Search NASA⌕ Search

SEARCH · Search NASA

Results for “tensor times same vector”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
DOE OSTI2019

Anomaly detection in scientific data using joint statistical moments

We propose an anomaly detection method for multi-variate scientific data based on analysis of high-order joint moments. Using kurtosis as a reliable measure of outliers, we suggest that principal kurtosis vectors, by analogy to principal component analysis (PCA) vectors, signify the principal directions along which outliers appear. The inception of an anomaly, then, manifests as a change in the principal values and vectors of kurtosis. Obtaining the principal kurtosis vectors requires decomposing a fourth order joint cumulant tensor for which we use a simple, computationally less expensive approach that involves performing a singular value decomposition (SVD) over the matricized tensor. We demonstrate the efficacy of this approach on synthetic data, and develop an algorithm to identify the occurrence of a spatial and/or temporal anomalous event in scientific phenomena. The algorithm decomposes the data into several spatial sub-domains and time steps to identify regions with such events. Feature moment metrics, based on the alignments of the principal kurtosis vectors, are computed at each sub-domain and time step for all features to quantify their relative importance towards the overall kurtosis in the data. Accordingly, spatial and temporal anomaly metrics for each sub-domain are proposed using the Hellinger distance of the feature moment metric distribution from a suitable nominal distribution. Finally, we apply the algorithm to two turbulent auto-ignition combustion cases and demonstrate that the anomaly metrics reliably capture the occurrence of auto-ignition in relevant spatial sub-domains at the right time steps.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Time-reversal symmetry, anomalies, and dualities in (2+1)$d$

We study continuum quantum field theories in 2+1 dimensions with time-reversal symmetry \cal T . The standard relation {\cal T}^2=(-1)^F is satisfied on all the “perturbative operators” i.e. polynomials in the fundamental fields and their derivatives. However, we find that it is often the case that acting on more complicated operators {\cal T}^2=(-1)^F {\cal M} with \cal M a non-trivial global symmetry. For example, acting on monopole operators, \cal M could be \pm1 ± 1 depending on the magnetic charge. We study in detail U(1) U ( 1 ) gauge theories with fermions of various charges. Such a modification of the time-reversal algebra happens when the number of odd charge fermions is 2 ~{\rm mod }~4 , e.g. in QED with two fermions. Our work also clarifies the dynamics of QED with fermions of higher charges. In particular, we argue that the long-distance behavior of QED with a single fermion of charge 2 2 is a free theory consisting of a Dirac fermion and a decoupled topological quantum field theory. The extension to an arbitrary even charge is straightforward. The generalization of these abelian theories to SO(N) S O ( N ) gauge theories with fermions in the vector or in two-index tensor representations leads to new results and new consistency conditions on previously suggested scenarios for the dynamics of these theories. Among these new results is a surprising non-abelian symmetry involving time-reversal.

Cordova, Clay↗
DOE OSTI2023

Phonon Hall Viscosity of Ionic Crystals

When time-reversal symmetry is broken, the low-energy description of acoustic lattice dynamics allows for a dissipationless component of the viscosity tensor, the phonon Hall viscosity, which captures how phonon chirality grows with the wave vector. In this work, we show that, in ionic crystals, a phonon Hall viscosity contribution is produced by the Lorentz forces on moving ions. We calculate typical values of the Lorentz force contribution to the Hall viscosity using a simple square lattice toy model, and we compare it with literature estimates of the strengths of other Hall-viscosity mechanisms.

36 MATERIALS SCIENCE↗
NASA NTRS1991

Optical Computation Of Matrices From Vectors

Proposed optical apparatus generates rectangular pattern of light and dark areas, brightnesses of which represent elements of matrix product of two vectors. Photorefractive effect gives rise to four-wave mixing, which generates output beam modulated spatially by matrix product xy(SupT). Optical multipliers used as real-time analog tensor generators, components of neural networks, and generators of patterns to steer electromagnetic beams by diffraction or to effect temporary interconnections in very-large-scale integrated circuits.

Liu, Hua-Kuang↗
DOE OSTI2024

Collocation methods for nonlinear differential equations on low-rank manifolds

We introduce new methods for integrating nonlinear differential equations on low-rank manifolds. These methods rely on interpolatory projections onto the tangent space, enabling low-rank time integration of vector fields that can be evaluated entry-wise. A key advantage of our approach is that it does not require the vector field to exhibit low-rank structure, thereby overcoming significant limitations of traditional dynamical low-rank methods based on orthogonal projection. To construct the interpolatory projectors, we develop a sparse tensor sampling algorithm based on the discrete empirical interpolation method (DEIM) that parameterizes tensor train manifolds and their tangent spaces with cross interpolation. Using these projectors, we propose two time integration schemes on low-rank tensor train manifolds. The first scheme integrates the solution at selected interpolation indices and constructs the solution with cross interpolation. The second scheme generalizes the well-known orthogonal projector-splitting integrator to interpolatory projectors. We demonstrate the proposed methods with applications to several tensor differential equations arising from the discretization of partial differential equations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Explicit simulation of the Brownian rotation of arbitrary shaped aerosol particles using quaternions

The shape of an aerosol particle strongly influences its mass and momentum transfer cross-sections, charging properties, and other physical properties. Here, we present an explicit time-stepping procedure to simulate the rotational Brownian motion of arbitrary shaped aerosol particles by solving Euler’s equation of rotation. A Langevin formulation of the rotation equations is used, wherein Brownian motion due to thermal collisions between a particle and background gas molecules is represented using a stochastic fluctuating torque and fluid resistance is included as a drag torque. To avoid singularities associated with describing the orientation of a shape with Euler angles, we employ a quaternion formulation that leads to first-order stochastic differential equations to describe the evolution of the angular position and angular velocity of a rigid body. We perform all the rotational dynamics calculations in the body-fixed frame of reference attached to the rotating shape whose basis vectors are the normalized eigenvectors of the inertia tensor of the particle. Numerical solutions to rotation under torque-free conditions, damped rotation without Brownian motion, and stochastic rotation for arbitrary shapes are presented and discussed. The presented method enables time-resolved simulation of Brownian rotation for direct comparison with experimentally measured trajectories or statistical measures. The second order accuracy of the used time-stepping procedure places a severe restriction on the timestep that can be used for obtaining accurate results. Animations of presented simulations are included for visualizing rotational motion at various gas pressures. To aid implementation, MATLAB ® codes are also provided. Extension to include translation Brownian motion is straightforward.

Roy, Mrittika↗
DOE OSTI2025

Observation of an Axial-Vector State in the Study of the Decay ψ ( 3686 ) → ϕ η η ′

Using ( 2712.4 ± 14.3 ) × 10 6 ψ ( 3686 ) events collected with the BESIII detector at BEPCII, a partial wave analysis of the decay ψ ( 3686 ) → ϕ η η ′ is performed with the covariant tensor approach. In addition to the established states h 1 ( 1900 ) and ϕ ( 2170 ) , an axial-vector state with a mass near 2.3 GeV / c 2 is observed for the first time. Its mass and width are measured to be 2316 ± 9 stat ± 3 0 syst MeV / c 2 and 89 ± 1 5 stat ± 2 6 syst MeV , respectively. The product branching fractions of B [ ψ ( 3686 ) → X ( 2300 ) η ′ ] B [ X ( 2300 ) → ϕ η ] and B [ ψ ( 3686 ) → X ( 2300 ) η ] B [ X ( 2300 ) → ϕ η ′ ] are determined to be ( 4.8 ± 1.3 stat ± 0.7 syst ) × 10 − 6 and ( 2.2 ± 0.7 stat ± 0.7 syst ) × 10 − 6 , respectively. The branching fraction B [ ψ ( 3686 ) → ϕ η η ′ ] is measured for the first time to be ( 3.14 ± 0.1 7 stat ± 0.2 4 syst ) × 10 − 5 . The first uncertainties are statistical and the second are systematic. Published by the American Physical Society 2025

Ablikim, M.↗
DOE OSTI2017

Spin-density fluctuations and the fluctuation-dissipation theorem in 3 d ferromagnetic metals

Spatial and time scales of spin-density fluctuations (SDFs) were analyzed in 3d ferromagnets using ab initio linear-response calculations of complete wave-vector and energy dependence of the dynamic spin susceptibility tensor. We demonstrate that SDFs are spread continuously over the entire Brillouin zone and while the majority of them reside within the 3d bandwidth, a significant amount comes from much higher energies. A validity of the adiabatic approximation in spin dynamics is discussed. The SDF spectrum is shown to have two main constituents: a minor low-energy spin-wave contribution and a much larger high-energy component from more localized excitations. Furthermore, using the fluctuation-dissipation theorem, the on-site spin correlator and the related effective fluctuating moment were properly evaluated and their universal dependence on the 3d band population is further discussed.

36 MATERIALS SCIENCE↗
NASA NTRS1993

Tensoral for post-processing users and simulation authors

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.

Dresselhaus, Eliot↗
DOE OSTI2019

Comment on “The Mössbauer rotor experiment and the general theory of relativity” [Ann. Physics 368 (2016) 258–266]

Highlights: •Our approach is considered from the viewpoint of arbitrary moving continuum. •Continuum characteristics are determined by a deformation tensor, a stress tensor, a strain velocity tensor, a spin tensor (Sing (1963)) and the first curvature vectors of the world lines of medium particles. •All these physical values are located on the hypersurfaces orthogonal to the world lines of medium particles and specify the “physical” space. •The time counting from the “physical” space permits to obtain the red shift of the frequency at the end of the tube that coincides with Corda result (Corda (2016)).

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Transition matrices and orbitals from reduced density matrix theory

In this contribution, we report two different methodologies for characterizing the electronic structure reorganization occurring when a chromophore undergoes an electronic transition. For the first method, we start by setting the theoretical background necessary to the reinterpretation through simple tensor analysis of (i) the transition density matrix and (ii) the natural transition orbitals in the scope of reduced density matrix theory. This novel interpretation is made more clear thanks to a short compendium of the one-particle reduced density matrix theory in a Fock space. The formalism is further applied to two different classes of excited states calculation methods, both requiring a single-determinant reference, that express an excited state as a hole-particle mono-excited configurations expansion, to which particle-hole correlation is coupled (time-dependent Hartree-Fock/time-dependent density functional theory) or not (configuration interaction single/Tamm-Dancoff approximation). For the second methodology presented in this paper, we introduce a novel and complementary concept related to electronic transitions with the canonical transition density matrix and the canonical transition orbitals. Their expression actually reflects the electronic cloud polarisation in the orbital space with a decomposition based on the actual contribution of one-particle excitations from occupied canonical orbitals to virtual ones. This approach validates our novel interpretation of the transition density matrix elements in terms of the Euclidean norm of elementary transition vectors in a linear tensor space. A proper use of these new concepts leads to the conclusion that despite the different principles underlying their construction, they provide two equivalent excited states topological analyses. This connexion is evidenced through simple illustrations of (in)organic dyes electronic transitions analysis.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

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

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.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

A Cartesian parametrization for the numerical analysis of material instability

We examine four parametrizations of the unit sphere in the context of material stability analysis by means of the singularity of the acoustic tensor. We then propose a Cartesian parametrization for vectors that lie a cube of side length two and use these vectors in lieu of unit normals to test for the loss of the ellipticity condition. This parametrization is then used to construct a tensor akin to the acoustic tensor. It is shown that both of these tensors become singular at the same time and in the same planes in the presence of a material instability. Furthermore, the performance of the Cartesian parametrization is compared against the other parametrizations, with the results of these comparisons showing that in general, the Cartesian parametrization is more robust and more numerically efficient than the others.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Results and forecasts on cosmic inflation from weak lensing

Here, we highlight the role of weak lensing measurements from current and upcoming stage-IV imaging surveys in the search for cosmic inflation, specifically in measuring the scalar spectral index n s . To do so, we combine the Dark Energy Survey 3 years of observation weak lensing and clustering data with Bicep/Keck, Planck, and Sloan Digital Sky Survey data in r⁢Λ⁢ CDM (cold dark matter) where r is the tensor-to-scalar ratio. While there is no significant improvement in constraining power, we obtain a 1⁢σ shift on n s . Additionally, we forecast a weak lensing and clustering data vector from the 10-year Legacy Survey of Space and Time by the Vera C. Rubin Observatory and show its combination with current data would improve their n s constraints by 25% in r⁢Λ⁢ CDM.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Impossibility of obtaining time-independent, three-dimensional, spherically symmetric densities of confined systems of relativistically moving constituents

The quantum-mechanical definition of probability, the uncertainty principle, and Poincaré invariance provide strong basic restrictions on the ability to define spatial densities associated with form factors describing the properties of confined systems of relativistically moving constituents. Despite this, many papers ignore one or more of these restrictions. Here I show how to obtain time-independent , two-dimensional densities that are consistent with the stated restrictions. This is done using the light-front, infinite momentum frame formalism. Two-dimensional density interpretations of the axial-vector form factor and all three gravitational form factors is obtained. The resulting mass radius is smaller than the charge radius. Additionally, an expression of a two-dimensional mass density related to the trace of the energy momentum tensor is obtained. I also show that all known methods for finding three-dimensional densities—using the Breit frame, Abel transformations, Wigner distributions, and spherically symmetric wave packets with vanishing spatial extent—violate the basic restrictions in different ways. Furthermore, the use of the latter leads to densities that vanish almost everywhere in space as time increases from an initial value.

form factors↗
NASA NTRS1986

Interactive color graphical postprocessing as a unifying influence in numerical analysis research

The general capabilities and the hardware environment of an interactive color graphical postprocessor for three-dimensional numerical analysis are described as well as the synergistic influence of this aspect of interactive graphics on the research environment. Areas of practical concern include finite element analysis, fracture propagation, surface and framed structures. The interactive color graphical postprocessor, POSTPRO3D, is capable of displaying the scalar, vector, and tensor results of finite difference, finite element, and boundary element analysis. In the case of fatigue cracking in steel crane-rail girders, it was shown that POSTPRO3D offers a high level of flexibility, interactivity and features which minimize response time.

Abel, J. F.↗
DOE OSTI2021

A diagrammatic approach for automatically deriving analytical gradients of tensor hyper-contracted electronic structure methods

In this work, we introduce a diagrammatic approach to facilitate the automatic derivation of analytical nuclear gradients for tensor hyper-contraction (THC) based electronic structure methods. The automatically derived gradients are guaranteed to have the same scaling in terms of both operation count and memory footprint as the underlying energy calculations, and the computation of a gradient is roughly three times as costly as the underlying energy. The new diagrammatic approach enables the first cubic scaling implementation of nuclear derivatives for THC tensors fitted in molecular orbital basis (MO-THC). Furthermore, application of this new approach to THC-MP2 analytical gradients leads to an implementation, which is at least four times faster than the previously reported, manually derived implementation. Finally, we apply the new approach to the 14 tensor contraction patterns appearing in the supporting subspace formulation of multireference perturbation theory, laying the foundation for developments of analytical nuclear gradients and nonadiabatic coupling vectors for multi-state CASPT2.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2017

Kinetic fluid moments closure for a magnetized plasma with collisions

A novel method aimed at a kinetic moments closure for a magnetized plasma with collisions is proposed. The velocity distribution function for each species is expanded in 8 Gaussian Radial Basis Functions (GRBFs) which are essentially shifted Maxwellians at eight representative 3D-velocity points of drift. The vector of 8 fluid moments (for particle density, 3 particle fluxes, total energy density, and 3 energy fluxes) has an 8x8 analytic linear matrix relation to the vector of 8 GRBF density weighs in 3D-real space. The 8 fluid moments with sources for each species are advanced in time while the 8 GRBF weighs are determined from the 8x8 inverse matrix. The two closure moments (for the stress tensor and the energy weighted stress tensor) are linearly determined from the GRBF weighs. Most importantly the velocity moments of the nonlinear Coulomb Fokker-Planck collision operator [Rosenbluth et al, Phys. Rev 107, 1957] are evaluated from the GRBF weights. Generalization from 8 to 12, 16, 20 .., in an energy weighted moment hierarchy is straightforward. The electric field follows from a generalized vorticity (quasi-neutral charge conservation) equation. A strong drift ordering approximation can be applied to eliminate any spuriously unstable high frequency cyclotron motions. A novel weak drift ordering two-time step scheme avoids the vorticity equation by following ion cyclotron motion in time to get the electric field with ion gyroaveraging. Inclusion of low-beta magnetic perturbations is straightforward.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗