Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “TENSOR FIELDS”

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 19 records
All sourcesNASA NTRSDOE OSTI
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↗
DOE OSTI2021

Systematic Generation of Moment Invariant Bases for 2D and 3D Tensor Fields

Moment invariants have been successfully applied to pattern detection tasks in 2D and 3D scalar, vector, and matrix valued data. However so far no flexible basis of invariants exists, i.e., no set that is optimal in the sense that it is complete and independent for every input pattern. Here, we prove that a basis of moment invariants can be generated that consists of tensor contractions of not more than two different moment tensors each under the conjecture of the set of all possible tensor contractions to be complete. This result allows us to derive the first generator algorithm that produces flexible bases of moment invariants with respect to orthogonal transformations by selecting a single non-zero moment to pair with all others in these two-factor products. Since at least one non-zero moment can be found in every non-zero pattern, this approach always generates a complete set of descriptors.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Non-compact gauge groups, tensor fields and Yang-Mills-Einstein amplitudes

Abstract Scattering amplitudes in Yang-Mills-Einstein theories have been investigated mostly for compact gauge groups. While non-compact gauge groups are not physically viable in Yang-Mills theory, non-compact gaugings feature prominently in the supergravity literature, where any choice of perturbative vacuum spontaneously breaks the gauge group to a compact subgroup. In this paper, we formulate double-copy constructions for several five-dimensional$$ \mathcal{N} $$ N = 2 supergravities with non-compact gauge groups. On one side of the double copy, we employ amplitudes from a super-Yang-Mills theory with a massive hypermultiplet. On the other, we use amplitudes from particular non-supersymmetric Yang-Mills-scalar theories with massive fermions, chosen to obey constraints coming from color/kinematics duality. Supergravities with massive self-dual tensors in five dimensions are also considered, showing that tensors are straightforwardly realized as double copies of gauge-theory fermions with suitable choices of signs in the corresponding solutions of the Dirac equation. We present several examples of these constructions, noting in particular the appearance of Heisenberg groups in the supergravity gauge symmetry and, in some cases, the possibility of exotic tensor-vector matter couplings.

Physics↗
DOE OSTI2024

Data-Efficient Dimensionality Reduction and Surrogate Modeling of High-Dimensional Stress Fields

Tensor datatypes representing field variables like stress, displacement, velocity, etc., have increasingly become a common occurrence in data-driven modeling and analysis of simulations. Numerous methods [such as convolutional neural networks (CNNs)] exist to address the meta-modeling of field data from simulations. As the complexity of the simulation increases, so does the cost of acquisition, leading to limited data scenarios. Modeling of tensor datatypes under limited data scenarios remains a hindrance for engineering applications. Here, in this article, we introduce a direct image-to-image modeling framework of convolutional autoencoders enhanced by information bottleneck loss function to tackle the tensor data types with limited data. The information bottleneck method penalizes the nuisance information in the latent space while maximizing relevant information making it robust for limited data scenarios. The entire neural network framework is further combined with robust hyperparameter optimization. We perform numerical studies to compare the predictive performance of the proposed method with a dimensionality reduction-based surrogate modeling framework on a representative linear elastic ellipsoidal void problem with uniaxial loading. The data structure focuses on the low-data regime (fewer than 100 data points) and includes the parameterized geometry of the ellipsoidal void as the input and the predicted stress field as the output. The results of the numerical studies show that the information bottleneck approach yields improved overall accuracy and more precise prediction of the extremes of the stress field. Additionally, an in-depth analysis is carried out to elucidate the information compression behavior of the proposed framework.

artificial intelligence↗
DOE OSTI2025

Synthetic tensor gauge fields

Synthetic gauge fields have provided physicists with a unique tool to explore a wide range of fundamentally important phenomena. However, most experiments have focused on synthetic vector gauge fields. The very rich physics brought about by coupling tensor gauge fields to fracton phases of matter remains unexplored in laboratories. Here, we propose schemes to realize synthetic tensor gauge fields that address dipoles instead of single particles. A lattice tilted by a strong linear potential and a weak quadratic potential yields a rank-2 electric field for a dipole formed by a particle-hole pair. Such a rank-2 electric field leads to a new type of Bloch oscillations, which modulates the quadrupole moment and preserves the dipole moment of the system. In higher dimensions, the interplay between interactions and vector gauge potentials imprints a phase to the ring-exchange interaction and thus generates synthetic tensor gauge fields. Such tensor gauge fields make it possible to realize a dipolar Harper-Hofstadter model in laboratories. The resultant dipolar Chern insulators feature chiral edge currents of dipoles in the absence of net charge currents. Published by the American Physical Society 2025

Zhang, Shaoliang (ORCID:000000016635044X)↗
DOE OSTI2024

Cosmological implications of Kalb-Ramond-like particles

The Kalb-Ramond field is an antisymmetric, rank-two tensor field which most notably appears in the context of string theory, but has largely been unexplored in the context of cosmology. In this work, motivated by the Kalb-Ramond field in string theory, and antisymmetric tensor fields that emerge in effective field theories ranging from particle physics to condensed matter, we study the primordial production of interacting massive Kalb-Ramond-like-particles (KRLPs). KRLPs contain features of both dark photon and axion models, which can be appreciated via their duality properties. While the massless non-interacting KRLP is dual to a pseudoscalar, and the massive non-interacting KRLP is dual to a pseudovector, the interacting massive KRLP can be distinguished from its scalar and vector counterparts. We study early-universe production of KRLPs via the freeze-in mechanism, considering a ‘dark photon-like’ interaction, an ‘axion-like’ interaction, and a ‘Higgs portal’ interaction, as well as production via cosmological gravitational particle production. We find that as a dark matter candidate, KRLPs can be produced by all of the above mechanisms and account for the relic density of dark matter today for a wide range of masses. Finally, we comment on the potential to obtain both warm and cold dark matter subcomponents, and speculate on observational and experimental prospects.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Machine learning of 27Al NMR electric field gradient tensors for crystalline structures from DFT

NMR crystallography has emerged as a promising technique for the determination and refinement of atomic coordinates in crystal structures. The crystal structure of compounds containing quadrupolar nuclei, such as 27Al, can be improved by directly comparing solid-state NMR measurements to DFT computations of the electric field gradient (EFG) tensor. The non-negligible computational cost of these first-principles calculations limits the applicability of this method to all but the most well-defined structures. We developed a fast, low-cost machine learning model to predict EFG parameters based on local structural motifs and elemental parameters. We computed 8081 EFG tensors from 1681 27Al crystalline solids using DFT and benchmarked them against 105 experimentally measured 27Al sites. Surprisingly, simple local geometric features dominate the predictive performance of the resulting random-forest model, yielding an R2 value of 0.98 and an RMSE of 0.61 MHz for CQ, the quadrupolar coupling constant. This model accuracy should enable pre-refining future structural assignments before finally validating with first-principles calculations. Such a catalogue of 27Al NMR tensors can serve as a tool for researchers assigning complex NMR spectra influenced by the nuclear electric quadrupole interaction.

Sun, He↗
DOE OSTI2020

Effect of Thomas Rotation on the Lorentz Transformation of Electromagnetic fields

A relativistic particle undergoing successive boosts which are non collinear will experience a rotation of its coordinate axes with respect to the boosted frame. This rotation of coordinate axes is caused by a relativistic phenomenon called Thomas Rotation. We assess the importance of Thomas rotation in the calculation of physical quantities like electromagnetic fields in the relativistic regime. We calculate the electromagnetic field tensor for general three dimensional successive boosts in the particle’s rest frame as well as the laboratory frame. We then compare the electromagnetic field tensors obtained by a direct boost β δβ → + → and successive boosts β → and Δβ → and check their consistency with Thomas rotation. This framework might be important to situations such as the calculation of frequency shifts for relativistic spin1/2 particles undergoing Larmor precession in electromagnetic fields with small field non-uniformities.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

cymyc: $\underline{C}$alabi-$\underline{Y}$au $\underline{M}$etrics, $\underline{Y}$ukawas, and $\underline{C}$urvature

We introduce cymyc, a high-performance Python library for numerical investigation of the geometry of a large class of string compactification manifolds and their associated moduli spaces. We develop a well-defined geometric ansatz to numerically model tensor fields of arbitrary degree on a large class of Calabi-Yau manifolds. cymyc includes a machine learning component which incorporates this ansatz to model tensor fields of interest on these spaces by finding an approximate solution to the system of partial differential equations they should satisfy.

differential and algebraic geometry↗
DOE OSTI2021

Traversable wormhole solution with a background Kalb–Ramond field

Highlights: • Wormhole solutions of gravity in a Lorentz breaking symmetry scenario are found. • Light deflection by the wormhole in a Lorentz breaking symmetry scenario is calculated. • It is shown the influence of the vacuum expectation value of a Kalb–Ramond field in deflection of light. We obtain a static spherically symmetric wormhole solution due to the vacuum expectation value (vev) of a Kalb–Ramond field. The Kalb–Ramond (vev) is a background tensor field which produces a local Lorentz symmetry breaking (LSB) of spacetime. Considering a non-minimal coupling between the Kalb–Ramond (vev) and the Ricci tensor, we found an exact traversable wormhole solution sustained by matter sources with a negative isotropic pressure. The matter source satisfies the energy conditions at the throat for particular choices of the LSB parameter. Moreover, we employ the Gauss–Bonnet method to analyze the deflection angle of light in the weak limit approximation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Automatic Calibration of a Geomechanical Model from Sparse Data for Estimating Stress in Deep Geological Formations

Summary In this study, we demonstrate geomechanical modeling with fully automatic parameter calibration to estimate the full geomechanical stress fields of a prospective US carbon dioxide (CO2) storage site, based on sparse measurement data. The goal is to compute full stress tensor field estimates (principal stresses and orientations) that are maximally compatible with observations within the constraints of the model assumptions, thereby extending pointwise, incomplete partial stress measurement to a simulated full formation stress field, as well as a rough assessment of the associated error. We use the Perch site, located in Otsego County, Michigan, USA, as our case study. The input data consist of partial stress tensor information inferred from in-situ borehole tests, geophysical well logs, and processing of seismic data. A static earth model (SEM) of the site was developed, and geomechanical simulation functionality of the open-source MATLAB Reservoir Simulation Toolbox (MRST) was used to model the stress field. Adjoint-based nonlinear optimization was used to adjust boundary conditions and material properties to calibrate simulated results of observations. Results were interpreted through a Bayesian framework. The focus of this paper is to demonstrate how the fully automatic calibration procedure works and discuss the results obtained; it does not attempt a detailed analysis of the stress field in the context of the proposed CO2 storage initiatives. Our work is part of a larger effort to noninvasively determine in-situ stresses in deep formations considered for CO2 storage. Guided by previously published research on geomechanical model calibration, our work presents a novel calibration approach supporting a potentially large number of linear or nonlinear calibration parameters to produce results optimally agreeing with available measurements and thus extend partial pointwise estimates to full tensor fields compatible with the physics of the site.

Engineering↗
DOE OSTI2023

Goldstone bosons and fluctuating hydrodynamics with dipole and momentum conservation

We develop a Schwinger-Keldysh effective field theory describing the hydrodynamics of a fluid with conserved charge and dipole moments, together with conserved momentum. The resulting hydrodynamic modes are highly unusual, including sound waves with quadratic (magnon-like) dispersion relation and subdiffusive decay rate. Hydrodynamics itself is unstable below four spatial dimensions. We show that the momentum density is, at leading order, the Goldstone boson for a dipole symmetry which appears spontaneously broken at finite charge density. Unlike an ordinary fluid, the presence or absence of energy conservation qualitatively changes the decay rates of the hydrodynamic modes. This effective field theory naturally couples to curved spacetime and background gauge fields; in the flat spacetime limit, we reproduce the “mixed rank tensor fields” previously coupled to fracton matter.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Strain fields in twisted bilayer graphene

Van der Waals heteroepitaxy allows deterministic control over lattice mismatch or azimuthal orientation between atomic layers to produce long-wavelength superlattices. The resulting electronic phases depend critically on the superlattice periodicity and localized structural deformations that introduce disorder and strain. In this study we used Bragg interferometry to capture atomic displacement fields in twisted bilayer graphene with twist angles < 2°. Nanoscale spatial fluctuations in twist angle and uniaxial heterostrain were statistically evaluated, revealing the prevalence of short-range disorder in moiré heterostructures. By quantitatively mapping strain tensor fields, we uncovered two regimes of structural relaxation and disentangled the electronic contributions of constituent rotation modes. Further, we found that applied heterostrain accumulates anisotropically in saddle-point regions, generating distinctive striped strain phases. Our results establish the reconstruction mechanics underpinning the twist-angle-dependent electronic behaviour of twisted bilayer graphene and provide a framework for directly visualizing structural relaxation, disorder and strain in moiré materials.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Black hole horizon edge partition functions

We extend a formula for 1-loop black hole determinants by Denef, Hartnoll, and Sachdev (DHS) to spinning fields on any (d + 1)-dimensional static spherically symmetric black hole. By carefully analyzing the regularity condition imposed on the Euclidean eigenfunctions, we reveal an unambiguous bulk-edge split in the 1-loop Euclidean partition function for tensor fields of arbitrary integer spin: the bulk part captures the “renormalized” thermal canonical partition function recently discussed in [1]; the edge part is related to quasinormal modes (QNMs) that fail to analytically continue to a subset of Euclidean modes with enhanced fall-offs near the origin. Since the edge part takes the form of a path integral on S d–1 , this suggests that these are associated with degrees of freedom living on the bifurcation surface in the Lorentzian two-sided black hole geometry. For massive higher spin on static BTZ and massive vector on Nariai black holes, we find that the edge partition function is related to the QNMs with lowest overtone numbers.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Stress inside the pion in holographic light-front QCD

In this work, we propose a method to compute the gravitational form factor D ( Q 2 ) in holographic QCD by exploiting the remarkable correspondence between semiclassical light-front QCD and semiclassical field theories in wrapped spacetime in five dimensions. The use of light-front holography bridges physics at large Q 2 as attained in light-front QCD and physics at small Q 2 where the coupling to scalar and tensor fields, e.g. glueballs, are dominant. As an application, we compute the D -term for the pion and compare the results with recent lattice simulations. Published by the American Physical Society 2024

Astronomy & Astrophysics↗