upregulation of ER stress markers GRP78/GRP94, and activation of protein kinase RNA-like ER kinase-eIF2α-activating transcription factor 4 pathway (including phosphorylation of both protein kinase RNA-like ER kinase and eIF2α and elevated level of activating transcription factor 4). CdTe QDs further promoted an increased C/EBP homologous protein expression, phosphorylation of c-JUN NH2-terminal kinase, and cleavage of ER-resident caspase-4, while the specific inhibitor (SP600125, Z-LEVD-fmk, or salubrinal) significantly attenuated QDs-triggered apoptosis, indicating that all three ER stress-mediated apoptosis pathways were activated and the direct participation of ER in the CdTe QDs-caused apoptotic cell death in HUVECs. Our
Tensoral for post-processing users and simulation authors
NASA Technical Reports Server (NTRS)
Dresselhaus, Eliot
1993-01-01
The CTR post-processing effort aims to make turbulence simulations and data more readily and usefully available to the research and industrial communities. The Tensoral language, which provides the foundation for this effort, is introduced here in the form of a user's guide. The Tensoral user's guide is presented in two main sections. Section one acts as a general introduction and guides database users who wish to post-process simulation databases. Section two gives a brief description of how database authors and other advanced users can make simulation codes and/or the databases they generate available to the user community via Tensoral database back ends. The two-part structure of this document conforms to the two-level design structure of the Tensoral language. Tensoral has been designed to be a general computer language for performing tensor calculus and statistics on numerical data. Tensoral's generality allows it to be used for stand-alone native coding of high-level post-processing tasks (as described in section one of this guide). At the same time, Tensoral's specialization to a minute task (namely, to numerical tensor calculus and statistics) allows it to be easily embedded into applications written partly in Tensoral and partly in other computer languages (here, C and Vectoral). Embedded Tensoral, aimed at advanced users for more general coding (e.g. of efficient simulations, for interfacing with pre-existing software, for visualization, etc.), is described in section two of this guide.
Effect of Multi-Axial Loading on Residual Strain Tensor for 12L14 Steel Alloy
Bunn, J. R.; Penumadu, Dayakar; Lou, Xin; Hubbard, Camden R
2014-01-01
Evaluating the state of residual strain or stress is critically important for structural materials and for reliable design of complex shape components that need to function in extreme environment subjected to large thermo-mechanical loading. When residual stress state is superposed to external loads, it can lead to reduction or increase in failure strength. Past diffraction studies for evaluating the residual strain state involved measuring lattice spacings in three orthogonal directions and do not often correspond to principal directions. To completely resolve the state of strain at a given location, a full strain tensor must be determined. This is especially important when characterizing materials or metallic components exposed to biaxial or complex loading. Neutron diffraction at the second Generation Neutron Residual Stress Facility (NRSF2) at Oak Ridge National Laboratory is used in this study to measure strain tensors associated with different modes of stress path. Hollow cylinder steel samples with 2 mm wall thickness are subjected to either pure axial extension or pure torsion to simulate multi-axial loading conditions. A virgin sample that is not subjected to any deformation, but subjected to identical manufacturing conditions and machining steps involved to obtain hollow cylinder geometry is used for obtaining reference d-spacing for given hkl planes at target spatial location(s). The two samples which are subjected to either pure tension or torsion are loaded to a deformation state that corresponded to equal amount of octahedral shear strain which is an invariant. This procedure is used so that a basis for comparison between the two samples can be made to isolate the stress path effects. A 2-circle Huber orienter is used to obtain strain measurements on identical gauge volume at a series of chi and psi values. The residual state of stress tensor corresponding to ex situ (upon unloading) conditions is presented for three lattice planes (211, 110, 200) for
Saliency Mapping Enhanced by Structure Tensor
He, Zhiyong; Chen, Xin; Sun, Lining
2015-01-01
We propose a novel efficient algorithm for computing visual saliency, which is based on the computation architecture of Itti model. As one of well-known bottom-up visual saliency models, Itti method evaluates three low-level features, color, intensity, and orientation, and then generates multiscale activation maps. Finally, a saliency map is aggregated with multiscale fusion. In our method, the orientation feature is replaced by edge and corner features extracted by a linear structure tensor. Following it, these features are used to generate contour activation map, and then all activation maps are directly combined into a saliency map. Compared to Itti method, our method is more computationally efficient because structure tensor is more computationally efficient than Gabor filter that is used to compute the orientation feature and our aggregation is a direct method instead of the multiscale operator. Experiments on Bruce's dataset show that our method is a strong contender for the state of the art. PMID:26788050
Extended scalar-tensor theories of gravity
NASA Astrophysics Data System (ADS)
Crisostomi, Marco; Koyama, Kazuya; Tasinato, Gianmassimo
2016-04-01
We study new consistent scalar-tensor theories of gravity recently introduced by Langlois and Noui with potentially interesting cosmological applications. We derive the conditions for the existence of a primary constraint that prevents the propagation of an additional dangerous mode associated with higher order equations of motion. We then classify the most general, consistent scalar-tensor theories that are at most quadratic in the second derivatives of the scalar field. In addition, we investigate the possible connection between these theories and (beyond) Horndeski through conformal and disformal transformations. Finally, we point out that these theories can be associated with new operators in the effective field theory of dark energy, which might open up new possibilities to test dark energy models in future surveys.
Tensors: A guide for undergraduate students
NASA Astrophysics Data System (ADS)
Battaglia, Franco; George, Thomas F.
2013-07-01
A guide on tensors is proposed for undergraduate students in physics or engineering that ties directly to vector calculus in orthonormal coordinate systems. We show that once orthonormality is relaxed, a dual basis, together with the contravariant and covariant components, naturally emerges. Manipulating these components requires some skill that can be acquired more easily and quickly once a new notation is adopted. This notation distinguishes multi-component quantities in different coordinate systems by a differentiating sign on the index labelling the component rather than on the label of the quantity itself. This tiny stratagem, together with simple rules openly stated at the beginning of this guide, allows an almost automatic, easy-to-pursue procedure for what is otherwise a cumbersome algebra. By the end of the paper, the reader will be skillful enough to tackle many applications involving tensors of any rank in any coordinate system, without index-manipulation obstacles standing in the way.
Symmetry constraints on the elastoresistivity tensor
NASA Astrophysics Data System (ADS)
Shapiro, M. C.; Hlobil, Patrik; Hristov, A. T.; Maharaj, Akash V.; Fisher, I. R.
2015-12-01
The elastoresistivity tensor mi j ,k l characterizes changes in a material's resistivity due to strain. As a fourth-rank tensor, elastoresistivity can be a uniquely useful probe of the symmetries and character of the electronic state of a solid. We present a symmetry analysis of mi j ,k l (both in the presence and absence of a magnetic field) based on the crystalline point group, focusing for pedagogic purposes on the D4 h point group (of relevance to several materials of current interest). We also discuss the relation between mi j ,k l and various thermodynamic susceptibilities, particularly where they are sensitive to critical fluctuations proximate to a critical point at which a point-group symmetry is spontaneously broken.
NASA Astrophysics Data System (ADS)
Senovilla, José M. M.
2010-11-01
The algebraic classification of the Weyl tensor in the arbitrary dimension n is recovered by means of the principal directions of its 'superenergy' tensor. This point of view can be helpful in order to compute the Weyl aligned null directions explicitly, and permits one to obtain the algebraic type of the Weyl tensor by computing the principal eigenvalue of rank-2 symmetric future tensors. The algebraic types compatible with states of intrinsic gravitational radiation can then be explored. The underlying ideas are general, so that a classification of arbitrary tensors in the general dimension can be achieved.
Inflation in anisotropic scalar-tensor theories
NASA Technical Reports Server (NTRS)
Pimentel, Luis O.; Stein-Schabes, Jaime
1988-01-01
The existence of an inflationary phase in anisotropic Scalar-Tensor Theories is investigated by means of a conformal transformation that allows us to rewrite these theories as gravity minimally coupled to a scalar field with a nontrivial potential. The explicit form of the potential is then used and the No Hair Theorem concludes that there is an inflationary phase in all open or flat anisotropic spacetimes in these theories. Several examples are constructed where the effect becomes manifest.
Tensor Forces and the Structure of Nuclei
Rocco Schiavilla
2009-12-01
The two preeminent features of the nucleon-nucleon interaction are its short-range repulsion and intermediate- to long-range tensor character. In the present talk, I review how these features influence two-nucleon densities in configuration and momentum space. The predicted large differences between the np and pp momentum distributions have been confirmed in 12C(e,e[prime] np) and 12C(e,e[prime] pp) experiments at Jefferson Lab.
Monte Carlo Volcano Seismic Moment Tensors
NASA Astrophysics Data System (ADS)
Waite, G. P.; Brill, K. A.; Lanza, F.
2015-12-01
Inverse modeling of volcano seismic sources can provide insight into the geometry and dynamics of volcanic conduits. But given the logistical challenges of working on an active volcano, seismic networks are typically deficient in spatial and temporal coverage; this potentially leads to large errors in source models. In addition, uncertainties in the centroid location and moment-tensor components, including volumetric components, are difficult to constrain from the linear inversion results, which leads to a poor understanding of the model space. In this study, we employ a nonlinear inversion using a Monte Carlo scheme with the objective of defining robustly resolved elements of model space. The model space is randomized by centroid location and moment tensor eigenvectors. Point sources densely sample the summit area and moment tensors are constrained to a randomly chosen geometry within the inversion; Green's functions for the random moment tensors are all calculated from modeled single forces, making the nonlinear inversion computationally reasonable. We apply this method to very-long-period (VLP) seismic events that accompany minor eruptions at Fuego volcano, Guatemala. The library of single force Green's functions is computed with a 3D finite-difference modeling algorithm through a homogeneous velocity-density model that includes topography, for a 3D grid of nodes, spaced 40 m apart, within the summit region. The homogenous velocity and density model is justified by long wavelength of VLP data. The nonlinear inversion reveals well resolved model features and informs the interpretation through a better understanding of the possible models. This approach can also be used to evaluate possible station geometries in order to optimize networks prior to deployment.
Quantum corrections for a cosmological string solution
Behrndt, K.
1994-08-01
The author investigates quantum corrections for a cosmological solution of the string effective action. Starting point is a classical solution containing an antisymmetric tensor field, a dilaton and a modulus field which has singularities in the scalar fields. As a first step he quantizes the scalar fields near the singularity with the result that the singularities disappear and that in general non-perturbative quantum corrections form a potential in the scalar fields.
Integrated calibration of magnetic gradient tensor system
NASA Astrophysics Data System (ADS)
Gang, Yin; Yingtang, Zhang; Hongbo, Fan; GuoQuan, Ren; Zhining, Li
2015-01-01
Measurement precision of a magnetic gradient tensor system is not only connected with the imperfect performance of magnetometers such as bias, scale factor, non-orthogonality and misalignment errors, but also connected with the external soft-iron and hard-iron magnetic distortion fields when the system is used as a strapdown device. So an integrated scalar calibration method is proposed in this paper. In the first step, a mathematical model for scalar calibration of a single three-axis magnetometer is established, and a least squares ellipsoid fitting algorithm is proposed to estimate the detailed error parameters. For the misalignment errors existing at different magnetometers caused by the installation process and misalignment errors aroused by ellipsoid fitting estimation, a calibration method for combined misalignment errors is proposed in the second step to switch outputs of different magnetometers into the ideal reference orthogonal coordinate system. In order to verify effectiveness of the proposed method, simulation and experiment with a cross-magnetic gradient tensor system are performed, and the results show that the proposed method estimates error parameters and improves the measurement accuracy of magnetic gradient tensor greatly.
Scalable tensor factorizations with incomplete data.
Morup, Morten; Dunlavy, Daniel M.; Acar, Evrim; Kolda, Tamara Gibson
2010-07-01
The problem of incomplete data - i.e., data with missing or unknown values - in multi-way arrays is ubiquitous in biomedical signal processing, network traffic analysis, bibliometrics, social network analysis, chemometrics, computer vision, communication networks, etc. We consider the problem of how to factorize data sets with missing values with the goal of capturing the underlying latent structure of the data and possibly reconstructing missing values (i.e., tensor completion). We focus on one of the most well-known tensor factorizations that captures multi-linear structure, CANDECOMP/PARAFAC (CP). In the presence of missing data, CP can be formulated as a weighted least squares problem that models only the known entries. We develop an algorithm called CP-WOPT (CP Weighted OPTimization) that uses a first-order optimization approach to solve the weighted least squares problem. Based on extensive numerical experiments, our algorithm is shown to successfully factorize tensors with noise and up to 99% missing data. A unique aspect of our approach is that it scales to sparse large-scale data, e.g., 1000 x 1000 x 1000 with five million known entries (0.5% dense). We further demonstrate the usefulness of CP-WOPT on two real-world applications: a novel EEG (electroencephalogram) application where missing data is frequently encountered due to disconnections of electrodes and the problem of modeling computer network traffic where data may be absent due to the expense of the data collection process.
Tensor integrand reduction via Laurent expansion
NASA Astrophysics Data System (ADS)
Hirschi, Valentin; Peraro, Tiziano
2016-06-01
We introduce a new method for the application of one-loop integrand reduction via the Laurent expansion algorithm, as implemented in the public C ++ library N inja. We show how the coefficients of the Laurent expansion can be computed by suitable contractions of the loop numerator tensor with cut-dependent projectors, making it possible to interface N inja to any one-loop matrix element generator that can provide the components of this tensor. We implemented this technique in the N inja library and interfaced it to M adL oop, which is part of the public M adG raph5_ aMC@NLO framework. We performed a detailed performance study, comparing against other public reduction tools, namely C utT ools, S amurai, IREGI, PJF ry++ and G olem95. We find that N inja out-performs traditional integrand reduction in both speed and numerical stability, the latter being on par with that of the tensor integral reduction tool Golem95 which is however more limited and slower than N inja. We considered many benchmark multi-scale processes of increasing complexity, involving QCD and electro-weak corrections as well as effective non-renormalizable couplings, showing that N inja's performance scales well with both the rank and multiplicity of the considered process.
Tensor integrand reduction via Laurent expansion
Hirschi, Valentin; Peraro, Tiziano
2016-06-09
We introduce a new method for the application of one-loop integrand reduction via the Laurent expansion algorithm, as implemented in the public C++ library Ninja. We show how the coefficients of the Laurent expansion can be computed by suitable contractions of the loop numerator tensor with cut-dependent projectors, making it possible to interface Ninja to any one-loop matrix element generator that can provide the components of this tensor. We implemented this technique in the Ninja library and interfaced it to MadLoop, which is part of the public MadGraph5_aMC@NLO framework. We performed a detailed performance study, comparing against other public reductionmore » tools, namely CutTools, Samurai, IREGI, PJFry++ and Golem95. We find that Ninja out-performs traditional integrand reduction in both speed and numerical stability, the latter being on par with that of the tensor integral reduction tool Golem95 which is however more limited and slower than Ninja. Lastly, we considered many benchmark multi-scale processes of increasing complexity, involving QCD and electro-weak corrections as well as effective non-renormalizable couplings, showing that Ninja’s performance scales well with both the rank and multiplicity of the considered process.« less
Irreducible Virasoro modules from tensor products
NASA Astrophysics Data System (ADS)
Tan, Haijun; Zhao, Kaiming
2016-04-01
In this paper, we obtain a class of irreducible Virasoro modules by taking tensor products of the irreducible Virasoro modules Ω(λ,b) with irreducible highest weight modules V(θ ,h) or with irreducible Virasoro modules Ind_{θ}(N) defined in Mazorchuk and Zhao (Selecta Math. (N.S.) 20:839-854, 2014). We determine the necessary and sufficient conditions for two such irreducible tensor products to be isomorphic. Then we prove that the tensor product of Ω(λ,b) with a classical Whittaker module is isomorphic to the module Ind_{θ, λ}({C}_{{m}}) defined in Mazorchuk and Weisner (Proc. Amer. Math. Soc. 142:3695-3703, 2014). As a by-product we obtain the necessary and sufficient conditions for the module Ind_{θ, λ}({C}_{{m}}) to be irreducible. We also generalize the module Ind_{θ, λ}({C}_{{m}}) to Ind_{θ,λ}({B}^{(n)}_{{s}}) for any non-negative integer n and use the above results to completely determine when the modules Ind_{θ,λ}({B}^{(n)}_{{s}}) are irreducible. The submodules of Ind_{θ,λ}({B}^{(n)}_{{s}}) are studied and an open problem in Guo et al. (J. Algebra 387:68-86, 2013) is solved. Feigin-Fuchs' Theorem on singular vectors of Verma modules over the Virasoro algebra is crucial to our proofs in this paper.
Fast Tensor Image Morphing for Elastic Registration
Yap, Pew-Thian; Wu, Guorong; Zhu, Hongtu; Lin, Weili; Shen, Dinggang
2009-01-01
We propose a novel algorithm, called Fast Tensor Image Morphing for Elastic Registration or F-TIMER. F-TIMER leverages multiscale tensor regional distributions and local boundaries for hierarchically driving deformable matching of tensor image volumes. Registration is achieved by aligning a set of automatically determined structural landmarks, via solving a soft correspondence problem. Based on the estimated correspondences, thin-plate splines are employed to generate a smooth, topology preserving, and dense transformation, and to avoid arbitrary mapping of non-landmark voxels. To mitigate the problem of local minima, which is common in the estimation of high dimensional transformations, we employ a hierarchical strategy where a small subset of voxels with more distinctive attribute vectors are first deployed as landmarks to estimate a relatively robust low-degrees-of-freedom transformation. As the registration progresses, an increasing number of voxels are permitted to participate in refining the correspondence matching. A scheme as such allows less conservative progression of the correspondence matching towards the optimal solution, and hence results in a faster matching speed. Results indicate that better accuracy can be achieved by F-TIMER, compared with other deformable registration algorithms [1, 2], with significantly reduced computation time cost of 4–14 folds. PMID:20426052
Minkowski tensors of anisotropic spatial structure
NASA Astrophysics Data System (ADS)
Schröder-Turk, G. E.; Mickel, W.; Kapfer, S. C.; Schaller, F. M.; Breidenbach, B.; Hug, D.; Mecke, K.
2013-08-01
This paper describes the theoretical foundation of and explicit algorithms for a novel approach to morphology and anisotropy analysis of complex spatial structure using tensor-valued Minkowski functionals, the so-called Minkowski tensors. Minkowski tensors are generalizations of the well-known scalar Minkowski functionals and are explicitly sensitive to anisotropic aspects of morphology, relevant for example for elastic moduli or permeability of microstructured materials. Here we derive explicit linear-time algorithms to compute these tensorial measures for three-dimensional shapes. These apply to representations of any object that can be represented by a triangulation of its bounding surface; their application is illustrated for the polyhedral Voronoi cellular complexes of jammed sphere configurations and for triangulations of a biopolymer fibre network obtained by confocal microscopy. The paper further bridges the substantial notational and conceptual gap between the different but equivalent approaches to scalar or tensorial Minkowski functionals in mathematics and in physics, hence making the mathematical measure theoretic formalism more readily accessible for future application in the physical sciences.
Cauchy's stress theorem for stresses represented by measures
NASA Astrophysics Data System (ADS)
Šilhavý, M.
2008-05-01
A version of Cauchy’s stress theorem is given in which the stress describing the system of forces in a continuous body is represented by a tensor valued measure with weak divergence a vector valued measure. The system of forces is formalized in the notion of an unbounded Cauchy flux generalizing the bounded Cauchy flux by Gurtin and Martins (Arch Ration Mech Anal 60:305-324, 1976). The main result of the paper says that unbounded Cauchy fluxes are in one-to-one correspondence with tensor valued measures with weak divergence a vector valued measure. Unavoidably, the force transmitted by a surface generally cannot be defined for all surfaces but only for almost every translation of the surface. Also conditions are given guaranteeing that the transmitted force is represented by a measure. These results are proved by using a new homotopy formula for tensor valued measure with weak divergence a vector valued measure.
Entanglement for all quantum states
NASA Astrophysics Data System (ADS)
de la Torre, A. C.; Goyeneche, D.; Leitao, L.
2010-03-01
It is shown that a state that is factorizable in the Hilbert space corresponding to some choice of degrees of freedom becomes entangled for a different choice of degrees of freedom. Therefore, entanglement is not a special case but is ubiquitous in quantum systems. Simple examples are calculated and a general proof is provided. The physical relevance of the change of tensor product structure is mentioned.
Exploiting Quantum Resonance to Solve Combinatorial Problems
NASA Technical Reports Server (NTRS)
Zak, Michail; Fijany, Amir
2006-01-01
Quantum resonance would be exploited in a proposed quantum-computing approach to the solution of combinatorial optimization problems. In quantum computing in general, one takes advantage of the fact that an algorithm cannot be decoupled from the physical effects available to implement it. Prior approaches to quantum computing have involved exploitation of only a subset of known quantum physical effects, notably including parallelism and entanglement, but not including resonance. In the proposed approach, one would utilize the combinatorial properties of tensor-product decomposability of unitary evolution of many-particle quantum systems for physically simulating solutions to NP-complete problems (a class of problems that are intractable with respect to classical methods of computation). In this approach, reinforcement and selection of a desired solution would be executed by means of quantum resonance. Classes of NP-complete problems that are important in practice and could be solved by the proposed approach include planning, scheduling, search, and optimal design.
Microearthquake moment tensors from the Coso Geothermal area
Julian, B.R.; G.R. Foulger; F. Monastero
2007-04-01
The Coso geothermal area, California, has produced hot water and steam for electricity generation for more than 20 years, during which time there has been a substantial amount of microearthquake activity in the area. Seismicity is monitored by a high-quality permanent network of 16 three-component digital borehole seismometers operated by the US Navy and supplemented by a ~ 14-station portable array of surface three-component digital instruments. The portable stations improve focal sphere coverage, providing seismic-wave polarity and amplitude data sets sufficient for determining full moment-tensor microearthquake mechanisms by the linearprogramming inversion method. We have developed a GUI-based interface to this inversion software that greatly increases its ease of use and makes feasible analyzing larger numbers of earthquakes than previously was practical. We show examples from an injection experiment conducted in well 34-9RD2, on the East Flank of the Coso geothermal area. This tight well was re-drilled February – March 2005 with the intention of hydrofracturing it, but instead, pervasive porosity and fractures were encountered at about 2660 m depth. Total drilling mud losses occurred, obviating the need to stimulate the well. These mud losses induced a 50-minute swarm of 44 microearthquakes, with magnitudes in the range -0.3 to 2.6. Most of the largest microearthquakes occurred in the first 2 minutes. Accurate relative relocations and moment tensors for the best-recorded subset reveal fine details of the fracture that was stimulated. This comprised a fault striking at N 20° E and dipping at 75° to the WNW, which propagated to the NNE and upward. Co-injection focal mechanisms reveal combined crack-opening and shear motion. Stress release and mode of failure differed between the pre-, co- and post-swarm periods. Some post-swarm events involved cavity collapse, suggesting that some of the cavity opening caused by the fluid injection was quickly reversed
Janka, Eshetu; Körner, Oliver; Rosenqvist, Eva; Ottosen, Carl-Otto
2015-05-01
Under a dynamic greenhouse climate control regime, temperature is adjusted to optimise plant physiological responses to prevailing irradiance levels; thus, both temperature and irradiance are used by the plant to maximise the rate of photosynthesis, assuming other factors are not limiting. The control regime may be optimised by monitoring plant responses, and may be promptly adjusted when plant performance is affected by extreme microclimatic conditions, such as high irradiance or temperature. To determine the stress indicators of plants based on their physiological responses, net photosynthesis (Pn) and four chlorophyll-a fluorescence parameters: maximum photochemical efficiency of PSII [Fv/Fm], electron transport rate [ETR], PSII operating efficiency [F'q/F'm], and non-photochemical quenching [NPQ] were assessed for potted chrysanthemum (Dendranthema grandiflora Tzvelev) 'Coral Charm' under different temperature (20, 24, 28, 32, 36 °C) and daily light integrals (DLI; 11, 20, 31, and 43 mol m(-2) created by a PAR of 171, 311, 485 and 667 μmol m(-2) s(-1) for 16 h). High irradiance (667 μmol m(-2) s(-1)) combined with high temperature (>32 °C) significantly (p < 0.05) decreased Fv/Fm. Under high irradiance, the maximum Pn and ETR were reached at 24 °C. Increased irradiance decreased the PSII operating efficiency and increased NPQ, while both high irradiance and temperature had a significant effect on the PSII operating efficiency at temperatures >28 °C. Under high irradiance and temperature, changes in the NPQ determined the PSII operating efficiency, with no major change in the fraction of open PSII centres (qL) (indicating a QA redox state). We conclude that 1) chrysanthemum plants cope with excess irradiance by non-radiative dissipation or a reversible stress response, with the effect on the Pn and quantum yield of PSII remaining low until the temperature reaches 28 °C and 2) the integration of online measurements to monitor photosynthesis and PSII
Continuous states for a relativistic problem plus tensor coupling in D-dimensional space
NASA Astrophysics Data System (ADS)
Eshghi, Mahdi; Mehraban, Hosein
2015-10-01
In this research, a relativistic particle scattering was investigated for particles with spin 1/2 in a hyperbolic potential including Coulomb-like tensor interaction in D-dimensional space. By using the Greene and Aldrich approximately, we presented solutions of the Dirac equation with this potential for any spin-orbit quantum number κ under spin symmetry. The normalized wave functions are expressed in terms of the hyper geometric series of continuous states on the k/ 2π scale. Also, the formula for the phase shifts is calculated. Some of the thermodynamics properties of a system Dirac electrons are also discussed.
Tensor-polarized structure functions: Tensor structure of deuteron in 2020's
NASA Astrophysics Data System (ADS)
Kumano, S.
2014-10-01
We explain spin structure for a spin-one hadron, in which there are new structure functions, in addition to the ones (F1, F2, g1, g2) which exist for the spin-1/2 nucleon, associated with its tensor structure. The new structure functions are b1, b2, b3, and b4 in deep inelastic scattering of a charged-lepton from a spin-one hadron such as the deuteron. Among them, twist- two functions are related by the Callan-Gross type relation b2 = 2xb1 in the Bjorken scaling limit. First, these new structure functions are introduced, and useful formulae are derived for projection operators of b1-4 from a hadron tensor Wμν. Second, a sum rule is explained for b1, and possible tensor-polarized distributions are discussed by using HERMES data in order to propose future experimental measurements and to compare them with theoretical models. A proposal was approved to measure b1 at the Thomas Jefferson National Accelerator Facility (JLab), so that much progress is expected for b1 in the near future. Third, formalisms of polarized proton-deuteron Drell-Yan processes are explained for probing especially tensor- polarized antiquark distributions, which were suggested by the HERMES data. The studies of the tensor-polarized structure functions will open a new era in 2020's for tensor-structure studies in terms of quark and gluon degrees of freedom, which are very different from ordinary descriptions in terms of nucleons and mesons.
Alonso-Alvarez, D.; Alen, B.; Ripalda, J. M.; Llorens, J. M.; Taboada, A. G.; Briones, F.; Roldan, M. A.; Hernandez-Saz, J.; Hernandez-Maldonado, D.; Herrera, M.; Molina, S. I.
2011-04-25
Quantum posts are assembled by epitaxial growth of closely spaced quantum dot layers, modulating the composition of a semiconductor alloy, typically InGaAs. In contrast with most self-assembled nanostructures, the height of quantum posts can be controlled with nanometer precision, up to a maximum value limited by the accumulated stress due to the lattice mismatch. Here, we present a strain compensation technique based on the controlled incorporation of phosphorous, which substantially increases the maximum attainable quantum post height. The luminescence from the resulting nanostructures presents giant linear polarization anisotropy.
A control volume study of the pressure tensor across a liquid-vapour interface
NASA Astrophysics Data System (ADS)
Braga, Carlos; Yatsyshin, Petr; Smith, Edward; Nold, Andreas; Goddard, Benjamin; Savva, Nikos; Schmuck, Markus; Duncan, Andrew; Sibley, David; Kalliadasis, Serafim
2015-11-01
The presence of an interface renders the properties of the system position dependent. The pressure tensor will no longer be uniform nor isotropic giving rise to the surface tension. The theory of Kirkwood-Buff gives a formal description of the surface tension based on the analysis of the local pressure tensor while capillary wave theory assumes the existence of an instantaneous intrinsic surface separating the liquid and vapour. Analysis of its Fourier components gives both structural and dynamical routes to compute the surface based on hydrodynamic theory. The defining equation of a capillary surface is given by the stress balance between the pressure tensors and the surface tension. Here, we employ the instantaneous interface as a representative surface across which we compute the local pressures following the seminal work of Irving and Kirkwood. The control volume approach to the Irving-Kirkwood expressions provides an exact balance between the stress and momentum transfer across the surface element allowing the study of the surface tension from a mechanical standpoint. We acknowledge financial support from European Research Council via Advanced Grant No. 247031.
Monserrat, Bartomeu Needs, Richard J.; Pickard, Chris J.
2014-10-07
We study the effects of atomic vibrations on the solid-state chemical shielding tensor using first principles density functional theory calculations. At the harmonic level, we use a Monte Carlo method and a perturbative expansion. The Monte Carlo method is accurate but computationally expensive, while the perturbative method is computationally more efficient, but approximate. We find excellent agreement between the two methods for both the isotropic shift and the shielding anisotropy. The effects of zero-point quantum mechanical nuclear motion are important up to relatively high temperatures: at 500 K they still represent about half of the overall vibrational contribution. We also investigate the effects of anharmonic vibrations, finding that their contribution to the zero-point correction to the chemical shielding tensor is small. We exemplify these ideas using magnesium oxide and the molecular crystals L-alanine and β-aspartyl-L-alanine. We therefore propose as the method of choice to incorporate the effects of temperature in solid state chemical shielding tensor calculations using the perturbative expansion within the harmonic approximation. This approach is accurate and requires a computational effort that is about an order of magnitude smaller than that of dynamical or Monte Carlo approaches, so these effects might be routinely accounted for.
More on loops in reheating: non-gaussianities and tensor power spectrum
Katirci, Nihan; Kaya, Ali; Tarman, Merve E-mail: ali.kaya@boun.edu.tr
2014-06-01
We consider the single field chaotic m{sup 2}φ{sup 2} inflationary model with a period of preheating, where the inflaton decays to another scalar field χ in the parametric resonance regime. In a recent work, one of us has shown that the χ modes circulating in the loops during preheating notably modify the (ζζ) correlation function. We first rederive this result using a different gauge condition hence reconfirm that superhorizon ζ modes are affected by the loops in preheating. Further, we examine how χ loops give rise to non-gaussianity and affect the tensor perturbations. For that, all cubic and some higher order interactions involving two χ fields are determined and their contribution to the non-gaussianity parameter f{sub NL} and the tensor power spectrum are calculated at one loop. Our estimates for these corrections show that while a large amount of non-gaussianity can be produced during reheating, the tensor power spectrum receive moderate corrections. We observe that the loop quantum effects increase with more χ fields circulating in the loops indicating that the perturbation theory might be broken down. These findings demonstrate that the loop corrections during reheating are significant and they must be taken into account for precision inflationary cosmology.
The infrared fundamental intensities and polar tensor of CH 3NC
NASA Astrophysics Data System (ADS)
Haiduke, R. L. A.; Hase, Y.; Bruns, R. E.
2003-01-01
The molecular force field and polar tensor of methyl isocyanide have been determined from its gas phase vibrational frequencies and infrared intensities. Quantum chemical results from MP2(FC), B3LYP and quadratic configuration interaction calculation including single and double substitutions procedures using a 6-311++G(3d,3p) basis set have been used to determine the signs of the dipole moment derivatives with respect to the normal coordinates as well as estimate individual fundamental intensities of the overlapped vl- v5 and v3- v6 band systems. Principal component graphical representations of the A1 and E symmetry polar tensor elements were useful in determining preferred sets of tensor elements. The mean dipole moment derivative (GAPT charge) of the methyl carbon in CH 3NC, 0.347 e, is between the corresponding values in CH 3CN, 0.110 e, and CH 3F, 0.541 e. The mean dipole moment derivatives obtained here indicate the correct 1s methyl carbon ionization energy as 293.35 eV which is 0.98 eV higher than the corresponding ionization energy of the terminal atom.
More on loops in reheating: non-gaussianities and tensor power spectrum
Katırcı, Nihan; Kaya, Ali; Tarman, Merve
2014-06-11
We consider the single field chaotic m{sup 2}ϕ{sup 2} inflationary model with a period of preheating, where the inflaton decays to another scalar field χ in the parametric resonance regime. In a recent work, one of us has shown that the χ modes circulating in the loops during preheating notably modify the <ζζ> correlation function. We first rederive this result using a different gauge condition hence reconfirm that superhorizon ζ modes are affected by the loops in preheating. Further, we examine how χ loops give rise to non-gaussianity and affect the tensor perturbations. For that, all cubic and some higher order interactions involving two χ fields are determined and their contribution to the non-gaussianity parameter f{sub NL} and the tensor power spectrum are calculated at one loop. Our estimates for these corrections show that while a large amount of non-gaussianity can be produced during reheating, the tensor power spectrum receive moderate corrections. We observe that the loop quantum effects increase with more χ fields circulating in the loops indicating that the perturbation theory might be broken down. These findings demonstrate that the loop corrections during reheating are significant and they must be taken into account for precision inflationary cosmology.
Quantum mechanics from invariance principles
NASA Astrophysics Data System (ADS)
Moldoveanu, Florin
2015-07-01
Quantum mechanics is an extremely successful theory of nature and yet it lacks an intuitive axiomatization. In contrast, the special theory of relativity is well understood and is rooted into natural or experimentally justified postulates. Here we introduce an axiomatization approach to quantum mechanics which is very similar to special theory of relativity derivation. The core idea is that a composed system obeys the same laws of nature as its components. This leads to a Jordan-Lie algebraic formulation of quantum mechanics. The starting assumptions are minimal: the laws of nature are invariant under time evolution, the laws of nature are invariant under tensor composition, the laws of nature are relational, together with the ability to define a physical state (positivity). Quantum mechanics is singled out by a fifth experimentally justified postulate: nature violates Bell's inequalities.
Automatic deformable diffusion tensor registration for fiber population analysis.
Irfanoglu, M O; Machiraju, R; Sammet, S; Pierpaoli, C; Knopp, M V
2008-01-01
In this work, we propose a novel method for deformable tensor-to-tensor registration of Diffusion Tensor Images. Our registration method models the distances in between the tensors with Geode-sic-Loxodromes and employs a version of Multi-Dimensional Scaling (MDS) algorithm to unfold the manifold described with this metric. Defining the same shape properties as tensors, the vector images obtained through MDS are fed into a multi-step vector-image registration scheme and the resulting deformation fields are used to reorient the tensor fields. Results on brain DTI indicate that the proposed method is very suitable for deformable fiber-to-fiber correspondence and DTI-atlas construction. PMID:18982704
Turbulent fluid motion 2: Scalars, vectors, and tensors
NASA Technical Reports Server (NTRS)
Deissler, Robert G.
1991-01-01
The author shows that the sum or difference of two vectors is a vector. Similarly the sum of any two tensors of the same order is a tensor of that order. No meaning is attached to the sum of tensors of different orders, say u(sub i) + u(sub ij); that is not a tensor. In general, an equation containing tensors has meaning only if all the terms in the equation are tensors of the same order, and if the same unrepeated subscripts appear in all the terms. These facts will be used in obtaining appropriate equations for fluid turbulence. With the foregoing background, the derivation of appropriate continuum equations for turbulence should be straightforward.
Scalable tensor factorizations with missing data.
Morup, Morten; Dunlavy, Daniel M.; Acar, Evrim; Kolda, Tamara Gibson
2010-04-01
The problem of missing data is ubiquitous in domains such as biomedical signal processing, network traffic analysis, bibliometrics, social network analysis, chemometrics, computer vision, and communication networks|all domains in which data collection is subject to occasional errors. Moreover, these data sets can be quite large and have more than two axes of variation, e.g., sender, receiver, time. Many applications in those domains aim to capture the underlying latent structure of the data; in other words, they need to factorize data sets with missing entries. If we cannot address the problem of missing data, many important data sets will be discarded or improperly analyzed. Therefore, we need a robust and scalable approach for factorizing multi-way arrays (i.e., tensors) in the presence of missing data. We focus on one of the most well-known tensor factorizations, CANDECOMP/PARAFAC (CP), and formulate the CP model as a weighted least squares problem that models only the known entries. We develop an algorithm called CP-WOPT (CP Weighted OPTimization) using a first-order optimization approach to solve the weighted least squares problem. Based on extensive numerical experiments, our algorithm is shown to successfully factor tensors with noise and up to 70% missing data. Moreover, our approach is significantly faster than the leading alternative and scales to larger problems. To show the real-world usefulness of CP-WOPT, we illustrate its applicability on a novel EEG (electroencephalogram) application where missing data is frequently encountered due to disconnections of electrodes.
Relativistic Lagrangian displacement field and tensor perturbations
NASA Astrophysics Data System (ADS)
Rampf, Cornelius; Wiegand, Alexander
2014-12-01
We investigate the purely spatial Lagrangian coordinate transformation from the Lagrangian to the basic Eulerian frame. We demonstrate three techniques for extracting the relativistic displacement field from a given solution in the Lagrangian frame. These techniques are (a) from defining a local set of Eulerian coordinates embedded into the Lagrangian frame; (b) from performing a specific gauge transformation; and (c) from a fully nonperturbative approach based on the Arnowitt-Deser-Misner (ADM) split. The latter approach shows that this decomposition is not tied to a specific perturbative formulation for the solution of the Einstein equations. Rather, it can be defined at the level of the nonperturbative coordinate change from the Lagrangian to the Eulerian description. Studying such different techniques is useful because it allows us to compare and develop further the various approximation techniques available in the Lagrangian formulation. We find that one has to solve the gravitational wave equation in the relativistic analysis, otherwise the corresponding Newtonian limit will necessarily contain spurious nonpropagating tensor artifacts at second order in the Eulerian frame. We also derive the magnetic part of the Weyl tensor in the Lagrangian frame, and find that it is not only excited by gravitational waves but also by tensor perturbations which are induced through the nonlinear frame dragging. We apply our findings to calculate for the first time the relativistic displacement field, up to second order, for a Λ CDM Universe in the presence of a local primordial non-Gaussian component. Finally, we also comment on recent claims about whether mass conservation in the Lagrangian frame is violated.
Irreducible Cartesian tensors of highest weight, for arbitrary order
NASA Astrophysics Data System (ADS)
Mane, S. R.
2016-03-01
A closed form expression is presented for the irreducible Cartesian tensor of highest weight, for arbitrary order. Two proofs are offered, one employing bookkeeping of indices and, after establishing the connection with the so-called natural tensors and their projection operators, the other one employing purely coordinate-free tensor manipulations. Some theorems and formulas in the published literature are generalized from SO(3) to SO(n), for dimensions n ≥ 3.
Redberry: a computer algebra system designed for tensor manipulation
NASA Astrophysics Data System (ADS)
Poslavsky, Stanislav; Bolotin, Dmitry
2015-05-01
In this paper we focus on the main aspects of computer-aided calculations with tensors and present a new computer algebra system Redberry which was specifically designed for algebraic tensor manipulation. We touch upon distinctive features of tensor software in comparison with pure scalar systems, discuss the main approaches used to handle tensorial expressions and present the comparison of Redberry performance with other relevant tools.
Braided Tensor Categories and Extensions of Vertex Operator Algebras
NASA Astrophysics Data System (ADS)
Huang, Yi-Zhi; Kirillov, Alexander; Lepowsky, James
2015-08-01
Let V be a vertex operator algebra satisfying suitable conditions such that in particular its module category has a natural vertex tensor category structure, and consequently, a natural braided tensor category structure. We prove that the notions of extension (i.e., enlargement) of V and of commutative associative algebra, with uniqueness of unit and with trivial twist, in the braided tensor category of V-modules are equivalent.
Beam-plasma dielectric tensor with Mathematica
NASA Astrophysics Data System (ADS)
Bret, A.
2007-03-01
We present a Mathematica notebook allowing for the symbolic calculation of the 3×3 dielectric tensor of an electron-beam plasma system in the fluid approximation. Calculation is detailed for a cold relativistic electron beam entering a cold magnetized plasma, and for arbitrarily oriented wave vectors. We show how one can elaborate on this example to account for temperatures, arbitrarily oriented magnetic field or a different kind of plasma. Program summaryTitle of program: Tensor Catalog identifier: ADYT_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADYT_v1_0 Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Computer for which the program is designed and others on which it has been tested: Computers: Any computer running Mathematica 4.1. Tested on DELL Dimension 5100 and IBM ThinkPad T42. Installations: ETSI Industriales, Universidad Castilla la Mancha, Ciudad Real, Spain Operating system under which the program has been tested: Windows XP Pro Programming language used: Mathematica 4.1 Memory required to execute with typical data: 7.17 Mbytes No. of bytes in distributed program, including test data, etc.: 33 439 No. of lines in distributed program, including test data, etc.: 3169 Distribution format: tar.gz Nature of the physical problem: The dielectric tensor of a relativistic beam plasma system may be quite involved to calculate symbolically when considering a magnetized plasma, kinetic pressure, collisions between species, and so on. The present Mathematica notebook performs the symbolic computation in terms of some usual dimensionless variables. Method of solution: The linearized relativistic fluid equations are directly entered and solved by Mathematica to express the first-order expression of the current. This expression is then introduced into a combination of Faraday and Ampère-Maxwell's equations to give the dielectric tensor. Some additional manipulations are needed to express the result in terms of the
Bounds on tensor wave and twisted inflation
NASA Astrophysics Data System (ADS)
Panda, Sudhakar; Sami, M.; Ward, John
2010-11-01
We study the bounds on tensor wave in a class of twisted inflation models, where D(4+2k)-branes are wrapped on cycles in the compact manifold and wrap the Kaluza-Klein direction in the corresponding effective field theory. While the lower bound is found to be analogous to that in type IIB models of brane inflation, the upper bound turns out to be significantly different. This is argued for a range of values for the parameter gsM satisfying the self-consistency relation and the WMAP data. Further, we observe that the wrapped D8-brane appears to be the most attractive from a cosmological perspective.
A Tensor Hyperviscosity Model in Kull
Ulitsky, M
2005-06-28
A tensor artificial hyper-viscosity model has recently been added to the available list of artificial viscosities that one can chose from when running KULL. This model is based on the theoretical work of A. Cook and B. Cabot, and the numerical results of running the model in the high-order spectral/compact finite difference framework of the Eulerian MIRANDA code. The viscosity model is based on filtering a Laplacian or bi-Laplacian of the strain rate magnitude, and it was desired to investigate whether the formalism that worked so well for the MIRANDA research code could be carried over to an unstructured ALE code like KULL.
NASA Astrophysics Data System (ADS)
Hosur, Pavan; Qi, Xiao-Liang; Roberts, Daniel A.; Yoshida, Beni
2016-02-01
We study chaos and scrambling in unitary channels by considering their entanglement properties as states. Using out-of-time-order correlation functions to diagnose chaos, we characterize the ability of a channel to process quantum information. We show that the generic decay of such correlators implies that any input subsystem must have near vanishing mutual information with almost all partitions of the output. Additionally, we propose the negativity of the tripartite information of the channel as a general diagnostic of scrambling. This measures the delocalization of information and is closely related to the decay of out-of-time-order correlators. We back up our results with numerics in two non-integrable models and analytic results in a perfect tensor network model of chaotic time evolution. These results show that the butterfly effect in quantum systems implies the information-theoretic definition of scrambling.
NASA Astrophysics Data System (ADS)
Zacharias, Mario; Paul, Indranil; Garst, Markus
2015-07-01
We discuss elastic instabilities of the atomic crystal lattice at zero temperature. Because of long-range shear forces of the solid, at such transitions the phonon velocities vanish, if at all, only along certain crystallographic directions, and, consequently, the critical phonon fluctuations are suppressed to a lower dimensional manifold and governed by a Gaussian fixed point. In the case of symmetry-breaking elastic transitions, a characteristic critical phonon thermodynamics arises that is found, e.g., to violate Debye's T3 law for the specific heat. We point out that quantum critical elasticity is triggered whenever a critical soft mode couples linearly to the strain tensor. In particular, this is relevant for the electronic Ising-nematic quantum phase transition in a tetragonal crystal as discussed in the context of certain cuprates, ruthenates, and iron-based superconductors.
Zacharias, Mario; Paul, Indranil; Garst, Markus
2015-07-10
We discuss elastic instabilities of the atomic crystal lattice at zero temperature. Because of long-range shear forces of the solid, at such transitions the phonon velocities vanish, if at all, only along certain crystallographic directions, and, consequently, the critical phonon fluctuations are suppressed to a lower dimensional manifold and governed by a Gaussian fixed point. In the case of symmetry-breaking elastic transitions, a characteristic critical phonon thermodynamics arises that is found, e.g., to violate Debye's T(3) law for the specific heat. We point out that quantum critical elasticity is triggered whenever a critical soft mode couples linearly to the strain tensor. In particular, this is relevant for the electronic Ising-nematic quantum phase transition in a tetragonal crystal as discussed in the context of certain cuprates, ruthenates, and iron-based superconductors. PMID:26207483
The Topology of Three-Dimensional Symmetric Tensor Fields
NASA Technical Reports Server (NTRS)
Lavin, Yingmei; Levy, Yuval; Hesselink, Lambertus
1994-01-01
We study the topology of 3-D symmetric tensor fields. The goal is to represent their complex structure by a simple set of carefully chosen points and lines analogous to vector field topology. The basic constituents of tensor topology are the degenerate points, or points where eigenvalues are equal to each other. First, we introduce a new method for locating 3-D degenerate points. We then extract the topological skeletons of the eigenvector fields and use them for a compact, comprehensive description of the tensor field. Finally, we demonstrate the use of tensor field topology for the interpretation of the two-force Boussinesq problem.
Emergent General Relativity and Local Translation Symmetry in Tensor Model
NASA Astrophysics Data System (ADS)
Sasakura, Naoki
2009-12-01
The tensor model is discussed as theory of dynamical fuzzy spaces and as a way to formulate gravity on fuzzy spaces. From numerical analyses, it is shown that the low-lying long-wavelength fluctuation spectra around Gaussian background solutions in the tensor model are in agreement with the geometric fluctuations on flat spaces in the general relativity. It is also shown that part of the orthogonal symmetry of the tensor model spontaneously broken by the backgrounds correspond to the local translation symmetry of the general relativity. Thus the tensor model can provide an interesting model of simultaneous emergence of space and the general relativity including the local translation symmetry.
Generalized Taub-NUT metrics and Killing-Yano tensors
NASA Astrophysics Data System (ADS)
Visinescu, Mihai
2000-06-01
The necessary condition that a Stäckel-Killing tensor of valence two should be the contracted product of a Killing-Yano tensor of valence two with itself is rederived for a Riemannian manifold. This condition is applied to the generalized Euclidean Taub-NUT metrics which admit a Kepler-type symmetry. It is shown that, in general, the Stäckel-Killing tensors involved in the Runge-Lenz vector cannot be expressed as a product of Killing-Yano tensors. The only exception is the original Taub-NUT metric.
Tensor Modeling Based for Airborne LiDAR Data Classification
NASA Astrophysics Data System (ADS)
Li, N.; Liu, C.; Pfeifer, N.; Yin, J. F.; Liao, Z. Y.; Zhou, Y.
2016-06-01
Feature selection and description is a key factor in classification of Earth observation data. In this paper a classification method based on tensor decomposition is proposed. First, multiple features are extracted from raw LiDAR point cloud, and raster LiDAR images are derived by accumulating features or the "raw" data attributes. Then, the feature rasters of LiDAR data are stored as a tensor, and tensor decomposition is used to select component features. This tensor representation could keep the initial spatial structure and insure the consideration of the neighborhood. Based on a small number of component features a k nearest neighborhood classification is applied.
Kopský, Vojtech
2006-03-01
The theory of domain states is reviewed as a prerequisite for consideration of tensorial distinction of domain states. It is then shown that the parameters of the first domain in a ferroic phase transition from a set of isomorphic groups of the same oriented Laue class can be systematically and suitably represented in terms of typical variables. On replacing these variables by actual tensor components according to the previous paper, we can reveal the tensorial parameters associated with each particular symmetry descent. Parameters are distinguished by the ireps to which they belong and this can be used to determine which of them are the principal parameters that distinguish all domain states, in contrast to secondary parameters which are common to several domain states. In general, the parameters are expressed as the covariant components of the tensors. A general procedure is described which is designed to transform the results to Cartesian components. It consists of two parts: the first, called the labelling of covariants, and its inverse, called the conversion equations. Transformation of parameters from the first domain state to other states is now reduced to irreducible subspaces whose maximal dimension is three in contrast with higher dimensions of tensor spaces. With this method, we can explicitly calculate tensor parameters for all domain states. To find the distinction of pairs of domain states, it is suitable to use the concept of the twinning group which is briefly described. PMID:16489243
A general theory of linear cosmological perturbations: scalar-tensor and vector-tensor theories
NASA Astrophysics Data System (ADS)
Lagos, Macarena; Baker, Tessa; Ferreira, Pedro G.; Noller, Johannes
2016-08-01
We present a method for parametrizing linear cosmological perturbations of theories of gravity, around homogeneous and isotropic backgrounds. The method is sufficiently general and systematic that it can be applied to theories with any degrees of freedom (DoFs) and arbitrary gauge symmetries. In this paper, we focus on scalar-tensor and vector-tensor theories, invariant under linear coordinate transformations. In the case of scalar-tensor theories, we use our framework to recover the simple parametrizations of linearized Horndeski and ``Beyond Horndeski'' theories, and also find higher-derivative corrections. In the case of vector-tensor theories, we first construct the most general quadratic action for perturbations that leads to second-order equations of motion, which propagates two scalar DoFs. Then we specialize to the case in which the vector field is time-like (à la Einstein-Aether gravity), where the theory only propagates one scalar DoF. As a result, we identify the complete forms of the quadratic actions for perturbations, and the number of free parameters that need to be defined, to cosmologically characterize these two broad classes of theories.
Minimal tensors and purely electric or magnetic spacetimes of arbitrary dimension
NASA Astrophysics Data System (ADS)
Hervik, Sigbjørn; Ortaggio, Marcello; Wylleman, Lode
2013-08-01
We consider time reversal transformations to obtain twofold orthogonal splittings of any tensor on a Lorentzian space of arbitrary dimension n. Applied to the Weyl tensor of a spacetime, this leads to a definition of its electric and magnetic parts relative to an observer (defined by a unit timelike vector field u), in any dimension. We study the cases where one of these parts vanishes in detail, i.e., purely electric (PE) or magnetic (PM) spacetimes. We generalize several results from four to higher dimensions and discuss new features of higher dimensions. For instance, we prove that the only permitted Weyl types are G, Ii and D, and discuss the possible relation of u with the Weyl aligned null directions (WANDs); we provide invariant conditions that characterize PE/PM spacetimes, such as Bel-Debever-like criteria, or constraints on scalar invariants, and connect the PE/PM parts to the kinematic quantities of u; we present conditions under which direct product spacetimes (and certain warps) are PE/PM, which enables us to construct explicit examples. In particular, it is also shown that all static spacetimes are necessarily PE, while stationary spacetimes (such as spinning black holes) are in general neither PE nor PM. Whereas ample classes of PE spacetimes exist, PM solutions are elusive; specifically, we prove that PM Einstein spacetimes of type D do not exist, in any dimension. Finally, we derive corresponding results for the electric/magnetic parts of the Riemann tensor, which is useful when considering spacetimes with matter fields, and moreover leads to first examples of PM spacetimes in higher dimensions. We also note in passing that PE/PM Weyl (or Riemann) tensors provide examples of minimal tensors, and we make the connection hereof with the recently proved alignment theorem (Hervik 2011 Class. Quantum Grav. 28 215009). This in turn sheds new light on the classification of the Weyl tensors based on null alignment, providing a further invariant
3D extension of Tensorial Polar Decomposition. Application to (photo-)elasticity tensors
NASA Astrophysics Data System (ADS)
Desmorat, Rodrigue; Desmorat, Boris
2016-06-01
The orthogonalized harmonic decomposition of symmetric fourth-order tensors (i.e. having major and minor indicial symmetries, such as elasticity tensors) is completed by a representation of harmonic fourth-order tensors H by means of two second-order harmonic (symmetric deviatoric) tensors only. A similar decomposition is obtained for non-symmetric tensors (i.e. having minor indicial symmetry only, such as photo-elasticity tensors or elasto-plasticity tangent operators) introducing a fourth-order major antisymmetric traceless tensor Z. The tensor Z is represented by means of one harmonic second-order tensor and one antisymmetric second-order tensor only. Representations of totally symmetric (rari-constant), symmetric and major antisymmetric fourth-order tensors are simple particular cases of the proposed general representation. Closed-form expressions for tensor decomposition are given in the monoclinic case. Practical applications to elasticity and photo-elasticity monoclinic tensors are finally presented. xml:lang="fr"
On the geometry of mixed states and the Fisher information tensor
NASA Astrophysics Data System (ADS)
Contreras, I.; Ercolessi, E.; Schiavina, M.
2016-06-01
In this paper, we will review the co-adjoint orbit formulation of finite dimensional quantum mechanics, and in this framework, we will interpret the notion of quantum Fisher information index (and metric). Following previous work of part of the authors, who introduced the definition of Fisher information tensor, we will show how its antisymmetric part is the pullback of the natural Kostant-Kirillov-Souriau symplectic form along some natural diffeomorphism. In order to do this, we will need to understand the symmetric logarithmic derivative as a proper 1-form, settling the issues about its very definition and explicit computation. Moreover, the fibration of co-adjoint orbits, seen as spaces of mixed states, is also discussed.
Direct Solution of the Chemical Master Equation Using Quantized Tensor Trains
Kazeev, Vladimir; Khammash, Mustafa; Nip, Michael; Schwab, Christoph
2014-01-01
The Chemical Master Equation (CME) is a cornerstone of stochastic analysis and simulation of models of biochemical reaction networks. Yet direct solutions of the CME have remained elusive. Although several approaches overcome the infinite dimensional nature of the CME through projections or other means, a common feature of proposed approaches is their susceptibility to the curse of dimensionality, i.e. the exponential growth in memory and computational requirements in the number of problem dimensions. We present a novel approach that has the potential to “lift” this curse of dimensionality. The approach is based on the use of the recently proposed Quantized Tensor Train (QTT) formatted numerical linear algebra for the low parametric, numerical representation of tensors. The QTT decomposition admits both, algorithms for basic tensor arithmetics with complexity scaling linearly in the dimension (number of species) and sub-linearly in the mode size (maximum copy number), and a numerical tensor rounding procedure which is stable and quasi-optimal. We show how the CME can be represented in QTT format, then use the exponentially-converging -discontinuous Galerkin discretization in time to reduce the CME evolution problem to a set of QTT-structured linear equations to be solved at each time step using an algorithm based on Density Matrix Renormalization Group (DMRG) methods from quantum chemistry. Our method automatically adapts the “basis” of the solution at every time step guaranteeing that it is large enough to capture the dynamics of interest but no larger than necessary, as this would increase the computational complexity. Our approach is demonstrated by applying it to three different examples from systems biology: independent birth-death process, an example of enzymatic futile cycle, and a stochastic switch model. The numerical results on these examples demonstrate that the proposed QTT method achieves dramatic speedups and several orders of magnitude
Direct solution of the Chemical Master Equation using quantized tensor trains.
Kazeev, Vladimir; Khammash, Mustafa; Nip, Michael; Schwab, Christoph
2014-03-01
The Chemical Master Equation (CME) is a cornerstone of stochastic analysis and simulation of models of biochemical reaction networks. Yet direct solutions of the CME have remained elusive. Although several approaches overcome the infinite dimensional nature of the CME through projections or other means, a common feature of proposed approaches is their susceptibility to the curse of dimensionality, i.e. the exponential growth in memory and computational requirements in the number of problem dimensions. We present a novel approach that has the potential to "lift" this curse of dimensionality. The approach is based on the use of the recently proposed Quantized Tensor Train (QTT) formatted numerical linear algebra for the low parametric, numerical representation of tensors. The QTT decomposition admits both, algorithms for basic tensor arithmetics with complexity scaling linearly in the dimension (number of species) and sub-linearly in the mode size (maximum copy number), and a numerical tensor rounding procedure which is stable and quasi-optimal. We show how the CME can be represented in QTT format, then use the exponentially-converging hp-discontinuous Galerkin discretization in time to reduce the CME evolution problem to a set of QTT-structured linear equations to be solved at each time step using an algorithm based on Density Matrix Renormalization Group (DMRG) methods from quantum chemistry. Our method automatically adapts the "basis" of the solution at every time step guaranteeing that it is large enough to capture the dynamics of interest but no larger than necessary, as this would increase the computational complexity. Our approach is demonstrated by applying it to three different examples from systems biology: independent birth-death process, an example of enzymatic futile cycle, and a stochastic switch model. The numerical results on these examples demonstrate that the proposed QTT method achieves dramatic speedups and several orders of magnitude storage
Moment tensor inversion of ground motion from mining-induced earthquakes, Trail Mountain, Utah
Fletcher, Joe B.; McGarr, A.
2005-01-01
A seismic network was operated in the vicinity of the Trail Mountain mine, central Utah, from the summer of 2000 to the spring of 2001 to investigate the seismic hazard to a local dam from mining-induced events that we expect to be triggered by future coal mining in this area. In support of efforts to develop groundmotion prediction relations for this situation, we inverted ground-motion recordings for six mining-induced events to determine seismic moment tensors and then to estimate moment magnitudes M for comparison with the network coda magnitudes Mc. Six components of the tensor were determined, for an assumed point source, following the inversion method of McGarr (1992a), which uses key measurements of amplitude from obvious features of the displacement waveforms. When the resulting moment tensors were decomposed into implosive and deviatoric components, we found that four of the six events showed a substantial volume reduction, presumably due to coseismic closure of the adjacent mine openings. For these four events, the volume reduction ranges from 27% to 55% of the shear component (fault area times average slip). Radiated seismic energy, computed from attenuation-corrected body-wave spectra, ranged from 2.4 ?? 105 to 2.4 ?? 106 J for events with M from 1.3 to 1.8, yielding apparent stresses from 0.02 to 0.06 MPa. The energy released for each event, approximated as the product of volume reduction and overburden stress, when compared with the corresponding seismic energies, revealed seismic efficiencies ranging from 0.5% to 7%. The low apparent stresses are consistent with the shallow focal depths of 0.2 to 0.6 km and rupture in a low stress/low strength regime compared with typical earthquake source regions at midcrustal depths.
Nguyen, Kathy C; Willmore, William G; Tayabali, Azam F
2013-04-01
The mechanisms of toxicity related to human hepatocellular carcinoma HepG2 cell exposures to cadmium telluride quantum dots (CdTe-QDs) were investigated. CdTe-QDs caused cytotoxicity in HepG2 cells in a dose- and time-dependent manner. Treated cells showed an increase in reactive oxygen species (ROS). Altered antioxidant levels were demonstrated by depletion of reduced glutathione (GSH), a decreased ratio of reduced glutathione to oxidized glutathione (GSH/GSSG) and an increased NF-E2-related Factor 2 (Nrf2) activation. Enzyme assays showed that superoxide dismutase (SOD) activity was elevated whereas catalase (CAT) and glutathione-S-transferase (GST) activities were depressed. Further analyses revealed that CdTe-QD exposure resulted in apoptosis, indicated by changes in levels of caspase-3 activity, poly ADP-ribose polymerase (PARP) cleavage and phosphatidylserine externalization. Extrinsic apoptotic pathway markers such as Fas levels and caspase-8 activity increased as a result of CdTe-QD exposure. Involvement of the intrinsic/mitochondrial apoptotic pathway was indicated by decreased levels of B-cell lymphoma 2 (Bcl2) protein and mitochondrial cytochrome c, and by increased levels of mitochondrial Bcl-2-associated X protein (Bax) and cytosolic cytochrome c. Further, mitogen-activated protein kinases (MAPKs) such as c-Jun N-terminal kinases (JNK), extracellular signal-regulated kinases (Erk1/2), and p38 were all activated. Our findings reveal that CdTe-QDs cause oxidative stress, interfere with antioxidant defenses and activate protein kinases, leading to apoptosis via both extrinsic and intrinsic pathways. Since the effects of CdTe-QDs on selected biomarkers were similar or greater compared to those of CdCl2 at equivalent concentrations of cadmium, the study suggests that the toxicity of CdTe-QDs arises from a combination of the effects of cadmium and ROS generated from the NPs. PMID:23485651
Xue, Zhong; Li, Hai; Guo, Lei; Wong, Stephen T C
2010-08-01
It is a key step to spatially align diffusion tensor images (DTI) to quantitatively compare neural images obtained from different subjects or the same subject at different timepoints. Different from traditional scalar or multi-channel image registration methods, tensor orientation should be considered in DTI registration. Recently, several DTI registration methods have been proposed in the literature, but deformation fields are purely dependent on the tensor features not the whole tensor information. Other methods, such as the piece-wise affine transformation and the diffeomorphic non-linear registration algorithms, use analytical gradients of the registration objective functions by simultaneously considering the reorientation and deformation of tensors during the registration. However, only relatively local tensor information such as voxel-wise tensor-similarity is utilized. This paper proposes a new DTI image registration algorithm, called local fast marching (FM)-based simultaneous registration. The algorithm not only considers the orientation of tensors during registration but also utilizes the neighborhood tensor information of each voxel to drive the deformation, and such neighborhood tensor information is extracted from a local fast marching algorithm around the voxels of interest. These local fast marching-based tensor features efficiently reflect the diffusion patterns around each voxel within a spherical neighborhood and can capture relatively distinctive features of the anatomical structures. Using simulated and real DTI human brain data the experimental results show that the proposed algorithm is more accurate compared with the FA-based registration and is more efficient than its counterpart, the neighborhood tensor similarity-based registration. PMID:20382233
Interactive Volume Rendering of Diffusion Tensor Data
Hlawitschka, Mario; Weber, Gunther; Anwander, Alfred; Carmichael, Owen; Hamann, Bernd; Scheuermann, Gerik
2007-03-30
As 3D volumetric images of the human body become an increasingly crucial source of information for the diagnosis and treatment of a broad variety of medical conditions, advanced techniques that allow clinicians to efficiently and clearly visualize volumetric images become increasingly important. Interaction has proven to be a key concept in analysis of medical images because static images of 3D data are prone to artifacts and misunderstanding of depth. Furthermore, fading out clinically irrelevant aspects of the image while preserving contextual anatomical landmarks helps medical doctors to focus on important parts of the images without becoming disoriented. Our goal was to develop a tool that unifies interactive manipulation and context preserving visualization of medical images with a special focus on diffusion tensor imaging (DTI) data. At each image voxel, DTI provides a 3 x 3 tensor whose entries represent the 3D statistical properties of water diffusion locally. Water motion that is preferential to specific spatial directions suggests structural organization of the underlying biological tissue; in particular, in the human brain, the naturally occuring diffusion of water in the axon portion of neurons is predominantly anisotropic along the longitudinal direction of the elongated, fiber-like axons [MMM+02]. This property has made DTI an emerging source of information about the structural integrity of axons and axonal connectivity between brain regions, both of which are thought to be disrupted in a broad range of medical disorders including multiple sclerosis, cerebrovascular disease, and autism [Mos02, FCI+01, JLH+99, BGKM+04, BJB+03].
Energy-momentum tensor of bouncing gravitons
Iofa, Mikhail Z.
2015-07-14
In models of the Universe with extra dimensions gravity propagates in the whole space-time. Graviton production by matter on the brane is significant in the early hot Universe. In a model of 3-brane with matter embedded in 5D space-time conditions for gravitons emitted from the brane to the bulk to return back to the brane are found. For a given 5-momentum of graviton falling back to the brane the interval between the times of emission and return to the brane is calculated. A method to calculate contribution to the energy-momentum tensor from multiple graviton bouncings is developed. Explicit expressions for contributions to the energy-momentum tensor of gravitons which have made one, two and three bounces are obtained and their magnitudes are numerically calculated. These expressions are used to solve the evolution equation for dark radiation. A relation connecting reheating temperature and the scale of extra dimension is obtained. For the reheating temperature T{sub R}∼10{sup 6} GeV we estimate the scale of extra dimension μ to be of order 10{sup −9} GeV (μ{sup −1}∼10{sup −5} cm)
Stability of Horndeski vector-tensor interactions
Jiménez, Jose Beltrán; Durrer, Ruth; Heisenberg, Lavinia; Thorsrud, Mikjel E-mail: ruth.durrer@unige.ch E-mail: mikjel.thorsrud@astro.uio.no
2013-10-01
We study the Horndeski vector-tensor theory that leads to second order equations of motion and contains a non-minimally coupled abelian gauge vector field. This theory is remarkably simple and consists of only 2 terms for the vector field, namely: the standard Maxwell kinetic term and a coupling to the dual Riemann tensor. Furthermore, the vector sector respects the U(1) gauge symmetry and the theory contains only one free parameter, M{sup 2}, that controls the strength of the non-minimal coupling. We explore the theory in a de Sitter spacetime and study the presence of instabilities and show that it corresponds to an attractor solution in the presence of the vector field. We also investigate the cosmological evolution and stability of perturbations in a general FLRW spacetime. We find that a sufficient condition for the absence of ghosts is M{sup 2} > 0. Moreover, we study further constraints coming from imposing the absence of Laplacian instabilities. Finally, we study the stability of the theory in static and spherically symmetric backgrounds (in particular, Schwarzschild and Reissner-Nordström-de Sitter). We find that the theory, quite generally, do have ghosts or Laplacian instabilities in regions of spacetime where the non-minimal interaction dominates over the Maxwell term. We also calculate the propagation speed in these spacetimes and show that superluminality is a quite generic phenomenon in this theory.
Dynamic polarizability tensor for circular cylinders
NASA Astrophysics Data System (ADS)
Strickland, Diana; Ayón, Arturo; Alù, Andrea
2015-02-01
Based on Mie scattering theory, we derive the complete dynamic polarizability tensor for circular, azimuthally symmetric cylinders excited by an arbitrary field distribution, and provide compact expressions for all of its elements. Our results comprise fully dynamic cylinder polarizabilities, improving existing approximate models that use averaged electric or magnetic current lines to describe the scattering response of moderately thin cylinders. We show that the derived polarizability tensor satisfies reciprocity and passivity relations, and analyze its response under different conditions, varying the excitation angle, material properties, and cylinder radius. Interestingly, magnetoelectric effects are shown to arise at oblique incidence, even in the case of centrosymmetric achiral thin cylinders, associated with a weak form of spatial dispersion. This finding is particularly relevant for the proper modeling of individual cylinders and arrays of them, as in the case of metamaterials. We expect this work to find applications in antenna and metamaterial design, and to improve the physical understanding of the wave interaction and spatial dispersion in artificial materials composed of elongated inclusions such as wire media.
Tensor networks and the numerical renormalization group
NASA Astrophysics Data System (ADS)
Weichselbaum, Andreas
2012-12-01
The full-density-matrix numerical renormalization group has evolved as a systematic and transparent setting for the calculation of thermodynamical quantities at arbitrary temperatures within the numerical renormalization group (NRG) framework. It directly evaluates the relevant Lehmann representations based on the complete basis sets introduced by Anders and Schiller [Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.95.196801 95, 196801 (2005)]. In addition, specific attention is given to the possible feedback from low-energy physics to high energies by the explicit and careful construction of the full thermal density matrix, naturally generated over a distribution of energy shells. Specific examples are given in terms of spectral functions (fdmNRG), time-dependent NRG (tdmNRG), Fermi-golden-rule calculations (fgrNRG) as well as the calculation of plain thermodynamic expectation values. Furthermore, based on the very fact that, by its iterative nature, the NRG eigenstates are naturally described in terms of matrix product states, the language of tensor networks has proven enormously convenient in the description of the underlying algorithmic procedures. This paper therefore also provides a detailed introduction and discussion of the prototypical NRG calculations in terms of their corresponding tensor networks.
The Heisenberg representation of quantum computers
Gottesman, D.
1998-06-24
Since Shor`s discovery of an algorithm to factor numbers on a quantum computer in polynomial time, quantum computation has become a subject of immense interest. Unfortunately, one of the key features of quantum computers--the difficulty of describing them on classical computers--also makes it difficult to describe and understand precisely what can be done with them. A formalism describing the evolution of operators rather than states has proven extremely fruitful in understanding an important class of quantum operations. States used in error correction and certain communication protocols can be described by their stabilizer, a group of tensor products of Pauli matrices. Even this simple group structure is sufficient to allow a rich range of quantum effects, although it falls short of the full power of quantum computation.
NASA Astrophysics Data System (ADS)
Bengtsson, Ingemar; Zyczkowski, Karol
2006-05-01
Quantum information theory is at the frontiers of physics, mathematics and information science, offering a variety of solutions that are impossible using classical theory. This book provides an introduction to the key concepts used in processing quantum information and reveals that quantum mechanics is a generalisation of classical probability theory. After a gentle introduction to the necessary mathematics the authors describe the geometry of quantum state spaces. Focusing on finite dimensional Hilbert spaces, they discuss the statistical distance measures and entropies used in quantum theory. The final part of the book is devoted to quantum entanglement - a non-intuitive phenomenon discovered by Schrödinger, which has become a key resource for quantum computation. This richly-illustrated book is useful to a broad audience of graduates and researchers interested in quantum information theory. Exercises follow each chapter, with hints and answers supplied. The first book to focus on the geometry of quantum states Stresses the similarities and differences between classical and quantum theory Uses a non-technical style and numerous figures to make the book accessible to non-specialists
Extracting g tensor values from experimental data with Markov Chain Monte Carlo methods
NASA Astrophysics Data System (ADS)
Kulkarni, Anagha; Liu, Weiwen; Zurakowski, Ryan; Doty, Matthew
Quantum Dot Molecules(QDMs) have emerged as a new platform for optoelectronic and spintronic devices.QDMs consist of multiple Quantum Dots (QDs) arranged in close proximity such that interactions between them can tailor their optical and spin properties.These properties can be tuned during growth and in-situ by applying electric fields that vary the coupling between QDs,which controls the formation of delocalized molecular-like states.Engineering the formation of molecular states in QDMS can be used to achieve new functionalities unavailable with individual QDs. Using molecular engineering approaches to tailor QDMs require precise knowledge of parameters such as binding energies of charge complexes,magnitude of many body interactions or components of the g tensor.Precise values of these parameters are difficult to extract from either experimental measurements or theoretical calculations.We develop and demonstrate a Markov Chain Monte Carlo method for extracting elements of the g tensor for a single hole confined in a QDM from photoluminescence data obtained as a function of electric and magnetic fields.This method can be applied to extract precise quantitative values of other physical parameters from sparse experimental data on a variety of systems.
Feature Surfaces in Symmetric Tensor Fields Based on Eigenvalue Manifold.
Palacios, Jonathan; Yeh, Harry; Wang, Wenping; Zhang, Yue; Laramee, Robert S; Sharma, Ritesh; Schultz, Thomas; Zhang, Eugene
2016-03-01
Three-dimensional symmetric tensor fields have a wide range of applications in solid and fluid mechanics. Recent advances in the (topological) analysis of 3D symmetric tensor fields focus on degenerate tensors which form curves. In this paper, we introduce a number of feature surfaces, such as neutral surfaces and traceless surfaces, into tensor field analysis, based on the notion of eigenvalue manifold. Neutral surfaces are the boundary between linear tensors and planar tensors, and the traceless surfaces are the boundary between tensors of positive traces and those of negative traces. Degenerate curves, neutral surfaces, and traceless surfaces together form a partition of the eigenvalue manifold, which provides a more complete tensor field analysis than degenerate curves alone. We also extract and visualize the isosurfaces of tensor modes, tensor isotropy, and tensor magnitude, which we have found useful for domain applications in fluid and solid mechanics. Extracting neutral and traceless surfaces using the Marching Tetrahedra method can cause the loss of geometric and topological details, which can lead to false physical interpretation. To robustly extract neutral surfaces and traceless surfaces, we develop a polynomial description of them which enables us to borrow techniques from algebraic surface extraction, a topic well-researched by the computer-aided design (CAD) community as well as the algebraic geometry community. In addition, we adapt the surface extraction technique, called A-patches, to improve the speed of finding degenerate curves. Finally, we apply our analysis to data from solid and fluid mechanics as well as scalar field analysis. PMID:26441450
NASA Astrophysics Data System (ADS)
Pallozzi Lavorante, Luca; Dirk Ebert, Hans
2008-07-01
Tensor3D is a geometric modeling program with the capacity to simulate and visualize in real-time the deformation, specified through a tensor matrix and applied to triangulated models representing geological bodies. 3D visualization allows the study of deformational processes that are traditionally conducted in 2D, such as simple and pure shears. Besides geometric objects that are immediately available in the program window, the program can read other models from disk, thus being able to import objects created with different open-source or proprietary programs. A strain ellipsoid and a bounding box are simultaneously shown and instantly deformed with the main object. The principal axes of strain are visualized as well to provide graphical information about the orientation of the tensor's normal components. The deformed models can also be saved, retrieved later and deformed again, in order to study different steps of progressive strain, or to make this data available to other programs. The shape of stress ellipsoids and the corresponding Mohr circles defined by any stress tensor can also be represented. The application was written using the Visualization ToolKit, a powerful scientific visualization library in the public domain. This development choice, allied to the use of the Tcl/Tk programming language, which is independent on the host computational platform, makes the program a useful tool for the study of geometric deformations directly in three dimensions in teaching as well as research activities.
Local thermodynamical equilibrium and the frame for a quantum relativistic fluid
NASA Astrophysics Data System (ADS)
Becattini, Francesco; Bucciantini, Leda; Grossi, Eduardo; Tinti, Leonardo
2015-05-01
We discuss the concept of local thermodynamical equilibrium in relativistic hydrodynamics in flat spacetime in a quantum statistical framework without an underlying kinetic description, suitable for strongly interacting fluids. We show that the appropriate definition of local equilibrium naturally leads to the introduction of a relativistic hydrodynamical frame in which the four-velocity vector is the one of a relativistic thermometer at equilibrium with the fluid, parallel to the inverse temperature four-vector , which then becomes a primary quantity. We show that this frame is the most appropriate for the expansion of the stress-energy tensor from local thermodynamical equilibrium and that therein the local laws of thermodynamics take on their simplest form. We discuss the difference between the frame and Landau frame and present an instance where they differ.
NASA Astrophysics Data System (ADS)
Błaszak, Maciej; Domański, Ziemowit
2012-02-01
This paper develops an alternative formulation of quantum mechanics known as the phase space quantum mechanics or deformation quantization. It is shown that the quantization naturally arises as an appropriate deformation of the classical Hamiltonian mechanics. More precisely, the deformation of the point-wise product of observables to an appropriate noncommutative ⋆-product and the deformation of the Poisson bracket to an appropriate Lie bracket are the key elements in introducing the quantization of classical Hamiltonian systems. The formalism of the phase space quantum mechanics is presented in a very systematic way for the case of any smooth Hamiltonian function and for a very wide class of deformations. The considered class of deformations and the corresponding ⋆-products contains as a special case all deformations which can be found in the literature devoted to the subject of the phase space quantum mechanics. Fundamental properties of ⋆-products of observables, associated with the considered deformations are presented as well. Moreover, a space of states containing all admissible states is introduced, where the admissible states are appropriate pseudo-probability distributions defined on the phase space. It is proved that the space of states is endowed with a structure of a Hilbert algebra with respect to the ⋆-multiplication. The most important result of the paper shows that developed formalism is more fundamental than the axiomatic ordinary quantum mechanics which appears in the presented approach as the intrinsic element of the general formalism. The equivalence of two formulations of quantum mechanics is proved by observing that the Wigner-Moyal transform has all properties of the tensor product. This observation allows writing many previous results found in the literature in a transparent way, from which the equivalence of the two formulations of quantum mechanics follows naturally. In addition, examples of a free particle and a simple harmonic
NASA Astrophysics Data System (ADS)
Lebiedowicz, Piotr; Nachtmann, Otto; Szczurek, Antoni
2016-03-01
We consider central exclusive diffractive dipion production in the reactions p p →p p π+π- and p p ¯ →p p ¯ π+π- at high energies. We include the dipion continuum, the dominant scalar f0(500 ), f0(980 ) , and tensor f2(1270 ) resonances decaying into the π+π- pairs. The calculation is based on a tensor Pomeron model and the amplitudes for the processes are formulated in terms of vertices respecting the standard crossing and charge-conjugation relations of quantum field theory. The formulas for the dipion continuum and tensor meson production are given here for the first time. The theoretical results are compared with existing STAR, CDF, CMS experimental data and predictions for planned or current experiments (ALICE, ATLAS) are presented. We show the influence of the experimental cuts on the integrated cross section and on various differential distributions for outgoing particles. Distributions in rapidities and transverse momenta of outgoing protons and pions as well as correlations in azimuthal angle between them are presented. We find that the relative contribution of the resonant f2(1270 ) and dipion continuum strongly depends on the cut on proton transverse momenta or four-momentum transfer squared t1 ,2 which may explain some controversial observations made by different ISR experiments in the past. The cuts may play then the role of a π π resonance filter. We suggest some experimental analyses to fix model parameters related to the Pomeron-Pomeron-f2 coupling.
Consistent cosmic microwave background spectra from quantum depletion
NASA Astrophysics Data System (ADS)
Casadio, Roberto; Kühnel, Florian; Orlandi, Alessio
2015-09-01
Following a new quantum cosmological model proposed by Dvali and Gomez, we quantitatively investigate possible modifications to the Hubble parameter and following corrections to the cosmic microwave background spectrum. In this model, scalar and tensor perturbations are generated by the quantum depletion of the background inflaton and graviton condensate respectively. We show how the inflaton mass affects the power spectra and the tensor-to-scalar ratio. Masses approaching the Planck scale would lead to strong deviations, while standard spectra are recovered for an inflaton mass much smaller than the Planck mass.
Charged and Electromagnetic Fields from Relativistic Quantum Geometry
NASA Astrophysics Data System (ADS)
Arcodía, Marcos; Bellini, Mauricio
2016-06-01
In the Relativistic Quantum Geometry (RQG) formalism recently introduced, was explored the possibility that the variation of the tensor metric can be done in a Weylian integrable manifold using a geometric displacement, from a Riemannian to a Weylian integrable manifold, described by the dynamics of an auxiliary geometrical scalar field $\\theta$, in order that the Einstein tensor (and the Einstein equations) can be represented on a Weyl-like manifold. In this framework we study jointly the dynamics of electromagnetic fields produced by quantum complex vector fields, which describes charges without charges. We demonstrate that complex fields act as a source of tetra-vector fields which describe an extended Maxwell dynamics.
NASA Astrophysics Data System (ADS)
Choudhury, Sayantan
2015-05-01
In this paper my prime objective is to explain the generation of large tensor-to-scalar ratio from the single field sub-Planckian inflationary paradigm within Randall-Sundrum (RS) single braneworld scenario in a model independent fashion. By explicit computation I have shown that the effective field theory prescription of brane inflation within RS single brane setup is consistent with sub-Planckian excursion of the inflaton field, which will further generate large value of tensor-to-scalar ratio, provided the energy density for inflaton degrees of freedom is high enough compared to the brane tension in high energy regime. Finally, I have mentioned the stringent theoretical constraint on positive brane tension, cut-off of the quantum gravity scale and bulk cosmological constant to get sub-Planckian field excursion along with large tensor-to-scalar ratio as recently observed by BICEP2 or at least generates the tensor-to-scalar ratio consistent with the upper bound of Planck (2013 and 2015) data and Planck+BICEP2+Keck Array joint constraint.
Dipole modulation in tensor modes: signatures in CMB polarization
NASA Astrophysics Data System (ADS)
Zarei, Moslem
2015-06-01
In this work we consider a dipole asymmetry in tensor modes and study the effects of this asymmetry on the angular power spectra of CMB. We derive analytical expressions for the and in the presence of such dipole modulation in tensor modes for . We also discuss on the amplitude of modulation term and show that the is considerably modified due to this term.
Dynamic rotation and stretch tensors from a dynamic polar decomposition
NASA Astrophysics Data System (ADS)
Haller, George
2016-01-01
The local rigid-body component of continuum deformation is typically characterized by the rotation tensor, obtained from the polar decomposition of the deformation gradient. Beyond its well-known merits, the polar rotation tensor also has a lesser known dynamical inconsistency: it does not satisfy the fundamental superposition principle of rigid-body rotations over adjacent time intervals. As a consequence, the polar rotation diverts from the observed mean material rotation of fibers in fluids, and introduces a purely kinematic memory effect into computed material rotation. Here we derive a generalized polar decomposition for linear processes that yields a unique, dynamically consistent rotation component, the dynamic rotation tensor, for the deformation gradient. The left dynamic stretch tensor is objective, and shares the principal strain values and axes with its classic polar counterpart. Unlike its classic polar counterpart, however, the dynamic stretch tensor evolves in time without spin. The dynamic rotation tensor further decomposes into a spatially constant mean rotation tensor and a dynamically consistent relative rotation tensor that is objective for planar deformations. We also obtain simple expressions for dynamic analogues of Cauchy's mean rotation angle that characterize a deforming body objectively.
Tensor spin observables and spin stucture at low Q2
Slifer, Karl J.
2015-04-01
We discuss recent spin structure results from Jefferson Lab, and outline an emerging program to study tensor spin observables using solid deuteron targets. These new experiments open the potential to study hidden color, the tensor nature of short range correlations, and to probe for exotic gluonic states.
PREFACE: 1st Tensor Polarized Solid Target Workshop
NASA Astrophysics Data System (ADS)
2014-10-01
These are the proceedings of the first Tensor Spin Observables Workshop that was held in March 2014 at the Thomas Jefferson National Accelerator Facility in Newport News, Virginia. The conference was convened to study the physics that can be done with the recently approved E12-13-011 polarized target. A tensor polarized target holds the potential of initiating a new generation of tensor spin physics at Jefferson Lab. Experiments which utilize tensor polarized targets can help clarify how nuclear properties arise from partonic degrees of freedom, provide unique insight into short-range correlations and quark angular momentum, and also help pin down the polarization of the quark sea with a future Electron Ion Collider. This three day workshop was focused on tensor spin observables and the associated tensor target development. The workshop goals were to stimulate progress in the theoretical treatment of polarized spin-1 systems, foster the development of new proposals, and to reach a consensus on the optimal polarized target configuration for the tensor spin program. The workshop was sponsored by the University of New Hampshire, the Jefferson Science Associates, Florida International University, and Jefferson Lab. It was organized by Karl Slifer (chair), Patricia Solvignon, and Elena Long of the University of New Hampshire, Douglas Higinbotham and Christopher Keith of Jefferson Lab, and Misak Sargsian of the Florida International University. These proceedings represent the effort put forth by the community to begin exploring the possibilities that a high-luminosity, high-tensor polarized solid target can offer.
The Kummer tensor density in electrodynamics and in gravity
NASA Astrophysics Data System (ADS)
Baekler, Peter; Favaro, Alberto; Itin, Yakov; Hehl, Friedrich W.
2014-10-01
Guided by results in the premetric electrodynamics of local and linear media, we introduce on 4-dimensional spacetime the new abstract notion of a Kummer tensor density of rank four, K. This tensor density is, by definition, a cubic algebraic functional of a tensor density of rank four T, which is antisymmetric in its first two and its last two indices: T=-T=-T. Thus, K∼T3, see Eq. (46). (i) If T is identified with the electromagnetic response tensor of local and linear media, the Kummer tensor density encompasses the generalized Fresnel wave surfaces for propagating light. In the reversible case, the wave surfaces turn out to be Kummer surfaces as defined in algebraic geometry (Bateman 1910). (ii) If T is identified with the curvature tensor R of a Riemann-Cartan spacetime, then K∼R3 and, in the special case of general relativity, K reduces to the Kummer tensor of Zund (1969). This K is related to the principal null directions of the curvature. We discuss the properties of the general Kummer tensor density. In particular, we decompose K irreducibly under the 4-dimensional linear group GL(4,R) and, subsequently, under the Lorentz group SO(1,3).
APPROXIMATING SYMMETRIC POSITIVE SEMIDEFINITE TENSORS OF EVEN ORDER*
BARMPOUTIS, ANGELOS; JEFFREY, HO; VEMURI, BABA C.
2012-01-01
Tensors of various orders can be used for modeling physical quantities such as strain and diffusion as well as curvature and other quantities of geometric origin. Depending on the physical properties of the modeled quantity, the estimated tensors are often required to satisfy the positivity constraint, which can be satisfied only with tensors of even order. Although the space P02m of 2mth-order symmetric positive semi-definite tensors is known to be a convex cone, enforcing positivity constraint directly on P02m is usually not straightforward computationally because there is no known analytic description of P02m for m > 1. In this paper, we propose a novel approach for enforcing the positivity constraint on even-order tensors by approximating the cone P02m for the cases 0 < m < 3, and presenting an explicit characterization of the approximation Σ2m ⊂ Ω2m for m ≥ 1, using the subset Ω2m⊂P02m of semi-definite tensors that can be written as a sum of squares of tensors of order m. Furthermore, we show that this approximation leads to a non-negative linear least-squares (NNLS) optimization problem with the complexity that equals the number of generators in Σ2m. Finally, we experimentally validate the proposed approach and we present an application for computing 2mth-order diffusion tensors from Diffusion Weighted Magnetic Resonance Images. PMID:23285313
The Kummer tensor density in electrodynamics and in gravity
Baekler, Peter; Favaro, Alberto; Itin, Yakov; Hehl, Friedrich W.
2014-10-15
Guided by results in the premetric electrodynamics of local and linear media, we introduce on 4-dimensional spacetime the new abstract notion of a Kummer tensor density of rank four, K{sup ijkl}. This tensor density is, by definition, a cubic algebraic functional of a tensor density of rank four T{sup ijkl}, which is antisymmetric in its first two and its last two indices: T{sup ijkl}=−T{sup jikl}=−T{sup ijlk}. Thus, K∼T{sup 3}, see Eq. (46). (i) If T is identified with the electromagnetic response tensor of local and linear media, the Kummer tensor density encompasses the generalized Fresnel wave surfaces for propagating light. In the reversible case, the wave surfaces turn out to be Kummer surfaces as defined in algebraic geometry (Bateman 1910). (ii) If T is identified with the curvature tensor R{sup ijkl} of a Riemann–Cartan spacetime, then K∼R{sup 3} and, in the special case of general relativity, K reduces to the Kummer tensor of Zund (1969). This K is related to the principal null directions of the curvature. We discuss the properties of the general Kummer tensor density. In particular, we decompose K irreducibly under the 4-dimensional linear group GL(4,R) and, subsequently, under the Lorentz group SO(1,3)
MATLAB tensor classes for fast algorithm prototyping : source code.
Bader, Brett William; Kolda, Tamara Gibson
2004-10-01
We present the source code for three MATLAB classes for manipulating tensors in order to allow fast algorithm prototyping. A tensor is a multidimensional or Nway array. This is a supplementary report; details on using this code are provided separately in SAND-XXXX.
NASA Astrophysics Data System (ADS)
Bakke, K.; Belich, H.
2015-11-01
We discuss the appearance of geometric quantum phases for a Dirac neutral particle in the context of relativistic quantum mechanics based on possible scenarios of the Lorentz symmetry violation tensor background in the CPT-even gauge sector of Standard Model Extension. We assume that the Lorentz symmetry breaking is determined by a tensor background given by (KF)μναβ, then, relativistic analogues of the Anandan quantum phase [J. Anandan, Phys. Lett. A 138, 347 (1989)] are obtained based on the parity-even and parity-odd sectors of the tensor (KF)μναβ.
Quantum Fluctuations and Thermodynamic Processes in the Presence of Closed Timelike Curves
NASA Astrophysics Data System (ADS)
Tanaka, Tsunefumi
1997-10-01
A closed timelike curve (CTC) is a closed loop in spacetime whose tangent vector is everywhere timelike. A spacetime which contains CTC's will allow time travel. One of these spacetimes is Grant space. It can be constructed from Minkowski space by imposing periodic boundary conditions in spatial directions and making the boundaries move toward each other. If Hawking's chronology protection conjecture is correct, there must be a physical mechanism preventing the formation of CTC's. Currently the most promising candidate for the chronology protection mechanism is the back reaction of the metric to quantum vacuum fluctuations. In this thesis the quantum fluctuations for a massive scalar field, a self-interacting field, and for a field at nonzero temperature are calculated in Grant space. The stress-energy tensor is found to remain finite everywhere in Grant space for the massive scalar field with sufficiently large field mass. Otherwise it diverges on chronology horizons like the stress-energy tensor for a massless scalar field. If CTC's exist they will have profound effects on physical processes. Causality can be protected even in the presence of CTC's if the self-consistency condition is imposed on all processes. Simple classical thermodynamic processes of a box filled with ideal gas in the presence of CTC's are studied. If a system of boxes is closed, its state does not change as it travels through a region of spacetime with CTC's. But if the system is open, the final state will depend on the interaction with the environment. The second law of thermodynamics is shown to hold for both closed and open systems. A similar problem is investigated at a statistical level for a gas consisting of multiple selves of a single particle in a spacetime with CTC's.
An inflationary model with small scalar and large tensor nongaussianities
NASA Astrophysics Data System (ADS)
Cook, Jessica L.; Sorbo, Lorenzo
2013-11-01
We study a model of inflation where the scalar perturbations are almost gaussian while there is sizable (equilateral) nongaussianity in the tensor sector. In this model, a rolling pseudoscalar gravitationally coupled to the inflaton amplifies the vacuum fluctuations of a vector field. The vector sources both scalar and tensor metric perturbations. Both kinds of perturbations are nongaussian, but, due to helicity conservation, the tensors have a larger amplitude, so that nongaussianity in the scalar perturbations is negligible. Moreover, the tensors produced this way are chiral. We study, in the flat sky approximation, how constraints on tensor nongaussianities affect the detectability of parity violation in the Cosmic Microwave Background. We expect the model to feature interesting patterns on nongaussianities in the polarization spectra of the CMB.
Tensor-optimized antisymmetrized molecular dynamics in nuclear physics
NASA Astrophysics Data System (ADS)
Myo, Takayuki; Toki, Hiroshi; Ikeda, Kiyomi; Horiuchi, Hisashi; Suhara, Tadahiro
2015-07-01
We develop a new formalism to treat nuclear many-body systems using the bare nucleon-nucleon interaction. It has become evident that the tensor interaction plays an important role in nuclear many-body systems due to the role of the pion in strongly interacting systems. We take the antisymmetrized molecular dynamics (AMD) as a basic framework and add a tensor correlation operator acting on the AMD wave function using the concept of the tensor-optimized shell model. We demonstrate a systematical and straightforward formulation utilizing the Gaussian integration and differentiation method and the antisymmetrization technique to calculate all the matrix elements of the many-body Hamiltonian. We can include the three-body interaction naturally and calculate the matrix elements systematically in the progressive order of the tensor correlation operator. We call the new formalism "tensor-optimized antisymmetrized molecular dynamics".
Automatic Deformable Diffusion Tensor Registration for Fiber Population Analysis
Irfanoglu, M.O.; Machiraju, R.; Sammet, S.; Pierpaoli, C.; Knopp, M.V.
2016-01-01
In this work, we propose a novel method for deformable tensor–to–tensor registration of Diffusion Tensor Images. Our registration method models the distances in between the tensors with Geode-sic–Loxodromes and employs a version of Multi-Dimensional Scaling (MDS) algorithm to unfold the manifold described with this metric. Defining the same shape properties as tensors, the vector images obtained through MDS are fed into a multi–step vector–image registration scheme and the resulting deformation fields are used to reorient the tensor fields. Results on brain DTI indicate that the proposed method is very suitable for deformable fiber–to–fiber correspondence and DTI–atlas construction. PMID:18982704
Reliability of structure tensors in representing soft tissues structure.
Lanir, Yoram; Namani, Ravi
2015-06-01
Structure tensors have been applied as descriptors of tissue morphology for constitutive modeling. Here the reliability of these tensors in representing tissues structure is investigated by model simulations of a few examples of generated and measured planar fiber orientation distributions. Reliability was evaluated by comparing the data with the orientation density distribution recovered from the structure tensor representation, and with a orientation density recovered from an alternative representation by Fourier series of spherical harmonics. The results show that except for the case of uniform or close to uniform orientation distributions, the distributions recovered from the structure tensor fit the data poorly. On the other hand, orientation distributions recovered from Fourier series of spherical harmonics converge to the data distributions provided sufficient terms are included in the truncated series. These results suggest that the structure tensor is a reliable descriptor of tissue structure only under very limited cases. PMID:25828155
On the energy-momentum tensor in Moyal space
Balasin, Herbert; Blaschke, Daniel N.; Gieres, François; Schweda, Manfred
2015-06-26
We study the properties of the energy-momentum tensor of gauge fields coupled to matter in non-commutative (Moyal) space. In general, the non-commutativity affects the usual conservation law of the tensor as well as its transformation properties (gauge covariance instead of gauge invariance). It is known that the conservation of the energy-momentum tensor can be achieved by a redefinition involving another starproduct. Furthermore, for a pure gauge theory it is always possible to define a gauge invariant energy-momentum tensor by means of a Wilson line. We show that the latter two procedures are incompatible with each other if couplings of gauge fields to matter fields (scalars or fermions) are considered: The gauge invariant tensor (constructed via Wilson line) does not allow for a redefinition assuring its conservation, and vice-versa the introduction of another star-product does not allow for gauge invariance by means of a Wilson line.
Chiral perturbation theory with tensor sources
Cata, Oscar; Cata, Oscar; Mateu, Vicent
2007-05-21
We construct the most general chirally-invariant Lagrangian for mesons in the presence of external sources coupled to the tensor current \\bar psi sigma_mu nu psi. In order to have only even terms in the chiral expansion, we consider the new source of O(p2). With this choice, we build the even-parity effective Lagrangian up to the p6-order (NLO). While there are only 4 new terms at the p4-order, at p6-order we find 78 terms for n_f=2 and 113 terms for n_f=3. We provide a detailed discussion on the different mechanisms that ensure that our final set of operators is complete and non-redundant. We also examine the odd-parity sector, to conclude that the first operators appear at the p8-order (NNLO).
Multigrid algorithms for tensor network states.
Dolfi, Michele; Bauer, Bela; Troyer, Matthias; Ristivojevic, Zoran
2012-07-13
The widely used density matrix renormalization group (DRMG) method often fails to converge in systems with multiple length scales, such as lattice discretizations of continuum models and dilute or weakly doped lattice models. The local optimization employed by DMRG to optimize the wave function is ineffective in updating large-scale features. Here we present a multigrid algorithm that solves these convergence problems by optimizing the wave function at different spatial resolutions. We demonstrate its effectiveness by simulating bosons in continuous space and study nonadiabaticity when ramping up the amplitude of an optical lattice. The algorithm can be generalized to tensor network methods and combined with the contractor renormalization group method to study dilute and weakly doped lattice models. PMID:23030148
f(R)-gravity from Killing tensors
NASA Astrophysics Data System (ADS)
Paliathanasis, Andronikos
2016-04-01
We consider f(R)-gravity in a Friedmann-Lemaître-Robertson-Walker spacetime with zero spatial curvature. We apply the Killing tensors of the minisuperspace in order to specify the functional form of f(R) and for the field equations to be invariant under Lie-Bäcklund transformations, which are linear in momentum (contact symmetries). Consequently, the field equations to admit quadratic conservation laws given by Noether’s theorem. We find three new integrable f(R)-models, for which, with the application of the conservation laws, we reduce the field equations to a system of two first-order ordinary differential equations. For each model we study the evolution of the cosmological fluid. We find that for each integrable model the cosmological fluid has an equation of state parameter, in which there is linear behavior in terms of the scale factor which describes the Chevallier, Polarski and Linder parametric dark energy model.
Electroproduction of tensor mesons in QCD
NASA Astrophysics Data System (ADS)
Braun, V. M.; Kivel, N.; Strohmaier, M.; Vladimirov, A. A.
2016-06-01
Due to multiple possible polarizations hard exclusive production of tensor mesons by virtual photons or in heavy meson decays offers interesting possibilities to study the helicity structure of the underlying short-distance process. Motivated by the first measurement of the transition form factor γ∗γ → f 2(1270) at large momentum transfers by the BELLE collaboration we present an improved QCD analysis of this reaction in the framework of collinear factorization including contributions of twist-three quark-antiquark-gluon operators and an estimate of soft end-point corrections using light-cone sum rules. The results appear to be in good agreement with the data, in particular the predicted scaling behavior is reproduced in all cases.
Bounds on tensor wave and twisted inflation
Panda, Sudhakar; Sami, M.; Ward, John
2010-11-15
We study the bounds on tensor wave in a class of twisted inflation models, where D(4+2k)-branes are wrapped on cycles in the compact manifold and wrap the Kaluza-Klein direction in the corresponding effective field theory. While the lower bound is found to be analogous to that in type IIB models of brane inflation, the upper bound turns out to be significantly different. This is argued for a range of values for the parameter g{sub s}M satisfying the self-consistency relation and the WMAP data. Further, we observe that the wrapped D8-brane appears to be the most attractive from a cosmological perspective.
A hitchhiker's guide to diffusion tensor imaging.
Soares, José M; Marques, Paulo; Alves, Victor; Sousa, Nuno
2013-01-01
Diffusion Tensor Imaging (DTI) studies are increasingly popular among clinicians and researchers as they provide unique insights into brain network connectivity. However, in order to optimize the use of DTI, several technical and methodological aspects must be factored in. These include decisions on: acquisition protocol, artifact handling, data quality control, reconstruction algorithm, and visualization approaches, and quantitative analysis methodology. Furthermore, the researcher and/or clinician also needs to take into account and decide on the most suited software tool(s) for each stage of the DTI analysis pipeline. Herein, we provide a straightforward hitchhiker's guide, covering all of the workflow's major stages. Ultimately, this guide will help newcomers navigate the most critical roadblocks in the analysis and further encourage the use of DTI. PMID:23486659
A hitchhiker's guide to diffusion tensor imaging
Soares, José M.; Marques, Paulo; Alves, Victor; Sousa, Nuno
2012-01-01
Diffusion Tensor Imaging (DTI) studies are increasingly popular among clinicians and researchers as they provide unique insights into brain network connectivity. However, in order to optimize the use of DTI, several technical and methodological aspects must be factored in. These include decisions on: acquisition protocol, artifact handling, data quality control, reconstruction algorithm, and visualization approaches, and quantitative analysis methodology. Furthermore, the researcher and/or clinician also needs to take into account and decide on the most suited software tool(s) for each stage of the DTI analysis pipeline. Herein, we provide a straightforward hitchhiker's guide, covering all of the workflow's major stages. Ultimately, this guide will help newcomers navigate the most critical roadblocks in the analysis and further encourage the use of DTI. PMID:23486659
Affinity learning with diffusion on tensor product graph.
Yang, Xingwei; Prasad, Lakshman; Latecki, Longin Jan
2013-01-01
In many applications, we are given a finite set of data points sampled from a data manifold and represented as a graph with edge weights determined by pairwise similarities of the samples. Often the pairwise similarities (which are also called affinities) are unreliable due to noise or due to intrinsic difficulties in estimating similarity values of the samples. As observed in several recent approaches, more reliable similarities can be obtained if the original similarities are diffused in the context of other data points, where the context of each point is a set of points most similar to it. Compared to the existing methods, our approach differs in two main aspects. First, instead of diffusing the similarity information on the original graph, we propose to utilize the tensor product graph (TPG) obtained by the tensor product of the original graph with itself. Since TPG takes into account higher order information, it is not a surprise that we obtain more reliable similarities. However, it comes at the price of higher order computational complexity and storage requirement. The key contribution of the proposed approach is that the information propagation on TPG can be computed with the same computational complexity and the same amount of storage as the propagation on the original graph. We prove that a graph diffusion process on TPG is equivalent to a novel iterative algorithm on the original graph, which is guaranteed to converge. After its convergence we obtain new edge weights that can be interpreted as new, learned affinities. We stress that the affinities are learned in an unsupervised setting. We illustrate the benefits of the proposed approach for data manifolds composed of shapes, images, and image patches on two very different tasks of image retrieval and image segmentation. With learned affinities, we achieve the bull's eye retrieval score of 99.99 percent on the MPEG-7 shape dataset, which is much higher than the state-of-the-art algorithms. When the data
Quantum information-geometry of dissipative quantum phase transitions.
Banchi, Leonardo; Giorda, Paolo; Zanardi, Paolo
2014-02-01
A general framework for analyzing the recently discovered phase transitions in the steady state of dissipation-driven open quantum systems is still lacking. To fill this gap, we extend the so-called fidelity approach to quantum phase transitions to open systems whose steady state is a Gaussian fermionic state. We endow the manifold of correlation matrices of steady states with a metric tensor g measuring the distinguishability distance between solutions corresponding to a different set of control parameters. The phase diagram can then be mapped out in terms of the scaling behavior of g and connections with the Liouvillean gap and the model correlation functions unveiled. We argue that the fidelity approach, thanks to its differential-geometric and information-theoretic nature, provides insights into dissipative quantum critical phenomena as well as a general and powerful strategy to explore them. PMID:25353417
Conductivity of pure graphene: Theoretical approach using the polarization tensor
NASA Astrophysics Data System (ADS)
Klimchitskaya, G. L.; Mostepanenko, V. M.
2016-06-01
We obtain analytic expressions for the conductivity of pristine (pure) graphene in the framework of the Dirac model using the polarization tensor in (2+1) dimensions defined along the real frequency axis. It is found that at both zero and nonzero temperature T the in-plane and out-of-plane conductivities of graphene are equal to each other with a high precision and essentially do not depend on the wave vector. At T =0 the conductivity of graphene is real and equal to σ0=e2/(4 ℏ ) up to small nonlocal corrections in accordance with many authors. At some fixed T ≠0 the real part of the conductivity varies between zero at low frequencies ω and σ0 for optical ω . If ω is fixed, the conductivity varies between σ0 at low T and zero at high T . The imaginary part of the conductivity of graphene is shown to depend on the ratio of ω to T . In accordance with the obtained asymptotic expressions, at fixed T it varies from infinity at ω =0 to a negative minimum value reached at some ω , and then approaches to zero with further increase of ω . At fixed ω the imaginary part of the conductivity varies from zero at T =0 , reaches a negative minimum at some T , and then goes to infinity together with T . The numerical computations of both the real and imaginary parts of the conductivity are performed. The above results are obtained in the framework of quantum electrodynamics at nonzero temperature and can be generalized for graphene samples with nonzero mass gap parameter and chemical potential.
NASA Astrophysics Data System (ADS)
Ford, S. R.; Dreger, D. S.; Walter, W. R.
2006-12-01
Seismic moment tensor analysis at regional distances commonly involves solving for the deviatoric moment tensor and decomposing it to characterize the tectonic earthquake source. The full seismic moment tensor solution can also recover the isotropic component of the seismic source, which is theoretically dominant in explosions and collapses, and present in volcanic events. Analysis of events with demonstrably significant isotropic energy can aid in understanding the source processes of volcanic and geothermal seismic events and the monitoring of nuclear explosions. Using a regional time-domain waveform inversion for the complete moment tensor we calculate the deviatoric and isotropic source components for several explosions at the Nevada Test Site (NTS) and earthquakes, collapses, and volcanic events in the surrounding region of the NTS (Western US). The events separate into specific populations according to their deviation from a pure double-couple and ratio of isotropic to deviatoric energy. The separation allows for anomalous event identification and discrimination of explosions, earthquakes, and collapses. Analysis of the source principal axes can characterize the regional stress field, and tectonic release due to explosions. Error in the moment tensor solutions and source parameters is also calculated. We investigate the sensitivity of the moment tensor solutions to Green's functions calculated with imperfect Earth models, inaccurate event locations, and data with a low signal-to-noise ratio. We also test the performance of the method under a range of recording conditions from excellent azimuthal coverage to cases of sparse coverage as might be expected for smaller events. This analysis will be used to determine the magnitude range where well-constrained solutions can be obtained.
NASA Astrophysics Data System (ADS)
Hohenstein, Edward G.; Parrish, Robert M.; Sherrill, C. David; Martínez, Todd J.
2012-12-01
The manipulation of the rank-four tensor of double excitation amplitudes represents a challenge to the efficient implementation of many electronic structure methods. We present a proof of concept for the approximation of doubles amplitudes in the tensor hypercontraction (THC) representation. In particular, we show how THC can be used to both reduce the scaling with respect to molecular size of coupled cluster singles and doubles (CCSD) (and related methods) by two orders [from O(N6) to O(N4)] and remove the memory bottleneck associated with storage of the doubles amplitudes. The accuracy of correlated methods as integral and amplitude approximations are introduced is examined. For a set of 20 small molecules, single and double-excitation configuration interaction (CISD), quadratic CISD (QCISD), and CCSD correlation energies could be reproduced with millihartree accuracy after the introduction of these approximations. Our approach exploits otherwise hidden factorizable tensor structure in both the electron repulsion integrals and the wavefunction coefficients and should be applicable with suitable modifications to many methods in electronic structure theory.
Quantum Strategies and Local Operations
NASA Astrophysics Data System (ADS)
Gutoski, Gus
2010-02-01
This thesis is divided into two parts. In Part I we introduce a new formalism for quantum strategies, which specify the actions of one party in any multi-party interaction involving the exchange of multiple quantum messages among the parties. This formalism associates with each strategy a single positive semidefinite operator acting only upon the tensor product of the input and output message spaces for the strategy. We establish three fundamental properties of this new representation for quantum strategies and we list several applications, including a quantum version of von Neumann's celebrated 1928 Min-Max Theorem for zero-sum games and an efficient algorithm for computing the value of such a game. In Part II we establish several properties of a class of quantum operations that can be implemented locally with shared quantum entanglement or classical randomness. In particular, we establish the existence of a ball of local operations with shared randomness lying within the space spanned by the no-signaling operations and centred at the completely noisy channel. The existence of this ball is employed to prove that the weak membership problem for local operations with shared entanglement is strongly NP-hard. We also provide characterizations of local operations in terms of linear functionals that are positive and "completely" positive on a certain cone of Hermitian operators, under a natural notion of complete positivity appropriate to that cone. We end the thesis with a discussion of the properties of no-signaling quantum operations.
Influence of seismic anisotropy on the cross correlation tensor: numerical investigations
NASA Astrophysics Data System (ADS)
Saade, M.; Montagner, J. P.; Roux, P.; Cupillard, P.; Durand, S.; Brenguier, F.
2015-05-01
Temporal changes in seismic anisotropy can be interpreted as variations in the orientation of cracks in seismogenic zones, and thus as variations in the stress field. Such temporal changes have been observed in seismogenic zones before and after earthquakes, although they are still not well understood. In this study, we investigate the azimuthal polarization of surface waves in anisotropic media with respect to the orientation of anisotropy, from a numerical point of view. This technique is based on the observation of the signature of anisotropy on the nine-component cross-correlation tensor (CCT) computed from seismic ambient noise recorded on pairs of three-component sensors. If noise sources are spatially distributed in a homogeneous medium, the CCT allows the reconstruction of the surface wave Green's tensor between the station pairs. In homogeneous, isotropic medium, four off-diagonal terms of the surface wave Green's tensor are null, but not in anisotropic medium. This technique is applied to three-component synthetic seismograms computed in a transversely isotropic medium with a horizontal symmetry axis, using a spectral element code. The CCT is computed between each pair of stations and then rotated, to approximate the surface wave Green's tensor by minimizing the off-diagonal components. This procedure allows the calculation of the azimuthal variation of quasi-Rayleigh and quasi-Love waves. In an anisotropic medium, in some cases, the azimuth of seismic anisotropy can induce a large variation in the horizontal polarization of surface waves. This variation depends on the relative angle between a pair of stations and the direction of anisotropy, the amplitude of the anisotropy, the frequency band of the signal and the depth of the anisotropic layer.
Voigt, J.; Knappe-Grüneberg, S.; Gutkelch, D.; Neuber, S.; Schnabel, A.; Burghoff, M.; Haueisen, J.
2015-05-15
Several experiments in fundamental physics demand an environment of very low, homogeneous, and stable magnetic fields. For the magnetic characterization of such environments, we present a portable SQUID system that measures the absolute magnetic flux density vector and the gradient tensor. This vector-tensor system contains 13 integrated low-critical temperature (LTc) superconducting quantum interference devices (SQUIDs) inside a small cylindrical liquid helium Dewar with a height of 31 cm and 37 cm in diameter. The achievable resolution depends on the flux density of the field under investigation and its temporal drift. Inside a seven-layer mu-metal shield, an accuracy better than ±23 pT for the components of the static magnetic field vector and ±2 pT/cm for each of the nine components of the gradient tensor is reached by using the shifting method.
Seismic moment tensors and estimated uncertainties in southern Alaska
NASA Astrophysics Data System (ADS)
Silwal, Vipul; Tape, Carl
2016-04-01
We present a moment tensor catalog of 106 earthquakes in southern Alaska, and we perform a conceptually based uncertainty analysis for 21 of them. For each earthquake, we use both body waves and surface waves to do a grid search over double couple moment tensors and source depths in order to find the minimum of the misfit function. Our uncertainty parameter or, rather, our confidence parameter is the average value of the curve 𝒫 (V), where 𝒫 (V) is the posterior probability as a function of the fractional volume V of moment tensor space surrounding the minimum misfit moment tensor. As a supplemental means for characterizing and visualizing uncertainties, we generate moment tensor samples of the posterior probability. We perform a series of inversion tests to quantify the impact of certain decisions made within moment tensor inversions and to make comparisons with existing catalogs. For example, using an L1 norm in the misfit function provides more reliable solutions than an L2 norm, especially in cases when all available waveforms are used. Using body waves in addition to surface waves, as well as using more stations, leads to the most accurate moment tensor solutions.
The tensor bi-spectrum in a matter bounce
NASA Astrophysics Data System (ADS)
Chowdhury, Debika; Sreenath, V.; Sriramkumar, L.
2015-11-01
Matter bounces are bouncing scenarios wherein the universe contracts as in a matter dominated phase at early times. Such scenarios are known to lead to a scale invariant spectrum of tensor perturbations, just as de Sitter inflation does. In this work, we examine if the tensor bi-spectrum can discriminate between the inflationary and the bouncing scenarios. Using the Maldacena formalism, we analytically evaluate the tensor bi-spectrum in a matter bounce for an arbitrary triangular configuration of the wavevectors. We show that, over scales of cosmological interest, the non-Gaussianity parameter hNL that characterizes the amplitude of the tensor bi-spectrum is quite small when compared to the corresponding values in de Sitter inflation. During inflation, the amplitude of the tensor perturbations freeze on super-Hubble scales, a behavior that results in the so-called consistency condition relating the tensor bi-spectrum and the power spectrum in the squeezed limit. In contrast, in the bouncing scenarios, the amplitude of the tensor perturbations grow strongly as one approaches the bounce, which suggests that the consistency condition will not be valid in such situations. We explicitly show that the consistency relation is indeed violated in the matter bounce. We discuss the implications of the results.
Tensor classification of structure in smoothed particle hydrodynamics density fields
NASA Astrophysics Data System (ADS)
Forgan, Duncan; Bonnell, Ian; Lucas, William; Rice, Ken
2016-04-01
As hydrodynamic simulations increase in scale and resolution, identifying structures with non-trivial geometries or regions of general interest becomes increasingly challenging. There is a growing need for algorithms that identify a variety of different features in a simulation without requiring a `by eye' search. We present tensor classification as such a technique for smoothed particle hydrodynamics (SPH). These methods have already been used to great effect in N-Body cosmological simulations, which require smoothing defined as an input free parameter. We show that tensor classification successfully identifies a wide range of structures in SPH density fields using its native smoothing, removing a free parameter from the analysis and preventing the need for tessellation of the density field, as required by some classification algorithms. As examples, we show that tensor classification using the tidal tensor and the velocity shear tensor successfully identifies filaments, shells and sheet structures in giant molecular cloud simulations, as well as spiral arms in discs. The relationship between structures identified using different tensors illustrates how different forces compete and co-operate to produce the observed density field. We therefore advocate the use of multiple tensors to classify structure in SPH simulations, to shed light on the interplay of multiple physical processes.
The tensor bi-spectrum in a matter bounce
NASA Astrophysics Data System (ADS)
Sreenath, V.; Chowdhury, Debika; Sriramkumar, L.
2016-03-01
Matter bounces are bouncing scenarios wherein the universe contracts as in a matter dominated phase at early times. Such scenarios are known to lead to a scale invariant spectrum of tensor perturbations, just as de Sitter inflation does. In this work, we examine if the tensor bi-spectrum can discriminate between the inflationary and the bouncing scenarios. Using the Maldacena formalism, we analytically evaluate the tensor bi-spectrum in a matter bounce for an arbitrary triangular configuration of the wavevectors. We show that, over scales of cosmological interest, the non-Gaussianity parameter hNL that characterizes the amplitude of the tensor bi-spectrum is quite small when compared to the corresponding values in de Sitter inflation. During inflation, the amplitude of the tensor perturbations freeze on super-Hubble scales, a behavior that results in the so-called consistency condition relating the tensor bi-spectrum and the power spectrum in the squeezed limit. In contrast, in the bouncing scenarios, the amplitude of the tensor perturbations grow strongly as one approaches the bounce, which suggests that the consistency condition will not be valid in such situations. We explicitly show that the consistency relation is indeed violated in the matter bounce.
Non-classical conditional probability and the quantum no-cloning theorem
NASA Astrophysics Data System (ADS)
Niestegge, Gerd
2015-09-01
The quantum mechanical no-cloning theorem for pure states is generalized and transfered to the quantum logics with a conditional probability calculus in a rather abstract, though simple and basic fashion without relying on a tensor product construction or finite dimension as required in other generalizations.
Power loss of a single electron charge distribution confined in a quantum plasma
Mehramiz, A.; Mahmoodi, J.; Sobhanian, S.
2011-05-15
The dielectric tensor for a quantum plasma is derived by using a linearized quantum hydrodynamic theory. The wave functions for a nanostructure bound system have been investigated. Finally, the power loss for an oscillating charge distribution of a mixed state will be calculated, using the dielectric function formalism.
Quantum vacuum energy in Taub-NUT (Newman-Unti-Tamburino)-type cosmologies
Hiscock, W.A.; Konkowski, D.A.
1982-09-15
The effects of vacuum polarization on the mildest possible sort of cosmological singularity, the Taub-NUT (Newman-Unti-Tamburino)-type singularities, are studied. Unlike stronger sorts of singularities where physical quantities (e.g., curvature, energy density) diverge, in these universes the only barrier is a pathological topology. Quantum effects, known to be important in regions of large spacetime curvature, are found to also be important in these universes, where the curvature may be arbitrarily small or even zero. The vacuum expectation value of the stress-energy tensor for a conformal scalar field is calculated on a flat archetype of the Taub-NUT-type universes, the Misner universe (flat Kasner spacetime with S/sup 1/ x R/sup 3/ topology). The vacuum stress energy diverges at the singularity and on its associated Cauchy horizons. This divergence, together with the ''fixed'' nature of the spacetime's topology, suggests that these boundaries will be replaced by curvature singularities in a better approximation to full quantum gravity.
Reconstruction of spatially inhomogeneous dielectric tensors through optical tomography.
Hammer, Hanno; Lionheart, William R B
2005-02-01
A method to reconstruct weakly anisotropic inhomogeneous dielectric tensors inside a transparent medium is proposed. The mathematical theory of integral geometry is cast into a workable framework that allows the full determination of dielectric tensor fields by scalar Radon inversions of the polarization transformation data obtained from six planar tomographic scanning cycles. Furthermore, a careful derivation of the usual equations of integrated photoelasticity in terms of heuristic length scales of the material inhomogeneity and anisotropy is provided, resulting in a self-contained account about the reconstruction of arbitrary three-dimensional, weakly anisotropic dielectric tensor fields. PMID:15717553
Flavor-spin symmetry estimate of the nucleon tensor charge.
Gamberg, L; Goldstein, G R
2001-12-10
The axial vector and tensor charge, defined as the first moments of the forward nucleon matrix elements of corresponding quark currents, are essential for characterizing the spin structure of the nucleon. There are no definitive theoretical predictions for the tensor charge, aside from several model-dependent calculations. We present a new approach that exploits the approximate mass degeneracy of the light axial vector mesons [ a1(1260), b1(1235), and h1(1170)] and uses pole dominance to calculate the tensor charge. The result is simple in form. It depends on the decay constants of the axial vector mesons and their couplings to the nucleons. PMID:11736495
Extracting the diffusion tensor from molecular dynamics simulation with Milestoning
Mugnai, Mauro L.; Elber, Ron
2015-01-07
We propose an algorithm to extract the diffusion tensor from Molecular Dynamics simulations with Milestoning. A Kramers-Moyal expansion of a discrete master equation, which is the Markovian limit of the Milestoning theory, determines the diffusion tensor. To test the algorithm, we analyze overdamped Langevin trajectories and recover a multidimensional Fokker-Planck equation. The recovery process determines the flux through a mesh and estimates local kinetic parameters. Rate coefficients are converted to the derivatives of the potential of mean force and to coordinate dependent diffusion tensor. We illustrate the computation on simple models and on an atomically detailed system—the diffusion along the backbone torsions of a solvated alanine dipeptide.
Effects of realistic tensor force on nuclear structure
Nakada, H.
2012-10-20
First-order tensor-force effects on nuclear structure are investigated in the self-consistent mean-field and RPA calculations with the M3Y-type semi-realistic interactions, which contain the realistic tensor force. The tensor force plays a key role in Z- or N-dependence of the shell structure, and in transitions involving spin degrees-of-freedom. It is demonstrated that the semi-realistic interactions successfully describe the N-dependence of the shell structure in the proton-magic nuclei (e.g. Ca and Sn), and the magnetic transitions (e.g. M1 transition in {sup 208}Pb).
Hyperbolicity of scalar-tensor theories of gravity
Salgado, Marcelo; Martinez del Rio, David; Alcubierre, Miguel; Nunez, Dario
2008-05-15
Two first order strongly hyperbolic formulations of scalar-tensor theories of gravity allowing nonminimal couplings (Jordan frame) are presented along the lines of the 3+1 decomposition of spacetime. One is based on the Bona-Masso formulation, while the other one employs a conformal decomposition similar to that of Baumgarte-Shapiro-Shibata-Nakamura. A modified Bona-Masso slicing condition adapted to the scalar-tensor theory is proposed for the analysis. This study confirms that the scalar-tensor theory has a well-posed Cauchy problem even when formulated in the Jordan frame.
Elasto-plastic model with second order defect density tensor
NASA Astrophysics Data System (ADS)
Cleja-Ţigoiu, Sanda
2011-05-01
The paper deals with a second order finite elasto-plastic model, which involves the defect density tensor, as a measure of the extra material defects existing in the damaged microstructure. The material behaviour is described with respect to an anholonomic configuration, which is introduced through the second order plastic deformation, consisting in plastic distortion and plastic connection. The defect density tensor enters the expression of the plastic connection through its gradient and represents a measure of non-metricity. The constitutive and evolution equations are derived to be compatible with the free energy imbalance. The evolution equation for the defect density tensor is non-local and coupled with the plastic distortion.
The general dielectric tensor for bi-kappa magnetized plasmas
NASA Astrophysics Data System (ADS)
Gaelzer, R.; Ziebell, L. F.; Meneses, A. R.
2016-06-01
In this paper, we derive the dielectric tensor for a plasma containing particles described by an anisotropic superthermal (bi-kappa) velocity distribution function. The tensor components are written in terms of the two-variables kappa plasma special functions, recently defined by Gaelzer and Ziebell [Phys. Plasmas 23, 022110 (2016)]. We also obtain various new mathematical properties for these functions, which are useful for the analytical treatment, numerical implementation, and evaluation of the functions and, consequently, of the dielectric tensor. The formalism developed here and in the previous paper provides a mathematical framework for the study of electromagnetic waves propagating at arbitrary angles and polarizations in a superthermal plasma.
Turbulence constitutive modeling of the square root of the Reynolds stress
NASA Astrophysics Data System (ADS)
Ariki, Taketo
2015-11-01
A methodology for turbulence constitutive modeling is discussed on the basis of the square-root tensor of the Reynolds stress. The present methodology can satisfy the realizability condition for the Reynolds stress proposed by Schumann [Phys. Fluids 20, 721 (1977)], 10.1063/1.861942 in a more general manner than the conventional methodologies. The definition and uniqueness of the square-root tensor have been discussed, and its boundary condition has been properly obtained consistently with that of the Reynolds stress. Examples of possible constitutive models of both tensor-expansion and transport-equation types have been proposed.
Turbulence constitutive modeling of the square root of the Reynolds stress.
Ariki, Taketo
2015-11-01
A methodology for turbulence constitutive modeling is discussed on the basis of the square-root tensor of the Reynolds stress. The present methodology can satisfy the realizability condition for the Reynolds stress proposed by Schumann [Phys. Fluids 20, 721 (1977)] in a more general manner than the conventional methodologies. The definition and uniqueness of the square-root tensor have been discussed, and its boundary condition has been properly obtained consistently with that of the Reynolds stress. Examples of possible constitutive models of both tensor-expansion and transport-equation types have been proposed. PMID:26651782
Quantum correlation via quantum coherence
NASA Astrophysics Data System (ADS)
Yu, Chang-shui; Zhang, Yang; Zhao, Haiqing
2014-06-01
Quantum correlation includes quantum entanglement and quantum discord. Both entanglement and discord have a common necessary condition—quantum coherence or quantum superposition. In this paper, we attempt to give an alternative understanding of how quantum correlation is related to quantum coherence. We divide the coherence of a quantum state into several classes and find the complete coincidence between geometric (symmetric and asymmetric) quantum discords and some particular classes of quantum coherence. We propose a revised measure for total coherence and find that this measure can lead to a symmetric version of geometric quantum correlation, which is analytic for two qubits. In particular, this measure can also arrive at a monogamy equality on the distribution of quantum coherence. Finally, we also quantify a remaining type of quantum coherence and find that for two qubits, it is directly connected with quantum nonlocality.
Echocardiography stress test; Stress test - echocardiography; CAD - stress echocardiography; Coronary artery disease - stress Echocardiography; Chest pain - stress echocardiography; Angina - stress echocardiography; ...
Cosmological implications of modified gravity induced by quantum metric fluctuations
NASA Astrophysics Data System (ADS)
Liu, Xing; Harko, Tiberiu; Liang, Shi-Dong
2016-08-01
We investigate the cosmological implications of modified gravities induced by the quantum fluctuations of the gravitational metric. If the metric can be decomposed as the sum of the classical and of a fluctuating part, of quantum origin, then the corresponding Einstein quantum gravity generates at the classical level modified gravity models with a non-minimal coupling between geometry and matter. As a first step in our study, after assuming that the expectation value of the quantum correction can be generally expressed in terms of an arbitrary second order tensor constructed from the metric and from the thermodynamic quantities characterizing the matter content of the Universe, we derive the (classical) gravitational field equations in their general form. We analyze in detail the cosmological models obtained by assuming that the quantum correction tensor is given by the coupling of a scalar field and of a scalar function to the metric tensor, and by a term proportional to the matter energy-momentum tensor. For each considered model we obtain the gravitational field equations, and the generalized Friedmann equations for the case of a flat homogeneous and isotropic geometry. In some of these models the divergence of the matter energy-momentum tensor is non-zero, indicating a process of matter creation, which corresponds to an irreversible energy flow from the gravitational field to the matter fluid, and which is direct consequence of the non-minimal curvature-matter coupling. The cosmological evolution equations of these modified gravity models induced by the quantum fluctuations of the metric are investigated in detail by using both analytical and numerical methods, and it is shown that a large variety of cosmological models can be constructed, which, depending on the numerical values of the model parameters, can exhibit both accelerating and decelerating behaviors.
Separate universes in loop quantum cosmology: Framework and applications
NASA Astrophysics Data System (ADS)
Wilson-Ewing, Edward
2016-06-01
I present a streamlined review of how the separate universe approach to cosmological perturbation theory can be used to study the dynamics of long-wavelength scalar perturbations in loop quantum cosmology (LQC), and then use it to calculate how long-wavelength curvature perturbations evolve across the LQC bounce assuming a constant equation of state. A similar calculation is possible for tensor modes using results from a complementary approach to cosmological perturbation theory in LQC based on an effective Hamiltonian constraint. An interesting result is that the tensor-to-scalar ratio can be suppressed or amplified by quantum gravity effects during the bounce, depending on the equation of state of the matter field dominating the dynamics. In particular, if the equation of state lies between ‑ 1/3 and 1, the value of the tensor-to-scalar ratio will be suppressed during the bounce, in some cases significantly.
NASA Astrophysics Data System (ADS)
Le Gouët, Jean-Louis; Moiseev, Sergey
2012-06-01
Interaction of quantum radiation with multi-particle ensembles has sparked off intense research efforts during the past decade. Emblematic of this field is the quantum memory scheme, where a quantum state of light is mapped onto an ensemble of atoms and then recovered in its original shape. While opening new access to the basics of light-atom interaction, quantum memory also appears as a key element for information processing applications, such as linear optics quantum computation and long-distance quantum communication via quantum repeaters. Not surprisingly, it is far from trivial to practically recover a stored quantum state of light and, although impressive progress has already been accomplished, researchers are still struggling to reach this ambitious objective. This special issue provides an account of the state-of-the-art in a fast-moving research area that makes physicists, engineers and chemists work together at the forefront of their discipline, involving quantum fields and atoms in different media, magnetic resonance techniques and material science. Various strategies have been considered to store and retrieve quantum light. The explored designs belong to three main—while still overlapping—classes. In architectures derived from photon echo, information is mapped over the spectral components of inhomogeneously broadened absorption bands, such as those encountered in rare earth ion doped crystals and atomic gases in external gradient magnetic field. Protocols based on electromagnetic induced transparency also rely on resonant excitation and are ideally suited to the homogeneous absorption lines offered by laser cooled atomic clouds or ion Coulomb crystals. Finally off-resonance approaches are illustrated by Faraday and Raman processes. Coupling with an optical cavity may enhance the storage process, even for negligibly small atom number. Multiple scattering is also proposed as a way to enlarge the quantum interaction distance of light with matter. The
NASA Astrophysics Data System (ADS)
Hobson, Art
2011-10-01
An earlier paper2 introduces quantum physics by means of four experiments: Youngs double-slit interference experiment using (1) a light beam, (2) a low-intensity light beam with time-lapse photography, (3) an electron beam, and (4) a low-intensity electron beam with time-lapse photography. It's ironic that, although these experiments demonstrate most of the quantum fundamentals, conventional pedagogy stresses their difficult and paradoxical nature. These paradoxes (i.e., logical contradictions) vanish, and understanding becomes simpler, if one takes seriously the fact that quantum mechanics is the nonrelativistic limit of our most accurate physical theory, namely quantum field theory, and treats the Schroedinger wave function, as well as the electromagnetic field, as quantized fields.2 Both the Schroedinger field, or "matter field," and the EM field are made of "quanta"—spatially extended but energetically discrete chunks or bundles of energy. Each quantum comes nonlocally from the entire space-filling field and interacts with macroscopic systems such as the viewing screen by collapsing into an atom instantaneously and randomly in accordance with the probability amplitude specified by the field. Thus, uncertainty and nonlocality are inherent in quantum physics. This paper is about quantum uncertainty. A planned later paper will take up quantum nonlocality.
Dark matter dispersion tensor in perturbation theory
NASA Astrophysics Data System (ADS)
Aviles, Alejandro
2016-03-01
We compute the dark matter velocity dispersion tensor up to third order in perturbation theory using the Lagrangian formalism, revealing growing solutions at the third and higher orders. Our results are general and can be used for any other perturbative formalism. As an application, corrections to the matter power spectrum are calculated, and we find that some of them have the same structure as those in the effective field theory of large-scale structure, with "EFT-like" coefficients that grow quadratically with the linear growth function and are further suppressed by powers of the logarithmic linear growth factor f ; other corrections present additional k dependence. Due to the velocity dispersions, there exists a free-streaming scale that suppresses the whole 1-loop power spectrum. Furthermore, we find that as a consequence of the nonlinear evolution, the free-streaming length is shifted towards larger scales, wiping out more structure than that expected in linear theory. Therefore, we argue that the formalism developed here is better suited for a perturbation treatment of warm dark matter or neutrino clustering, where the velocity dispersion effects are well known to be important. We discuss implications related to the nature of dark matter.
PHYSLIB: A C++ tensor class library
Budge, K.G.
1991-10-09
C++ is the first object-oriented programming language which produces sufficiently efficient code for consideration in computation-intensive physics and engineering applications. In addition, the increasing availability of massively parallel architectures requires novel programming techniques which may prove to be relatively easy to implement in C++. For these reasons, Division 1541 at Sandia National Laboratories is devoting considerable resources to the development of C++ libraries. This document describes the first of these libraries to be released, PHYSLIB, which defines classes representing Cartesian vectors and (second-order) tensors. This library consists of the header file physlib.h, the inline code file physlib.inl, and the source file physlib.C. The library is applicable to both three-dimensional and two-dimensional problems; the user selects the 2-D version of the library by defining the symbol TWO D in the header file physlib.h and recompiling physlib.C and his own code. Alternately, system managers may wish to provide duplicate header and object modules of each dimensionality. This code was produced under the auspices of Sandia National Laboratories, a federally-funded research center administered for the United States Department of Energy on a non-profit basis by AT T. This code is available to US citizens, and institutions under research, government use and/or commercial license agreements.
Analysis of Social Networks by Tensor Decomposition
NASA Astrophysics Data System (ADS)
Sizov, Sergej; Staab, Steffen; Franz, Thomas
The Social Web fosters novel applications targeting a more efficient and satisfying user guidance in modern social networks, e.g., for identifying thematically focused communities, or finding users with similar interests. Large scale and high diversity of users in social networks poses the challenging question of appropriate relevance/authority ranking, for producing fine-grained and rich descriptions of available partners, e.g., to guide the user along most promising groups of interest. Existing methods for graph-based authority ranking lack support for fine-grained latent coherence between user relations and content (i.e., support for edge semantics in graph-based social network models). We present TweetRank, a novel approach for faceted authority ranking in the context of social networks. TweetRank captures the additional latent semantics of social networks by means of statistical methods in order to produce richer descriptions of user relations. We model the social network by a 3-dimensional tensor that enables the seamless representation of arbitrary semantic relations. For the analysis of that model, we apply the PARAFAC decomposition, which can be seen as a multi-modal counterpart to common Web authority ranking with HITS. The result are groupings of users and terms, characterized by authority and navigational (hub) scores with respect to the identified latent topics. Sample experiments with life data of the Twitter community demonstrate the ability of TweetRank to produce richer and more comprehensive contact recommendations than other existing methods for social authority ranking.
Trace anomaly on a quantum spacetime manifold
Spallucci, Euro; Smailagic, Anais; Nicolini, Piero
2006-04-15
In this paper we investigate the trace anomaly in a space-time where single events are delocalized as a consequence of short distance quantum coordinate fluctuations. We obtain a modified form of heat kernel asymptotic expansion which does not suffer from short distance divergences. Calculation of the trace anomaly is performed using an IR regulator in order to circumvent the absence of UV infinities. The explicit form of the trace anomaly is presented and the corresponding 2D Polyakov effective action and energy-momentum tensor are obtained. The vacuum expectation value of the energy-momentum tensor in the Boulware, Hartle-Hawking and Unruh vacua is explicitly calculated in a rt section of a recently found, noncommutative inspired, Schwarzschild-like solution of the Einstein equations. The standard short distance divergences in the vacuum expectation values are regularized in agreement with the absence of UV infinities removed by quantum coordinate fluctuations.
Traffic Speed Data Imputation Method Based on Tensor Completion
Ran, Bin; Feng, Jianshuai; Liu, Ying; Wang, Wuhong
2015-01-01
Traffic speed data plays a key role in Intelligent Transportation Systems (ITS); however, missing traffic data would affect the performance of ITS as well as Advanced Traveler Information Systems (ATIS). In this paper, we handle this issue by a novel tensor-based imputation approach. Specifically, tensor pattern is adopted for modeling traffic speed data and then High accurate Low Rank Tensor Completion (HaLRTC), an efficient tensor completion method, is employed to estimate the missing traffic speed data. This proposed method is able to recover missing entries from given entries, which may be noisy, considering severe fluctuation of traffic speed data compared with traffic volume. The proposed method is evaluated on Performance Measurement System (PeMS) database, and the experimental results show the superiority of the proposed approach over state-of-the-art baseline approaches. PMID:25866501
String cosmology with a time-dependent antisymmetric tensor potential
Copeland, E.J.; Lahiri, A.; Wands, D. )
1995-02-15
We present a class of exact solutions for homogeneous, anisotropic cosmologies in four dimensions derived from the low-energy string effective action including a homogeneous dilaton [phi] and antisymmetric tensor potential [ital B][sub [mu][nu
Dirac Equation for Scalar, Vector and Tensor Generalized Cornell Interaction
NASA Astrophysics Data System (ADS)
Zarrinkamar, S.; Panahi, H.; Rezaei, M.; Baradaran, M.
2016-03-01
We consider spin and pseudospin symmetry limits of Dirac equation in the presence of scalar, vector and tensor generalized Cornell interaction and report the solutions via the quasi-exact analytical ansatz approach.
Heterogeneous Tensor Decomposition for Clustering via Manifold Optimization.
Sun, Yanfeng; Gao, Junbin; Hong, Xia; Mishra, Bamdev; Yin, Baocai
2016-03-01
Tensor clustering is an important tool that exploits intrinsically rich structures in real-world multiarray or Tensor datasets. Often in dealing with those datasets, standard practice is to use subspace clustering that is based on vectorizing multiarray data. However, vectorization of tensorial data does not exploit complete structure information. In this paper, we propose a subspace clustering algorithm without adopting any vectorization process. Our approach is based on a novel heterogeneous Tucker decomposition model taking into account cluster membership information. We propose a new clustering algorithm that alternates between different modes of the proposed heterogeneous tensor model. All but the last mode have closed-form updates. Updating the last mode reduces to optimizing over the multinomial manifold for which we investigate second order Riemannian geometry and propose a trust-region algorithm. Numerical experiments show that our proposed algorithm compete effectively with state-of-the-art clustering algorithms that are based on tensor factorization. PMID:27046492
Hidden symmetries and killing tensors on curved spaces
Ianus, S.; Visinescu, M.; Vilcu, G. E.
2010-11-15
Higher-order symmetries corresponding to Killing tensors are investigated. The intimate relation between Killing-Yano tensors and nonstandard supersymmetries is pointed out. In the Dirac theory on curved spaces, Killing-Yano tensors generate Dirac-type operators involved in interesting algebraic structures as dynamical algebras or even infinite dimensional algebras or superalgebras. The general results are applied to space-times which appear in modern studies. One presents the infinite dimensional superalgebra of Dirac type operators on the 4-dimensional Euclidean Taub-NUT space that can be seen as a twisted loop algebra. The existence of the conformal Killing-Yano tensors is investigated for some spaces with mixed 3-Sasakian structures.
The non-abelian tensor multiplet in loop space
NASA Astrophysics Data System (ADS)
Gustavsson, Andreas
2006-01-01
We introduce a non-abelian tensor multiplet directly in the loop space associated with flat six-dimensional Miskowski space-time, and derive the supersymmetry variations for on-shell Script N = (2,0) supersymmetry.
The structure of correlation tensors in homogeneous anisotropic turbulence
NASA Technical Reports Server (NTRS)
Matthaeus, W. H.; Smith, C.
1980-01-01
The study of turbulence with spatially homogeneous but anisotropic statistical properties has applications in space physics and laboratory plasma physics. The first step in the systematic study of such fluctuations is the elucidation of the kinematic properties of the relevant statistical objects, which are the correlation tensors. The theory of isotropic tensors, developed by Robertson, Chandrasekhar and others, is reviewed and extended to cover the general case of turbulence with a pseudo-vector preferred direction, without assuming mirror reflection invariance. Attention is focused on two point correlation functions and it is shown that the form of the decomposition into proper and pseudo-tensor contributions is restricted by the homogeneity requirement. It is also shown that the vector and pseudo-vector preferred direction cases yield different results. An explicit form of the two point correlation tensor is presented which is appropriate for analyzing interplanetary magnetic fluctuations. A procedure for determining the magnetic helicity from experimental data is presented.
Reducing tensor magnetic gradiometer data for unexploded ordnance detection
Bracken, Robert E.; Brown, Philip J.
2005-01-01
We performed a survey to demonstrate the effectiveness of a prototype tensor magnetic gradiometer system (TMGS) for detection of buried unexploded ordnance (UXO). In order to achieve a useful result, we designed a data-reduction procedure that resulted in a realistic magnetic gradient tensor and devised a simple way of viewing complicated tensor data, not only to assess the validity of the final resulting tensor, but also to preview the data at interim stages of processing. The final processed map of the surveyed area clearly shows a sharp anomaly that peaks almost directly over the target UXO. This map agrees well with a modeled map derived from dipolar sources near the known target locations. From this agreement, it can be deduced that the reduction process is valid, making the prototype TMGS a foundation for development of future systems and processes.
Airborne full tensor magnetic gradiometry surveys in the Thuringian basin, Germany
NASA Astrophysics Data System (ADS)
Queitsch, M.; Schiffler, M.; Goepel, A.; Stolz, R.; Meyer, M.; Meyer, H.; Kukowski, N.
2013-12-01
In this contribution we introduce a newly developed fully operational full tensor magnetic gradiometer (FTMG) instrument based on Superconducting Quantum Interference Devices (SQUIDs) and show example data acquired in 2012 within the framework of the INFLUINS (Integrated Fluid Dynamics in Sedimentary basins) project. This multidisciplinary project aims for a better understanding of movements and interaction between shallow and deep fluids in the Thuringian Basin in the center of Germany. In contrast to mapping total magnetic field intensity (TMI) in conventional airborne magnetic surveys for industrial exploration of mineral deposits and sedimentary basins, our instrument measures all components of the magnetic field gradient tensor using highly sensitive SQUID gradiometers. This significantly constrains the solutions of the inverse problem. Furthermore, information on the ratio between induced and remanent magnetization is obtained. Special care has been taken to reduce motion noise while acquiring data in airborne operation. Therefore, the sensors are mounted in a nonmagnetic and aerodynamically shaped bird made of fiberglas with a high drag tail which stabilizes the bird even at low velocities. The system is towed by a helicopter and kept at 30m above ground during data acquisition. Additionally, the system in the bird incorporates an inertial unit for geo-referencing and enhanced motion noise compensation, a radar altimeter for topographic correction and a GPS system for high precision positioning. Advanced data processing techniques using reference magnetometer and inertial unit data result in a very low system noise of less than 60 pT/m peak to peak in airborne operation. To show the performance of the system we present example results from survey areas within the Thuringian basin and along its bordering highlands. The mapped gradient tensor components show a high correlation to existing geologic maps. Furthermore, the measured gradient components indicate
Discriminating induced seismicity from natural earthquakes using moment tensors and source spectra
NASA Astrophysics Data System (ADS)
Zhang, Hongliang; Eaton, David W.; Li, Ge; Liu, Yajing; Harrington, Rebecca M.
2016-02-01
Earthquake source mechanisms and spectra can provide important clues to aid in discriminating between natural and induced events. In this study, we calculate moment tensors and stress drop values for eight recent induced earthquakes in the Western Canadian Sedimentary Basin with magnitudes between 3.2 and 4.4, as well as a nearby magnitude 5.3 event that is interpreted as a natural earthquake. We calculate full moment tensor solutions by performing a waveform-fitting procedure based on a 1-D transversely isotropic velocity model. In addition to a dominant double-couple (DC) signature that is common to nearly all events, most induced events exhibit significant non-double-couple components. A parameter sensitivity analysis indicates that spurious non-DC components are negligible if the signal to noise ratio (SNR) exceeds 10 and if the 1-D model differs from the true velocity structure by less than 5%. Estimated focal depths of induced events are significantly shallower than the typical range of focal depths for intraplate earthquakes in the Canadian Shield. Stress drops of the eight induced events were estimated using a generalized spectral-fitting method and fall within the typical range of 2 to 90 MPa for tectonic earthquakes. Elastic moduli changes due to the brittle damage production at the source, presence of multiple intersecting fractures, dilatant jogs created at the overlapping areas of multiple fractures, or non-planar pre-existing faults may explain the non-DC components for induced events.