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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 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
NASA NTRS1987

Edge detection - Image-plane versus digital processing

To optimize edge detection with the familiar Laplacian-of-Gaussian operator, it has become common to implement this operator with a large digital convolution mask followed by some interpolation of the processed data to determine the zero crossings that locate edges. It is generally recognized that this large mask causes substantial blurring of fine detail. It is shown that the spatial detail can be improved by a factor of about four with either the Wiener-Laplacian-of-Gaussian filter or an image-plane processor. The Wiener-Laplacian-of-Gaussian filter minimizes the image-gathering degradations if the scene statistics are at least approximately known and also serves as an interpolator to determine the desired zero crossings directly. The image-plane processor forms the Laplacian-of-Gaussian response by properly combining the optical design of the image-gathering system with a minimal three-by-three lateral-inhibitory processing mask. This approach, which is suggested by Marr's model of early processing in human vision, also reduces data processing by about two orders of magnitude and data transmission by up to an order of magnitude.

Huck, Friedrich O.↗
NASA NTRS1990

Partitioning sparse matrices with eigenvectors of graphs

The problem of computing a small vertex separator in a graph arises in the context of computing a good ordering for the parallel factorization of sparse, symmetric matrices. An algebraic approach for computing vertex separators is considered in this paper. It is shown that lower bounds on separator sizes can be obtained in terms of the eigenvalues of the Laplacian matrix associated with a graph. The Laplacian eigenvectors of grid graphs can be computed from Kronecker products involving the eigenvectors of path graphs, and these eigenvectors can be used to compute good separators in grid graphs. A heuristic algorithm is designed to compute a vertex separator in a general graph by first computing an edge separator in the graph from an eigenvector of the Laplacian matrix, and then using a maximum matching in a subgraph to compute the vertex separator. Results on the quality of the separators computed by the spectral algorithm are presented, and these are compared with separators obtained from other algorithms for computing separators. Finally, the time required to compute the Laplacian eigenvector is reported, and the accuracy with which the eigenvector must be computed to obtain good separators is considered. The spectral algorithm has the advantage that it can be implemented on a medium-size multiprocessor in a straightforward manner.

Pothen, Alex↗
NASA NTRS1993

A Spectral Algorithm for Envelope Reduction of Sparse Matrices

The problem of reordering a sparse symmetric matrix to reduce its envelope size is considered. A new spectral algorithm for computing an envelope-reducing reordering is obtained by associating a Laplacian matrix with the given matrix and then sorting the components of a specified eigenvector of the Laplacian. This Laplacian eigenvector solves a continuous relaxation of a discrete problem related to envelope minimization called the minimum 2-sum problem. The permutation vector computed by the spectral algorithm is a closest permutation vector to the specified Laplacian eigenvector. Numerical results show that the new reordering algorithm usually computes smaller envelope sizes than those obtained from the current standard algorithms such as Gibbs-Poole-Stockmeyer (GPS) or SPARSPAK reverse Cuthill-McKee (RCM), in some cases reducing the envelope by more than a factor of two.

Barnard, Stephen T.↗
DOE OSTI2025

Spectral Bounds on Hyperbolic 3-Manifolds: Associativity and the Trace Formula

We constrain the low-energy spectra of Laplace operators on closed hyperbolic manifolds and orbifolds in three dimensions, including the standard Laplace--Beltrami operator on functions and the Laplacian on powers of the cotangent bundle. Our approach employs linear programming techniques to derive rigorous bounds by leveraging two types of spectral identities. The first type, inspired by the conformal bootstrap, arises from the consistency of the spectral decomposition of the product of Laplace eigensections, and involves the Laplacian spectra as well as integrals of triple products of eigensections. We formulate these conditions in the language of representation theory of PSL 2 (C) and use them to prove upper bounds on the first and second Laplacian eigenvalues. The second type of spectral identities follows from the Selberg trace formula. We use them to find upper bounds on the spectral gap of the Laplace--Beltrami operator on hyperbolic 3-orbifolds, as well as on the systole length of hyperbolic 3-manifolds, as a function of the volume. Further, we prove that the spectral gap λ 1 of the Laplace--Beltrami operator on all closed hyperbolic 3-manifolds satisfies λ 1 < 47.32. Along the way, we use the trace formula to estimate the low-energy spectra of a large set of example orbifolds and compare them with our general bounds, finding that the bounds are nearly sharp in several cases.

Bonifacio, James [University of Mississippi, MS (U↗
NASA NTRS1995

An equivalent body surface charge model representing three-dimensional bioelectrical activity

A new surface-source model has been developed to account for the bioelectrical potential on the body surface. A single-layer surface-charge model on the body surface has been developed to equivalently represent bioelectrical sources inside the body. The boundary conditions on the body surface are discussed in relation to the surface-charge in a half-space conductive medium. The equivalent body surface-charge is shown to be proportional to the normal component of the electric field on the body surface just outside the body. The spatial resolution of the equivalent surface-charge distribution appears intermediate between those of the body surface potential distribution and the body surface Laplacian distribution. An analytic relationship between the equivalent surface-charge and the surface Laplacian of the potential was found for a half-space conductive medium. The effects of finite spatial sampling and noise on the reconstruction of the equivalent surface-charge were evaluated by computer simulations. It was found through computer simulations that the reconstruction of the equivalent body surface-charge from the body surface Laplacian distribution is very stable against noise and finite spatial sampling. The present results suggest that the equivalent body surface-charge model may provide an additional insight to our understanding of bioelectric phenomena.

NASA Discipline Regulatory Physiology↗
NASA NTRS2020

Dynamic Stability And Adaptive Control of Networked Evolving Formations with Weak Nonlinearities

The dynamic stability of formation geometry is vital to the design of large scale multiagent systems. In this paper, we probe into the structure of the formation system matrix using the Laplacian of a digraph to develop several fundamental theoretical results on the stability of formation geometry. Our key-results include the integration of the graph Laplacian into linear and weak-nonlinear relative dynamics, the development of several new coordinate transformations that expose the influence of the graph Laplacian matrix on the control laws of the agents, and the use of direct adaptive control as stability restoring devices. We also develop two fundamental results that provide upper bounds for stable formation evolution under nonlinear perturbations of agent dynamics. Finally, we use an illustrative example to demonstrate our theoretical findings.

Gehlot, Vinod P.↗
DOE OSTI2021

A Fast Solver for the Fractional Helmholtz Equation

The purpose of this paper is to study a Helmholtz problem with a spectral fractional Laplacian, instead of the standard Laplacian. Recently, it has been established that such a fractional Helmholtz problem better captures the underlying behavior in Geophysical Electromagnetics. In this work, we establish the well-posedness and regularity of this problem. We introduce a hybrid spectral-finite element approach to discretize it and show well-posedness of the discrete system. In addition, we derive a priori discretization error estimates. Finally, we introduce an efficient solver that scales aswell as the best possible solver for the classical integer-order Helmholtz equation. We conclude withseveral illustrative examples that confirm our theoretical findings.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

A matrix-free hyperviscosity formulation for high-order ALE hydrodynamics

The numerical approximation of compressible hydrodynamics is at the core of high-energy density (HED) multiphysics simulations as shocks are the driving force in experiments like inertial confinement fusion (ICF). In this work, we describe our extension of the hyperviscosity technique, originally developed for shock treatment in finite difference simulations, for use in arbitrarily high-order finite element methods for Lagrangian hydrodynamics. Hyperviscosity enables shock capturing while preserving the high-order properties of the underlying discretization away from the shock region. Specifically, we compute a high-order term based on a product of the mesh length scale to a high power scaled by a hyper-Laplacian operator applied to a scalar field. We then form the total artificial viscosity by taking a non-linear blend of this term and a traditional artificial viscosity term. We also present a matrix-free formulation for computing the finite element based hyper-Laplacian operator. Such matrix-free methods have superior performance characteristics compared to traditional full matrix assembly approaches and offer advantages for GPU based HPC hardware. We demonstrate the numerical convergence of our method and its application to complex, multi-material ALE simulations on high-order (curved) meshes.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Distributed and communication-efficient solutions to linear equations with special sparse structure

In this paper we report two distributed and communication-efficient algorithms based on the multi-agent system are proposed to solve a system of linear equations with the Laplacian sparse system matrix. One algorithm is based on the gradient descent method in optimization. In this algorithm, the agents only share partial information instead of all of their collective state vectors to save significant communication. The other algorithm is obtained by approximating Newton’s method for a faster convergence rate. Although it requires twice as much communication as the first one, it is still communication-efficient given the low dimension of the information shared among agents. The convergence at a linear rate is proved for both algorithms, and a comprehensive comparison of their convergence rate, communication burden, and computation costs is also performed. The proposed algorithms can be applied to various systems to solve those problems that can be modeled as a system of linear equations with a Laplacian sparse system matrix. Simulation results with the electric power system illustrate their effectiveness.

42 ENGINEERING↗
DOE OSTI2021

Oscillatory Spreading and Inertia in Power Grids

The increase in variable renewable generators (VRGs) in power systems has altered the dynamics from a historical experience. VRGs introduce new sources of power oscillations, and the stabilizing response provided by synchronous generators (SGs, e.g., natural gas, coal, etc.), which help avoid some power fluctuations, will lessen as VRGs replace SGs. These changes have led to the need for new methods and metrics to quickly assess the likely oscillatory behavior for a particular network without performing computationally expensive simulations. This work studies the impact of a critical dynamical parameter - the inertia value - on the rest of a power system's oscillatory response to representative VRG perturbations. We use a known localization metric in a novel way to quantify the number of nodes responding to a perturbation and the magnitude of those responses. This metric allows us to relate the spread and severity of a system's power oscillations with inertia. We find that as inertia increases, the system response to node perturbations transitions from localized (only a few close nodes respond) to delocalized (many nodes across the network respond). We introduce a heuristic computed from the network Laplacian to relate this oscillatory transition to the network structure. We show that our heuristic accurately describes the spread of oscillations for a realistic power-system test case. Using a heuristic to determine the likely oscillatory behavior of a system given a set of parameters has wide applicability in power systems, and it could decrease the computational workload of planning and operation.

dynamical systems↗
DOE OSTI2022

Spatially enhanced electric field induced second harmonic (SEEFISH) generation for measurements of electric field distributions in high-pressure plasmas

Abstract The spatial resolution of the ps electric field induced second harmonic (EFISH) generation has been enhanced by using non-collinear pump laser beam arrangements. The pump laser beam (1064 nm, nominal pulse duration 150 ps, pulse energy 20–40 mJ) is separated into two coaxial or crossing beams, overlapping only near the focal point. The spatially enhanced EFISH (SEEFISH) signal is generated over a shorter beam overlap region compared to the collinear beam arrangement. Blocking of either of the two beams results in a complete suppression of the signal. The signal is spatially isolated from the ‘conventional’ EFISH signal and measured by a photomultiplier detector. Measurements of a known Laplacian field generated between two parallel cylinder electrodes in ambient air shows that SEEFISH improves the spatial resolution of the measurements by up to a factor of 2, such that the measurement results agree with the Laplacian field distribution. The spatial resolution is improved further by reducing the focal distance of the lens. The magnitude of the SEEFISH signal is significantly lower compared to that of the single-beam EFISH and decreases rapidly as the beam crossing angle is increased, due to the phase mismatch. This approach has a significant potential for measurements of electric field distributions in high-pressure plasmas, with an additional benefit of removing the stray second harmonic signal from the optical access windows.

Physics↗
DOE OSTI2023

Gaps labeling theorem for the bubble-diamond self-similar graphs

Abstract Motivated by the appearance of fractals in several areas of physics, especially in solid state physics and the physics of aperiodic order, and in other sciences, including the quantum information theory, we present a detailed spectral analysis for a new class of fractal-type diamond graphs, referred to as bubble-diamond graphs, and provide a gap-labeling theorem in the sense of Bellissard for the corresponding probabilistic graph Laplacians using the technique of spectral decimation. Labeling the gaps in the Cantor set by the normalized eigenvalue counting function, also known as the integrated density of states, we describe the gap labels as orbits of a second dynamical system that reflects the branching parameter of the bubble construction and the decimation structure. The spectrum of the natural Laplacian on limit graphs is shown generically to be pure point supported on a Cantor set, though one particular graph has a mixture of pure point and singularly continuous components.

Physics↗
DOE OSTI2024

Automorphic spectra and the conformal bootstrap

We describe a new method for constraining Laplacian spectra of hyperbolic surfaces and 2-orbifolds. The main ingredient is consistency of the spectral decomposition of integrals of products of four automorphic forms. Using a combination of representation theory of PSL 2 (R) and semidefinite programming, the method yields rigorous upper bounds on the Laplacian spectral gap. In several examples, the bound is nearly sharp. For instance, our bound on all genus-2 surfaces is λ 1 ≤ 3.8388976481, while the Bolza surface has λ 1 ≈ 3.838887258. The bounds also allow us to determine the set of spectral gaps attained by all hyperbolic 2-orbifolds. Our methods can be generalized to higher-dimensional hyperbolic manifolds and to yield stronger bounds in the two-dimensional case. The ideas were closely inspired by modern conformal bootstrap.

Kravchuk, Petr↗
DOE OSTI2023

Gapped lineon and fracton models on graphs

We introduce a $\mathbb{Z}_N$ stabilizer code that can be defined on any spatial lattice of the form $\Gamma\times C_{L_z}$, where $\Gamma$ is a general graph. We also present the low-energy limit of this stabilizer code as a Euclidean lattice action, which we refer to as the anisotropic $\mathbb{Z}_N$ Laplacian model. It is gapped, robust (i.e., stable under small deformations), and has lineons. Its ground state degeneracy (GSD) is expressed in terms of a "mod $N$-reduction" of the Jacobian group of the graph $\Gamma$. In the special case when space is an $L\times L\times L_z$ cubic lattice, the logarithm of the GSD depends on $L$ in an erratic way and grows no faster than $O(L)$. Furthermore, we also discuss another gapped model, the $\mathbb{Z}_N$ Laplacian model, which can be defined on any graph. It has fractons and a similarly strange GSD.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Structural Impact of Grid-Forming Inverters on Power System Coherency

This paper addresses the following fundamental research question: how does the integration of grid-forming inverters (GFMs) replacing conventional synchronous generators (SGs) impact the slow coherent eigen-structure and the low frequency oscillatory behavior of future power systems? Due to time-scale separated dynamics, generator states inside a coherent area synchronize over a fast time-scale due to stronger coupling, while the areas themselves synchronize over a slower time scale. Our mathematical analysis shows that due to the large-scale integration of GFMs, the weighted Laplacian structure of the frequency dynamics is preserved, however, the entries of the Laplacian may be significantly modified based on the location and penetration levels of the GFMs. This can impact and potentially significantly alter the coherency structure of the system. We have validated our findings with numerical results using the IEEE 68-bus test system.

Mukherjee, Sayak [BATTELLE (PACIFIC NW LAB)]↗
DOE OSTI2023

Reduced-Order Models of Static Power Grids based on Spectral Clustering

For large-scale interconnected power systems that cover large geographical areas, certain electrical studies are required so that appropriate decisions ensure system reliability and low cost. For such studies, it is often neither practical nor necessary to model in detail the entire power system, which is increasingly complex due to a more diverse range of grid assets to choose from in both short and long-term planning. The goal of this paper is to present a methodology to reduce the order of large-scale power networks based on spectral graph theory given that current methods for static network reduction are not scalable. A brief analysis of some spectral clustering properties to determine which graph Laplacian matrix should be used and why is included. The analysis shows that the utilization of the normalized graph Laplacian is more advantageous for clustering purposes. Techniques are proposed to approximate cost functions for the aggregated generators. This is done via linear regression. The reduced-order model obtained with the proposed methodology has an accuracy above 94% and solves the scalability issue commonly present in other reduction methods. If the utilization of the reduced-order model is either constrained to load levels above mid-peak demand, or cost functions of aggregated units are approximated via a piecewise quadratic approach, then the error distribution is in the order of 10^-3. .

Baquedano-Aguilar, Mario D.↗
DOE OSTI2024

A Performance and Energy Study of GPU-Resident Preconditioners for Conjugate Gradient Solvers: In the Context of Existing and Novel Approaches

Optimizing a particular subprogram out of the set of Basic (sparse) Linear Algebra Subprograms (BLAS) for a given architecture is a common topic of research. In applications, however, these BLAS functions rarely appear in isolation; usually, many of them are used together, in various combinations and with varying inputs. As the need to solve a large, sparse linear system is ubiquitous throughout HPC applications, linear solvers constitute a realistic, sufficiently complex and well-defined representative use case for composite BLAS routines. To this end, based on a representative set of matrices drawn from a diverse set of fields, we present a framework to study, from the performance and energy perspective, the efficacy of GPU- resident parallel Conjugate Gradient (CG) linear solver with different preconditioner options, including Gauss-Seidel, Jacobi, and incomplete Cholesky. We also propose a novel GPU-based preconditioner, in which the triangular solves are approximated by an iterative process. The development of this preconditioner was motivated by solving large graph Laplacian linear systems, for which the existing preconditioners either perform slow on GPU-based platforms or are not applicable. We compare the performance of these preconditioners on different hardware accelerator architectures, i.e., AMD MI250X, MI100, Nvidia A100, V100, and Jetson. Our experiments reveal performance trade-offs and provide information on how to select the best strategy for the given linear system, dictated by its properties, and the platform of interest. We demonstrate the application of our novel preconditioner for solving CG and graph Laplacian systems. Overall, the framework can be utilized as a benchmark to guide informed decisions in choosing a specific preconditioner, i.e., whether it is better to rely on the performance of a triangular solver or on the performance of sparse matrix-vector product. Finally, by considering power consumption to solve the linear systems, we report the energy footprint for the solvers.

Preconditioned Conjugate Gradient, GPUs, iterative↗
DOE OSTI2023

Graph Sparsification by Approximate matrix Multiplication

Graphs arising in statistical problems, signal processing, large networks, combinatorial optimization, and data analysis are often dense, which causes both computational and storage bottlenecks. One way of sparsifying a weighted graph, while sharing the same vertices as the original graph but reducing the number of edges, is through spectral sparsification. We study this problem through the perspective of RandNLA. Specifically, we utilize randomized matrix multiplication to give a clean and simple analysis of how sampling according to edge weights gives a spectral approximation to graph Laplacians, without requiring spectral information. Through the CR–MM algorithm, we attain a simple and computationally efficient sparsifier whose resulting Laplacian estimate is unbiased and of minimum variance. Here, we define a new notion of additive spectral sparsifiers, which has not been considered in the literature.

97 MATHEMATICS AND COMPUTING↗