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Results for “adjacency tensor”

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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17 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Scalable Tensor Methods for Nonuniform Hypergraphs

While multilinear algebra appears natural for studying the multiway interactions modeled by hypergraphs, tensor methods for general hypergraphs have been stymied by theoretical and practical barriers. A recently proposed adjacency tensor is applicable to nonuniform hypergraphs, but is prohibitively costly to form and analyze in practice. We develop tensor times same vector (TTSV) algorithms for this tensor which improve complexity from $O(n^r)$ to a low-degree polynomial in $r$, where $n$ is the number of vertices and $r$ is the maximum hyperedge size. Our algorithms are implicit, avoiding formation of the order $r$ adjacency tensor. Here, we demonstrate the flexibility and utility of our approach in practice by developing tensor-based hypergraph centrality and clustering algorithms. We also show these tensor measures offer complementary information to analogous graph-reduction approaches on data, and are also able to detect higher-order structure that many existing matrix-based approaches provably cannot.

97 MATHEMATICS AND COMPUTING↗
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 OSTI2015

Confined-exotic-matter wormholes with no gluing effects—Imaging supermassive wormholes and black holes

We classify wormholes endowed with redshift effects and finite mass into three types. Type I wormholes have their radial pressure dying out faster, as one moves away from the throat, than any other component of the stress-energy and thus violate the least the local energy conditions. In type II (resp. III) wormholes the radial and transverse pressures are asymptotically proportional and die out faster (resp. slower) than the energy density. We introduce a novel and generalizable method for deriving, with no cutoff in the stress-energy or gluing, a class of each of the three wormhole types. We focus on type I wormholes and construct different asymptotically flat solutions with finite, upper- and lower-bounded, mass M. It is observed that the radial pressure is negative, and the null energy condition is violated, only inside a narrow layer, adjacent to the throat, of relative spacial extent ε. Reducing the relative size of the layer, without harming the condition of traversability, yields an inverse square law of ε versus M for supermassive wormholes. We show that the diameter of the shadow of this type I supermassive wormhole overlaps with that of the black hole candidate at the center of the Milky Way and that the recent derivation, using the up-to-date millimeter-wavelength very long baseline interferometry made in Astrophys. J. (795) (2014) 134 [\arXivid(1409.4690)], remains inconclusive. We show that redshift-free wormholes, with positive energy density, have one of their barotropic equations of state in the phantom regime (at least in the region adjacent to the throat), have their stress energy tensor traceless, and are anisotropic. They are all type III wormholes having their variable equations of state approaching 1 and −1 at spatial infinity. We also introduce a new approach for deriving new redshift-free wormholes.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Geothermal Fault Zone and Fluid Imaging through Joint Airborne ZTEM and Ground MT Data Inversion Analysis

This project has aimed to achieve detailed electrical resistivity resolution at geothermal reservoir scales by combining airborne natural electromagnetic (EM) field surveying (ZTEM) with ground magnetotelluric (MT) measurements to approximate an airborne MT geophysical method. MT alone is relatively expensive and may have permitting challenges in sensitive areas. Airborne ZTEM field data contains only the magnetic field, requires a background assumption, and has been limited to relatively high frequencies, thus suffering uniqueness problems. Based on proto-type 2D simulations, ZTEM ambiguities may be reduced through formal incorporation with possibly sparse ground MT soundings, which we pursued in full 3D for this project. The methodology was tested at the high-temperature Roosevelt Hot Springs geothermal system, Utah, which was considered advantageous given the near total exposure of crystalline reservoir rocks across the project area. ZTEM and ground MT survey data were acquired in 2017, subcontracted to outside parties with which we have worked in the past. These included 80 remote-referenced tensor MT soundings over the Mineral Mountains and adjacent Roosevelt Hot Spring producing geothermal system. These MT stations abut later coverage of a similar number of MT stations taken for the Utah FORGE project providing excellent total data aperture to re-solve structure beneath both project areas better than either set alone. The airborne ZTEM survey covered 704 line kilometers in E-W flight lines with a 250 m line spacing. Although this survey was timed during a maintenance-related shutdown of power production at the Roosevelt Hot Springs, other noise sources difficult to identify but including two high-voltage state-scale transmission lines compromised the ZTEM survey badly leading to unusable responses. Thus, with DOE management concurrence, the project proceeded to emphasize inversion and interpretation of the joint SubTER-FORGE MT data sets with regard to the Roosevelt Hot Springs reservoir recharge and to deep heat sources for both it and the Utah FORGE EGS project area. We also investigated the joint ZTEM-MT sampling concept with data sets from the Eleven Mile Canyon prospect area donated by the U.S. Navy (A. Sabin, PoC). Inversion of the SubTER-FORGE MT data using the HexMT 3D finite element algorithm reveals a large, low-resistivity anomaly extending sub-vertically through the depth range of the crust beneath the western Mineral Mountains. The steep conductive zone connects in the lower crust to a more tabular conductor characteristic of much of the Great Basin that generally is ascribed to current mafic magmatic underplating, hybridization and fluid release. The location of the resolved anomaly relative to the recent (0.5-0.8 Ma) eruptive centers of the Mineral Mountains implicates it as remnants of the magma body which fed these centers. This structure appears to be currently feeding heat and fluids upward into the Roosevelt Hot Springs hydrothermal system, as well as heat laterally to the FORGE project area. Separate and joint inversion models were carried out for the donated Eleven Mile Canyon MT-ZTEM data set to demonstrate concept. ZTEM only inversion showed two main alteration zones in the western portion of the project area known from geological mapping. Joint inversion including an E-W profile of MT soundings sharpened these features considerably. It also resolved in much greater detail the graben related normal faulting structure of the central project area which lies at depths exceeding the sensitivity of ZTEM alone. The sparse number of MT da-ta relative to the ZTEM required upweighting the former by a factor of several, but an exact procedure awaits future research. Our final impression is that sparse MT data can improve resolution of the subsurface over that of ZTEM alone. However, well sampled MT data are to be preferred and offer the simplicity of interpreting just one data type, and possess the superior resolution capability coming with the electric field everywhere, and from their high bandwidth.

15 GEOTHERMAL ENERGY↗
DOE OSTI2019

Nonconforming Mesh Refinement for High-Order Finite Elements

In this study, we propose a general algorithm for nonconforming adaptive mesh refinement (AMR) of unstructured meshes in high-order finite element codes. Our focus is on $h$-refinement with a fixed polynomial order. The algorithm handles triangular, quadrilateral, hexahedral, and prismatic meshes of arbitrarily high-order curvature, for any order finite element space in the de Rham sequence. We present a flexible data structure for meshes with hanging nodes and a general procedure to construct the conforming interpolation operator, both in serial and in parallel. The algorithm and data structure allow anisotropic refinement of tensor product elements in two and three dimensions and support unlimited refinement ratios of adjacent elements. We report numerical experiments verifying the correctness of the algorithms and perform a parallel scaling study to show that we can adapt meshes containing billions of elements and run efficiently on 393,000 parallel tasks. Finally, we illustrate the integration of dynamic AMR into a high-order Lagrangian hydrodynamics solver.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

A Visual Understanding of Circular Dichroism Spectroscopy

Mapping chemical and structural properties to electronic and magnetic responses is critical to many applications such as quantum information science, where the precise storage and transmission of unique information is paramount. Specifically, constructing molecules and materials that provide strong polarized responses at tunable frequencies and with large anisotropies is key to optical processing of quantum information. Chiral molecules provide chiroptical response to circularly polarized light, making them attractive for quantum information science and other applications related to sensing, polarized photodetectors, and spintronics. Predicting a molecular design, a priori, with large anisotropies to circularly polarized light is challenging due to the complex interplay between electric and magnetic components of the optical response. In this work, we explore a visual representation of the electronic chiroptical response by decomposing the rotary strength into its constituent components. Here, we make use of the intuitive electronic oscillator framework to develop classical intuition regarding the rotary strength and its constituents. We explore three model chemical systems that exhibit local and global chirality. Our analysis reveals that local chirality necessarily exhibits competition between the local chiral center and chirality induced in other fragments of the molecule, resulting in both unexpected nonmonotonic trends and sign flips in chemically adjacent geometries. Furthermore, we can visually distinguish between local and global chirality via examination of the transition chiral tensor. Interestingly, we make strong connections to ferromagnetic and antiferromagnetic spin systems in that chiroptically inactive transitions exhibit antiferromagnetic-like alternating orbital patterns while active transitions show domain formation in an ferromagnetic-like alignment that produces a net chiroptical response.

36 MATERIALS SCIENCE↗
DOE OSTI2020

A High-Throughput Solver for Marginalized Graph Kernels on GPU

Here, we present the design and optimization of a solver for efficient and high-throughput computation of the marginalized graph kernel on General Purpose GPUs. The graph kernel is computed using the conjugate gradient method to solve a generalized Laplacian of the tensor product between a pair of graphs. To cope with the large gap between the instruction throughput and the memory bandwidth of the GPUs, our solver forms the graph tensor product on-the-fly without storing it in memory. This is achieved by using threads in a warp cooperatively to stream the adjacency and edge label matrices of individual graphs by small square matrix blocks called tiles, which are then staged in registers and the shared memory for later reuse. Warps across a thread block can further share tiles via the shared memory to increase data reuse. We exploit the sparsity of the graphs hierarchically by storing only non-empty tiles using a coordinate format and nonzero elements within each tile using bitmaps. We propose a new partition-based reordering algorithm for aggregating nonzero elements of the graphs into fewer but denser tiles to further exploit sparsity. We carry out extensive theoretical analyses on the graph tensor product primitives for tiles of various density and evaluate their performance on synthetic and real-world datasets. Our solver delivers three to four orders of magnitude speedup over existing CPU-based solvers such as GraKeL and GraphKernels. The capability of the solver enables kernel-based learning tasks at unprecedented scales.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Kinetic-scale flux rope reconnection in periodic and line-tied geometries

The collisionless reconnection of two parallel flux ropes driven by both the coalescence and kink instabilities is examined using fully kinetic simulations in periodic and line-tied geometries. The three-dimensional reconnection rate is computed from the maximum of the quasi-potential, Ξ≡−∫E·dℓ, where the integral of the electric field is taken along the magnetic field lines across the system. In periodic simulations in which the kink mode is nearly suppressed, reconnection is driven by the coalescence instability, and the peak rate is within 3%–8% of comparable 2D simulations. When a strong kink growth is observed, the peak reconnection rate drops by 10%–25%, and there is a larger drop for lower guide field. With line-tied boundary conditions, the kink instability plays a key role in allowing the flux ropes to interact and partially reconnect. In this limit, the field lines with maximum quasi-potential are associated with a quasi-separatrix layer, and the electric field along these special field lines is supported predominantly by the divergence of the electron pressure tensor. Both of these features, along with the observed reconnection rate, are consistent with recent laboratory experiments on kinetic-scale flux ropes. In kinetic simulations, the non-gyrotropic pressure tensor terms contribute significantly more to the reconnecting electric field than do the gyrotropic terms, while contributions from the electron inertia are significant for field lines adjacent to the quasi-separatrix layer.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Giant Modulation of Refractive Index from Picoscale Atomic Displacements

Abstract It is shown that structural disorder—in the form of anisotropic, picoscale atomic displacements—modulates the refractive index tensor and results in the giant optical anisotropy observed in BaTiS 3 , a quasi‐1D hexagonal chalcogenide. Single‐crystal X‐ray diffraction studies reveal the presence of antipolar displacements of Ti atoms within adjacent TiS 6 chains along the c ‐axis, and threefold degenerate Ti displacements in the a – b plane. 47/49 Ti solid‐state NMR provides additional evidence for those Ti displacements in the form of a three‐horned NMR lineshape resulting from a low symmetry local environment around Ti atoms. Scanning transmission electron microscopy is used to directly observe the globally disordered Ti a–b plane displacements and find them to be ordered locally over a few unit cells. First‐principles calculations show that the Ti a – b plane displacements selectively reduce the refractive index along the ab ‐plane, while having minimal impact on the refractive index along the chain direction, thus resulting in a giant enhancement in the optical anisotropy. By showing a strong connection between structural disorder with picoscale displacements and the optical response in BaTiS 3 , this study opens a pathway for designing optical materials with high refractive index and functionalities such as large optical anisotropy and nonlinearity.

36 MATERIALS SCIENCE↗
DOE OSTI2018

Continuity conditions for tensor product Q-Bézier surfaces of degree (m, n)

Based on a kind of Q-Bézier surfaces with shape parameters, the basic properties of the surfaces and the geometric significance of the shape parameters are analyzed. To resolve the problem of shape control and adjustment of composite surfaces, the continuity conditions for Q-Bézier surfaces of degree (m, n) are investigated. Taking advantage of the terminal properties of generalized Bernstein basis functions, we derive the conditions of G{sup 1} and G{sup 2} continuity between two adjacent Q-Bézier surfaces. In addition, the specific steps of smooth continuity between Q-Bézier surfaces and the shape adjustment function of shape parameters for composite surfaces are discussed. The modeling examples show that the proposed smooth continuity conditions are not only intuitive and easy to implement, but also greatly enhance the shape adjustability, which provide a useful method for constructing complex surfaces in engineering design.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Orientational Pair Correlations and Local Structure of Benzonitrile from Molecular Dynamics Simulations with Comparisons to Experiments [plus supplemental information]

Here, we present an experimentally parametrized molecular dynamics study of single-molecule and collective orientational relaxation in neat benzonitrile through the analysis of the reorientational anisotropy and polarizability anisotropy time-correlation function (PA-TCF). The simulations show that the PA-TCF is dominated by collective reorientation after 20 ps. Collective reorientation is found to be slower than single-molecule reorientation by a factor of 1.67, consistent with recent experiments. The simulations provide direct evidence of local antiparallel benzonitrile configurations. These structures, which have been the center of some debate, are responsible for the slower rate of collective vs. single-molecule reorientation in the liquid. Further structural analysis indicates that significant Coulombic interactions between the nitrile group and hydrogen atoms on adjacent molecules play a role in the formation of the antiparallel structures. The single-molecule dynamics reflected in the anisotropy are complex and consist of a ballistic regime, restricted angular diffusion, and spatially anisotropic free diffusion. The principal components of the rotational diffusion tensor are independently obtained and shown to reproduce the free diffusion regime of the anisotropy for each principal axis according to the predictions of a previous theory.

14 SOLAR ENERGY↗
DOE OSTI2022

Bootstrapping a stress-tensor form factor through eight loops

We bootstrap the three-point form factor of the chiral stress-tensor multiplet in planar $\mathcal{N}$ = 4 supersymmetric Yang-Mills theory at six, seven, and eight loops, using boundary data from the form factor operator product expansion. This may represent the highest perturbative order to which multi-variate quantities in a unitary four-dimensional quantum field theory have been computed. In computing this form factor, we observe and employ new restrictions on pairs and triples of adjacent letters in the symbol. We provide details about the function space required to describe the form factor through eight loops. Plotting the results on various lines provides striking numerical evidence for a finite radius of convergence of perturbation theory. By the principle of maximal transcendentality, our results are expected to give the highest weight part of the gg → Hg and H → ggg amplitudes in the heavy-top limit of QCD through eight loops. These results were also recently used to discover a new antipodal duality between this form factor and a six-point amplitude in the same theory.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2015

THE ARROWHEAD MINI-SUPERCLUSTER OF GALAXIES

Superclusters of galaxies can be defined kinematically from local evaluations of the velocity shear tensor. The location where the smallest eigenvalue of the shear is positive and maximal defines the center of a basin of attraction. Velocity and density fields are reconstructed with Wiener Filter techniques. Local velocities due to the density field in a restricted region can be separated from external tidal flows, permitting the identification of boundaries separating inward flows toward a basin of attraction and outward flows. This methodology was used to define the Laniakea Supercluster that includes the Milky Way. Large adjacent structures include Perseus–Pisces, Coma, Hercules, and Shapley but current kinematic data are insufficient to capture their full domains. However, there is a small region trapped between Laniakea, Perseus–Pisces, and Coma that is close enough to be reliably characterized and that satisfies the kinematic definition of a supercluster. Because of its shape, it is given the name the Arrowhead Supercluster. This entity does not contain any major clusters. A characteristic dimension is ∼25 Mpc and the contained mass is only ∼10{sup 15} M{sub ⊙}.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Estimation of micro-Hall-Petch coefficients for prismatic slip system in Mg-4Al as a function of grain boundary parameters

Grain size strengthening, referred to as the Hall-Petch effect, is a common strategy to improve the yield strength of magnesium (Mg) alloys. Several experimental studies have reported that the Hall-Petch slope strongly depends on the texture of the alloy. This effect arises from altering grain boundaries (GBs) resistance to different slip systems to transfer across adjacent grains. The grain boundary barrier strength of certain grain boundaries to basal slip, referred to as basal micro-Hall-Petch, was investigated in the previous work. Here in this study, the micro-Hall-Petch coefficient values for the prismatic slip $(k^{prismatic}_{μ})$ in Mg-4Al and their correlation with the grain boundary parameters were investigated. An experimental method was developed to initiate the prismatic slip band at low-stress levels. High-resolution electron backscatter diffraction (HR-EBSD) was used to measure the residual stress tensor, from which the resolved shear stress ahead of blocked prismatic slip bands was computed for seven different grain boundaries. $(k^{prismatic}_{μ})$ values for each individual GB were calculated by coupling the stress profile information with a continuum dislocation pile-up model. The $(k^{prismatic}_{μ})$ values vary from 0.138 MPa.m 1/2 to 0.685 MPa. m 1/2 which are almost three times larger than the calculated values for the basal micro-Hall-Petch. The $(k^{prismatic}_{μ})$ values were correlated with the GB parameters, and a functional relationship depending on the two most effective angles, the angle between the traces of the slip planes on the GB plane ($\phi$) and the angle between incoming and outgoing slip directions (κ), was proposed to estimate the Hall-Petch barrier for prismatic slip system. The work provides coefficients that can be supplied as input to crystal plasticity models to couple the effect of texture and grain size effectively.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Accelerating GNNs on GPU Sparse Tensor Cores through N:M Sparsity-Oriented Graph Reordering

Recent advancements in GPU hardware support have introduced the capability to leverage N:M sparse patterns for substantial performance gains. Graphs in Graph Neural Networks (GNNs) are typically sparse, but the sparsity is often irregular, not conforming to such sparse patterns. In this paper, we propose a novel graph reordering algorithm, the first of its kind, to reshape irregular graph data into the N:M structured sparse pattern at the tile level, allowing linear-algebra-based graph operations in GNNs to benefit from the N:M sparse hardware. The optimization is lossless, maintaining the accuracy of GNN. It can remove 98-100\% violations of the N:M sparse patterns at the vector level, and increase the proportion of conforming graphs in SuiteSparse collection from 5-9\% to 88.7-93.5\%. On A100 GPUs, the optimization accelerates Sparse Matrix Matrix (SpMM) by up to 43X (2.3X -- 7.5X on average) and speeds up the key graph operations in GNNs on real graphs by as much as 8.6X (3.5X on average).

artificial intelligence, graph neural networks↗
DOE OSTI2024

Opto-twistronic Hall effect in a three-dimensional spiral lattice

Studies of moire systems have elucidated the exquisite effect of quantum geometry on the electronic bands and their properties, leading to the discovery of new correlated phases. However, most experimental studies have been confined to a few layers in the 2D limit. The extension of twistronics to its 3D limit, where the twist is extended into the third dimension between adjacent layers, remains underexplored due to the challenges in precisely stacking layers. Here, in this study, we focus on 3D twistronics on a platform of self-assembled spiral superlattice of multilayered WS 2 . Our findings reveal an opto-twistronic Hall effect in the spiral superlattice. This mesoscopic response is an experimental manifestation of the noncommutative geometry that arises when translational symmetry is replaced by a non-symmorphic screw operation. We also discover signatures of altered laws of optical excitation, manifested as an unconventional photon momentum-lattice interaction owing to moire of moire modulations in the 3D twistronic system. Crucially, our findings mark the initial identification of higher-order quantum geometrical tensors in light-matter interactions. This breakthrough opens new avenues for designing quantum materials-based optical lattices with large nonlinearities, paving the way for the development of advanced quantum nanophotonic devices.

Ji, Zhurun↗
DOE OSTI2022

Reflection and transmission of electromagnetic pulses at a planar dielectric interface -- theory and quantum lattice simulations

There is considerable interest in the application of quantum information science to advance computations in plasma physics. A particular point of curiosity is whether it is possible to take advantage of quantum computers to speed up numerical simulations relative to conventional computers. Many of the topics in fusion plasma physics are classical in nature. In order to implement them on quantum computers it will require couching a classical problem in the language of quantum mechanics. Electromagnetic waves are routinely used in fusion experiments to heat a plasma or to generate currents in the plasma. The propagation of electromagnetic waves is described by Maxwell equations with an appropriate description of the plasma as a dielectric medium. Before advancing to the tensor dielectric of a magnetized plasma, this paper considers electromagnetic wave propagation in a one-dimensional inhomogeneous scalar dielectric. The classic theory of scattering of plane electromagnetic waves at a planar interface, separating two different dielectric media, leads to Fresnel equations for reflection and transmission coefficients. In contrast to plane waves, this paper is on the reflection and transmission of a spatially confined electromagnetic pulse. Following an analytical formulation for the scattering of a Gaussian pulse, it is deduced that the maximum transmission coefficient for a pulse is $\sqrt{n_2/n_1}$ times that for a plane wave; the incident and transmitted pulses propagating in dielectric media with refractive indices $n_1$ and $n_2$, respectively. The analytical theory is complemented by numerical simulations using a quantum lattice algorithm for Maxwell equations. The algorithm, based on the Riemann-Silberstein-Weber representation of the electromagnetic fields and expressed in term of qubits, is an interleaved sequence of entangling operators at each lattice site and unitary streaming operators which transmit information from one site to an adjacent lattice site. Besides substantiating results from the theory for Gaussian pulses, numerical simulations show their validity for non-Gaussian pulses. Apart from their time-asymptotic forms, the simulations display an interplay between the incident, reflected, and transmitted pulses in the vicinity of the transition region between two dielectric media.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗