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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.

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At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
NASA NTRS1981

An objective method for determining the generalized transport tensor for two-dimensional Eulerian models

An objective method for deriving the components of a generalized transport tensor for a two-dimensional model is presented. Representative meridional and vertical velocities and thermodynamic scalars at a uniform grid are used to reduce the problem to the solution of two flux equations for two unknowns. One unknown is the stream-function, coefficient of an antisymmetric tensor, which corrects the Eulerian mean motions for Stokes drift; the other is a time constant, which converts the deviatory velocity tensor to a symmetric transport tensor. The complete asymmetric tensor, called a transport tensor, has a divergence which yields both advection and diffusion by the deviatory velocities. Advantages and disadvantages of Lagrangian and Eulerian averages are discussed, and meridional-vertical velocity correlations are provided.

Danielsen, E. F.↗
DOE OSTI2023

Fast Parallel Tensor Times Same Vector for Hypergraphs

Hypergraphs are a popular paradigm to rep- resent complex real-world networks exhibiting multi-way relationships of varying sizes. Mining centrality in hyper- graphs via symmetric adjacency tensors has only recently become computationally feasible for large and complex datasets. To enable scalable computation of these and related hypergraph analytics, here we focus on the Sparse Symmetric Tensor Times Same Vector (S3TTVC) oper- ation. We introduce the Compound Compressed Sparse Symmetric (CCSS) format, an extension of the compact CSS format for hypergraphs of varying hyperedge sizes and present a shared-memory parallel algorithm to compute S3TTVC. We experimentally show S3TTVC computation using the CCSS format achieves better performance than the naive baseline, and is subsequently more performant for hypergraph H-eigenvector centrality.

Shivakumar, Shruti↗
DOE OSTI2021

Efficient Parallel Sparse Symmetric Tucker Decomposition for High-Order Tensors

Tensor based methods are receiving renewed attention in recent years due to their prevalence in diverse real-world applications. There is considerable literature on tensor representations and algorithms for tensor decompositions, both for dense and sparse tensors. Many applications in hypergraph analytics, machine learning, psychometry, and signal processing result in tensors that are both sparse and symmetric, making it an important class for further study. Similar to the critical Tensor Times Matrix chain operation (TTMc) in general sparse tensors, the Sparse Symmetric Tensor Times Same Matrix chain (S3TTMc) operation is compute and memory intensive due to high tensor order and the associated factorial explosion in the number of non-zeros. In this work, we present a novel compressed storage format CSS for sparse symmetric tensors, along with an efficient parallel algorithm for the S3TTMc operation. We theoretically establish that S3TTMc on CSS achieves a better memory versus run-time trade-off compared to state-of-the-art implementations. We demonstrate experimental findings that confirm these results and achieve up to 2.9× speedup on synthetic and real datasets.

Shivakumar, Shruti↗
DOE OSTI2024

Emergent Canonical Spin Tensor in the Chiral-Symmetric Hot QCD

The spin tensor is fundamental to relativistic spin hydrodynamics, but its definition is ambiguous due to the pseudogauge symmetry. We show that this ambiguity can be solved in interacting field theories. We prove that the mean-field limit of a modified Nambu-Jona-Lasinio model with spin-spin interactions is equivalent to nondissipative spin hydrodynamics with a canonical spin tensor. Published by the American Physical Society 2024

Buzzegoli, Matteo (ORCID:0000000221145431)↗
NASA NTRS1976

A tensor formulation of the equation of transfer for spherically symmetric flows

A tensor formulation of the equation of radiative transfer is derived in a seven-dimensional Riemannian space such that the resulting equation constitutes a divergence in any coordinate system. After being transformed to a spherically symmetric comoving coordinate system, the transfer equation contains partial derivatives in angle and frequency, as well as optical depth due to the effects of aberration and the Doppler shift. However, by virtue of the divergence form of this equation, the divergence theorem may be applied to yield a numerical differencing scheme which is expected to be stable and to conserve luminosity. It is shown that the equation of transfer derived by this method in a Lagrangian coordinate system may be reduced to that given by Castor (1972), although it is, of course, desirable to leave the equation in divergence form.

Haisch, B. M.↗
DOE OSTI2021

Gauge-symmetrization method for energy-momentum tensors in high-order electromagnetic field theories

For electromagnetic field theories, canonical energy-momentum conservation laws can be derived from the underpinning spacetime translation symmetry according to the Noether procedure. However, the canonical energy-momentum tensors (EMTs) are neither symmetric nor gauge-symmetric (gauge invariant). The Belinfante-Rosenfeld (BR) method is a well-known procedure to symmetrize the EMTs, which also renders them gauge symmetric for first-order field theories. High-order electromagnetic field theories appear in the study of gyrokinetic systems for magnetized plasmas and the Podolsky system for the radiation reaction of classical charged particles. For these high-order field theories, gauge-symmetric EMTs are not necessarily symmetric and vice versa. In the present study, we develop a new gauge-symmetrization method for EMTs in high-order electromagnetic field theories. The Noether procedure is carried out using the Faraday tensor $F_{μν}$, instead of the 4-potential $A_{μ}$, to derive a canonical EMT $T^{μν}_{N}$. We show that the gauge-dependent part of $T^{μν}_{N}$ can be removed using the displacement-potential tensor $F^{σμν}$ ≡ $D^{σμ}A^{ν}/4π$, where $D^{σμ}$ is the antisymmetric electric displacement tensor. This method gauge-symmetrizes the EMT without necessarily making it symmetric, which is adequate for applications not involving general relativity. For first-order electromagnetic field theories, such as the standard Maxwell system, $F^{σμν}$ reduces to the familiar BR superpotential $S^{σμν}$, and the method developed can be used as a simpler procedure to calculate $S^{σμν}$ without employing the angular momentum tensor in 4D spacetime. When the electromagnetic system is coupled to classical charged particles, the gauge-symmetrization method for EMTs is shown to be effective as well.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Sparse Symmetric Format for Tucker Decomposition

Tensor-based methods are receiving renewed attention in recent years due to their prevalence in diverse real-world applications. There is considerable literature on tensor representations and algorithms for tensor decompositions, both for dense and sparse tensors. Many applications in hypergraph analytics, machine learning, psychometry, and signal processing result in tensors that are both sparse and symmetric, making them an important class for further study. Similar to the critical Tensor Times Matrix chain operation (TTM c ) in general sparse tensors, the $\underline{S}$ parse $\underline{S}$ ymmetric $\underline{T}$ ensor $\underline{T}$ imes $\underline{S}$ ame $\underline{M}$ atrix $\underline{c}$ hain (S 3 TTM c ) operation is compute and memory intensive due to high tensor order and the associated factorial explosion in the number of non-zeros. We present the novel Compressed Sparse Symmetric (CSS) format for sparse symmetric tensors, along with an efficient parallel algorithm for the S 3 TTM c operation. We theoretically establish that S 3 TTM c on CSS achieves a better memory versus run-time trade-off compared to state-of-the-art implementations, and visualize the variation of the performance gap over the parameter space. We demonstrate experimental findings that confirm these results and achieve up to 2.72× speedup on synthetic and real datasets. The scaling of the algorithm on different test architectures is also showcased to highlight the effect of machine characteristics on algorithm performance.

42 ENGINEERING↗
DOE OSTI2021

Higher-rank tensor field theory of non-abelian fracton and embeddon

We formulate a new class of tensor gauge field theories in any dimension that is a hybrid class between symmetric higher-rank tensor gauge theory (i.e., higher-spin gauge theory) and anti-symmetric tensor topological field theory. Our theory describes a mixed unitary phase interplaying between gapless and gapped topological order phases (which can live with or without Euclidean, Poincaré, or anisotropic symmetry, at least in ultraviolet high or intermediate energy field theory, but not yet to a lattice cutoff scale). The “gauge structure” can be compact, continuous, abelian or non-abelian. Our theory sits outside the paradigm of Maxwell electromagnetic theory in 1865 and Yang–Mills isospin/color theory in 1954. We discuss its local gauge transformation in terms of the ungauged vector-like or tensor-like higher-moment global symmetry. The non-abelian gauge structure is caused by gauging the non-commutative symmetries: a higher-moment symmetry and a charge conjugation (particle–hole) symmetry. Vector global symmetries along time direction may exhibit time crystals. We explore the relation of these long-range entangled matters to a non-abelian generalization of Fracton order in condensed matter, a field theory formulation of foliation, the spacetime embedding and Embeddon that we newly introduce, and possible fundamental physics applications to dark matter or dark energy.

36 MATERIALS SCIENCE↗
NASA NTRS1977

Sakata-Taketani spin-0 theory with external field interactions - Lagrangian formalism and causal properties

To illustrate that a relativistic field theory need not be manifestly covariant, Lorentz-invariant Lagrangian densities are constructed that yield the equation satisfied by an interacting (two-component) Sakata-Taketani spin-0 field. Six types of external field couplings are considered, two scalars, two vectors, an antisymmetric second-rank tensor, and a symmetric second-rank tensor, with the results specialized to electromagnetic interactions. For either of the two second-rank couplings, the equation is found to describe noncausal wave propagation, a property that is apparent from the dependence of the coefficients of the space derivatives on the external field; in contrast, the noncausality of the corresponding manifestly covariant Duffin-Kemmer-Petiau spin-0 equation is not so obvious. The possibilities for generalizing the results to higher spin theories involving only the essential 2(2J + 1) components for a particle with a definite spin J and mass m are discussed in considerable detail.

Guertin, R. F.↗
DOE OSTI2023

DFT-Based Calculation of Molecular Hyperpolarizability and SFG Intensity of Symmetric and Asymmetric Stretch Modes of Alkyl Groups

Vibrational sum frequency generation (SFG) spectroscopy has been extensively used for obtaining structural information of molecular functional groups at two-dimensional (2D) interfaces buried in the gas or liquid medium. Although the SFG experiment can be done elegantly, interpreting the measured intensity in terms of molecular orientation with respect to the lab coordinate is quite complicated. One of the main reasons is the difficulty of determining the hyperpolarizability tensors of even simple molecules that govern their SFG responses. The single-bond polarizability derivative (SBPD) model has been proposed to estimate the relative magnitude of SFG-active hyperpolarizability by assuming that the perturbation associated to each vibration is negligible. In this study, density functional theory (DFT) was used to calculate the polarizability and dipole derivative tensors of the CH 3 stretch mode of CH 3 I, CH 3 CH 2 I, CH 3 OH, CH 3 CH 2 OH. Then, the hyperpolarizability tensors of symmetric and asymmetric vibration modes were calculated considering the Boltzmann distribution of representative conformers, which allowed theoretical calculation of their SFG intensities at all polarization combinations as a function of the tilt angle of the CH 3 group with respect to the surface normal direction. Then the ratios of the calculated SFG intensities for the CH 3 peaks used in experimental studies for the CH 3 tilt angle determination were compared. This comparison clearly showed the effect of vibrational coupling among neighboring functional groups. As a result, this study presents new parameters that can be used in determining the average tilt angle of the CH 3 group at the 2D interface with SFG measurements as well as limitations of the method.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS2011

Scale Dependence of Magnetic Helicity in the Solar Wind

We determine the magnetic helicity, along with the magnetic energy, at high latitudes using data from the Ulysses mission. The data set spans the time period from 1993 to 1996. The basic assumption of the analysis is that the solar wind is homogeneous. Because the solar wind speed is high, we follow the approach first pioneered by Matthaeus et al. by which, under the assumption of spatial homogeneity, one can use Fourier transforms of the magnetic field time series to construct one-dimensional spectra of the magnetic energy and magnetic helicity under the assumption that the Taylor frozen-in-flow hypothesis is valid. That is a well-satisfied assumption for the data used in this study. The magnetic helicity derives from the skew-symmetric terms of the three-dimensional magnetic correlation tensor, while the symmetric terms of the tensor are used to determine the magnetic energy spectrum. Our results show a sign change of magnetic helicity at wavenumber k approximately equal to 2AU(sup -1) (or frequency nu approximately equal to 2 microHz) at distances below 2.8AU and at k approximately equal to 30AU(sup -1) (or nu approximately equal to 25 microHz) at larger distances. At small scales the magnetic helicity is positive at northern heliographic latitudes and negative at southern latitudes. The positive magnetic helicity at small scales is argued to be the result of turbulent diffusion reversing the sign relative to what is seen at small scales at the solar surface. Furthermore, the magnetic helicity declines toward solar minimum in 1996. The magnetic helicity flux integrated separately over one hemisphere amounts to about 10(sup 45) Mx(sup 2) cycle(sup -1) at large scales and to a three times lower value at smaller scales.

Brandenburg, Axel↗
NASA NTRS1992

Visualization of second order tensor fields and matrix data

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.

Delmarcelle, Thierry↗
NASA NTRS1996

[Two-phase Interfaces in Weak External Fields]

Our aim has been that of understanding from first principles the behavior of two-phase interfaces in the absence of gravitational constraints. This is fundamental to our ability to deal with the fluid structures that abound in the real biological, chemical, and physical world. A substantial effort was mounted to determine how familiar hydrodynamic concepts have to be modified and interpreted to make them appropriate to the multi-level structure alluded to above. This was primarily in the context of the microscopic symmetric pressure tensor, which was, for the first time, expressed in the invaluable density functional format, and the used to follow the predictions of popular microscopic models of the energetics of interfacial systems. In the course of these investigations, the previous murky relation between pressure tensor and thermodynamics was completely clarified. The process of extending thermodynamic information to interfacial dynamics was initiated along two paths. One was from the viewpoint of an inertialess lattice gas, resulting in the surprising conclusion that at this level, all transport is governed by precisely the thermodynamic free energy, albeit with a non-trivial effective particle mobility. The other aimed at understanding the fashion in which slow macroscopic motions, accounted for by a time-varying microscopic energy, generate effective hydrodynamic parameters. By examining a solvable model system, it was found that all current procedures for doing so are deficient, and suitable alleviation suggested. The major effect of this project was to set the stage for the analysis of the substantial dynamical regimes in which extensive equilibrium information provides the dominant background. This produces a smooth junction to the models of Araki and Munakata, Giacomin and Lebowitz, and Oxtoby. It is also crucial to our understanding of the complex interfacial equilibrium configurations required for intermediate stages of two-phase separation, for which the "phase-field" techniques we have been developing are uniquely effective. And it puts us within striking range of the physical experiments that can provide incisive tests of the theoretical framework.

Percus, J. K.↗
NASA NTRS1995

Visualization of 2-D and 3-D Tensor Fields

In previous work we have developed a novel approach to visualizing second order symmetric 2-D tensor fields based on degenerate point analysis. At degenerate points the eigenvalues are either zero or equal to each other, and the hyperstreamlines about these points give rise to trisector or wedge points. These singularities and their connecting hyperstreamlines determine the topology of the tensor field. In this study we are developing new methods for analyzing and displaying 3-D tensor fields. This problem is considerably more difficult than the 2-D one, as the richness of the data set is much larger. Here we report on our progress and a novel method to find, analyze and display 3-D degenerate points. First we discuss the theory, then an application involving a 3-D tensor field, the Boussinesq problem with two forces.

Hesselink, Lambertus↗
NASA NTRS1997

Visualization of 2-D and 3-D Tensor Fields

In previous work we have developed a novel approach to visualizing second order symmetric 2-D tensor fields based on degenerate point analysis. At degenerate points the eigenvalues are either zero or equal to each other, and the hyper-streamlines about these points give rise to tri-sector or wedge points. These singularities and their connecting hyper-streamlines determine the topology of the tensor field. In this study we are developing new methods for analyzing and displaying 3-D tensor fields. This problem is considerably more difficult than the 2-D one, as the richness of the data set is much larger. Here we report on our progress and a novel method to find , analyze and display 3-D degenerate points. First we discuss the theory, then an application involving a 3-D tensor field, the Boussinesq problem with two forces.

Hesselink, Lambertus↗