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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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All sourcesNASA NTRSDOE OSTI
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 NTRS2000

Initial OSSE Sky Survey Observation: Deep Survey in the Virgo Region

The OSSE Virgo survey covered about 1% of the sky, using eight weeks of observing time on the Compton Gamma Ray Observatory, and was performed in conjunction with the EGRET and COMPTEL instruments on CGRO. A fundamental aspect of the survey was the development of data reduction techniques for the scanning data from the OSSE detectors. A direct algebraic approach for spatially deconvolving the data was developed. For the survey work, no background observations isolated from the survey region were acquired, unlike normal discrete source observations. The survey, reduction method covers the mapped region with a grid of pixels, and estimates the flux from each pixel by least-squares agreement with the data, assuming positivity constraints. This technique has led to the detection of compact sources at hard X-ray energies within the Virgo region, and the OSSE survey studies have been extended to the south galactic pole and north Ecliptic pole, with similar analysis techniques.

Cameron, Robert↗
NASA NTRS2005

Geometric analysis of Arabidopsis root apex reveals a new aspect of the ethylene signal transduction pathway in development

Structurally, ethylene is the simplest phytohormone and regulates multiple aspects of plant growth and development. Its effects are mediated by a signal transduction cascade involving receptors, MAP kinases and transcription factors. Many morphological effects of ethylene in plant development, including root size, have been previously described. In this article a combined geometric and algebraic approach has been used to analyse the shape and the curvature in the root apex of Arabidopsis seedlings. The process requires the fitting of Bezier curves that reproduce the root apex shape, and the calculation of the corresponding curvatures. The application of the method has allowed us to identify significant differences in the root curvatures of ethylene insensitive mutants (ein2-1 and etr1-1) with respect to the wild-type Columbia.

Arabidopsis/genetics/growth & development↗
DOE OSTI2026

APSO-enhanced algebraic derivative estimation approach for real-time traffic flow prediction on critical road sections during wildfire evacuation

In rapid-onset disaster scenarios such as wildfires, evacuation traffic often significantly deviates from historical patterns, rendering conventional data-driven forecasting methods less effective. To address this challenge, we propose an improved algebraic derivative estimation (ADE) incorporating particle swarm optimization (PSO) for real-time traffic flow prediction. Our approach dynamically adjusts the ADE prediction time window at each step by minimizing a cost function based on the mean and variance of accumulated forecasting errors within the window, thereby balancing bias and variability. We evaluate the method using traffic data from the January 2025 California wildfires, focusing on key road segments critical for large-scale evacuations. The results demonstrate that our approach surpasses established machine learning and deep learning models—XGBoost, LSTM, and GRU—in predictive accuracy and maintains high computational efficiency. Notably, the proposed method eliminates the need for offline model training. Moreover, rapid PSO-based tuning enables real-time deployment, which provides a crucial advantage in scenarios where evacuation timings and road closures change dynamically. In conclusion, these findings highlight the benefits of the PSO-enhanced ADE framework for emergency traffic management, where rapid, data-sparse forecasts are essential for effective evacuation planning.

Algebraic derivative estimation↗
DOE OSTI2020

Battery models, systems, and methods using robust fail-safe iteration free approach for solving differential algebraic equations

Battery models using robust fail-safe iteration free approach for solving Differential Algebraic Equations, and associated systems and methods are disclosed. In one embodiment, a method includes generating a model of the rechargeable battery; determining one or more initial conditions for one or more algebraic variables of the model using a solver; holding differential variables of the model static by a switch function while determining the one or more initial conditions; applying the initial conditions to the model by the switch function; and determining one or more parameters for the rechargeable battery by solving the algebraic and differential equations.

25 ENERGY STORAGE↗
NASA NTRS1990

Extensions of algebraic image operators: An approach to model-based vision

Researchers extend their previous research on a highly structured and compact algebraic representation of grey-level images which can be viewed as fuzzy sets. Addition and multiplication are defined for the set of all grey-level images, which can then be described as polynomials of two variables. Utilizing this new algebraic structure, researchers devised an innovative, efficient edge detection scheme. An accurate method for deriving gradient component information from this edge detector is presented. Based upon this new edge detection system researchers developed a robust method for linear feature extraction by combining the techniques of a Hough transform and a line follower. The major advantage of this feature extractor is its general, object-independent nature. Target attributes, such as line segment lengths, intersections, angles of intersection, and endpoints are derived by the feature extraction algorithm and employed during model matching. The algebraic operators are global operations which are easily reconfigured to operate on any size or shape region. This provides a natural platform from which to pursue dynamic scene analysis. A method for optimizing the linear feature extractor which capitalizes on the spatially reconfiguration nature of the edge detector/gradient component operator is discussed.

Lerner, Bao-Ting↗
NASA NTRS1994

Algorithm For Control Of Underactuated Manipulators

Algorithm for improved control of underactuated multiple-link robotic manipulators developed via spatial-algebra-operator approach. Aspects of this approach described in several previous articles in NASA Tech Briefs-most recently "Robot Control Based on Spatial-Operator Algebra" (NPO-17918). Underactuated manipulator has fewer actuators than it has degrees of freedom. Complexity of underactuated systems managed by unified analysis. It has implications for fault-tolerant control, and many practical manipulators underactuated. Examples include manipulators with flexible joints and/or flexible links; space/underwater robots; manipulators that operate with some actuators that turned off because of failure or because of need to conserve energy; manipulators that grasp objects loosely, and manipulators that grasp objects with internal degrees of freedom (e.g., plungers, rollers).

Jain, Abhinandan↗
DOE OSTI2024

U(1) fields from qubits: An approach via D-theory algebra

A new quantum link microstructure was proposed for the lattice quantum chromodynamics (QCD) Hamiltonian, replacing the Wilson gauge links with a bilinear of fermionic qubits, later generalized to D-theory. This formalism provides a general framework for building lattice field theory algorithms for quantum computing. We focus mostly on the simplest case of a quantum rotor for a single compact U(1) field. We also make some progress for non-Abelian setups, making it clear that the ideas developed in the U(1) case extend to other groups. These in turn are building blocks for 1 + 0 -dimensional ( 1 + 0 -D) matrix models, 1 + 1 -D sigma models and non-Abelian gauge theories in 2 + 1 and 3 + 1 dimensions. By introducing multiple flavors for the U(1) field, where the flavor symmetry is gauged, we can efficiently approach the infinite-dimensional Hilbert space of the quantum O(2) rotor with increasing flavors. The emphasis of the method is on preserving the symplectic algebra exchanging fermionic qubits by sigma matrices (or hard bosons) and developing a formal strategy capable of generalization to a SU ( 3 ) field for lattice QCD and other non-Abelian 1 + 1 -D sigma models or 3 + 1 -D gauge theories. For U(1), we discuss briefly the qubit algorithms for the study of the discrete 1 + 1 -D sine-Gordon equation. Published by the American Physical Society 2024

Astronomy & Astrophysics↗
NASA NTRS1991

Linearizing feedforward/feedback attitude control

An approach to attitude control theory is introduced in which a linear form is postulated for the closed-loop rotation error dynamics, then the exact control law required to realize it is derived. The nonminimal (four-component) quaternion form is used to attitude because it is globally nonsingular, but the minimal (three-component) quaternion form is used for attitude error because it has no nonlinear constraints to prevent the rotational error dynamics from being linearized, and the definition of the attitude error is based on quaternion algebra. This approach produces an attitude control law that linearizes the closed-loop rotational error dynamics exactly, without any attitude singularities, even if the control errors become large.

Paielli, Russell A.↗
DOE OSTI2024

Robust 3D multi-material hydrodynamics using discontinuous Galerkin methods

A high-order discontinuous Galerkin (DG) method is presented for nonequilibrium multi-material (m ≥ 2) flow with sharp interfaces. Material interfaces are reconstructed using the algebraic THINC approach, resulting in a sharp interface resolution. The system assumes stiff velocity relaxation and pressure nonequilibrium. The presented DG method uses Dubiner's orthogonal basis functions on tetrahedral elements. This results in a unique combination of sharp multimaterial interfaces and high-order accurate solutions in smooth single-material regions. A novel shock indicator based on the interface conservation condition is introduced to mark regions with discontinuities. Slope limiting techniques are applied only in these regions so that nonphysical oscillations are eliminated while maintaining high-order accuracy in smooth regions. A local projection is applied on the limited solution to ensure discrete closure law preservation. The effectiveness of this novel limiting strategy is demonstrated for complex three-dimensional multi-material problems, where robustness of the method is critical. The presented numerical problems demonstrate that more accurate and efficient multi-material solutions can be obtained by the DG method, as compared to second-order finite volume methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

EXAGRAPH: Graph and combinatorial methods for enabling exascale applications

Combinatorial algorithms in general and graph algorithms in particular play a critical enabling role in numerous scientific applications. However, the irregular memory access nature of these algorithms makes them one of the hardest algorithmic kernels to implement on parallel systems. With tens of billions of hardware threads and deep memory hierarchies, the exascale computing systems in particular pose extreme challenges in scaling graph algorithms. The codesign center on combinatorial algorithms, ExaGraph, was established to design and develop methods and techniques for efficient implementation of key combinatorial (graph) algorithms chosen from a diverse set of exascale applications. Algebraic and combinatorial methods have a complementary role in the advancement of computational science and engineering, including playing an enabling role on each other. In this paper, we survey the algorithmic and software development activities performed under the auspices of ExaGraph from both a combinatorial and an algebraic perspective. In particular, we detail our recent efforts in porting the algorithms to manycore accelerator (GPU) architectures. We also provide a brief survey of the applications that have benefited from the scalable implementations of different combinatorial algorithms to enable scientific discovery at scale. We believe that several applications will benefit from the algorithmic and software tools developed by the ExaGraph team.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1980

Finite difference grid generation by multivariate blending function interpolation

The General Interpolants Method (GIM) code which solves the multidimensional Navier-Stokes equations for arbitrary geometric domains is described. The geometry module in the GIM code generates two and three dimensional grids over specified flow regimes, establishes boundary condition information and computes finite difference analogs for use in the GIM code numerical solution module. The technique can be classified as an algebraic equation approach. The geometry package uses multivariate blending function interpolation of vector-values functions which define the shapes of the edges and surfaces bounding the flow domain. By employing blending functions which conform to the cardinality conditions the flow domain may be mapped onto a unit square (2-D) or unit cube (3-D), thus producing an intrinsic coordinate system for the region of interest. The intrinsic coordinate system facilitates grid spacing control to allow for optimum distribution of nodes in the flow domain.

Anderson, P. G.↗
NASA NTRS1984

Conduct of the International Multigrid Conference

The 1983 International Multigrid Conference was held at Colorado's Copper Mountain Ski Resort, April 5-8. It was organized jointly by the Institute for Computational Studies at Colorado State University, U.S.A., and the Gasellschaft fur Mathematik und Datenverarbeitung Bonn, F.R. Germany, and was sponsored by the Air Force Office of Sponsored Research and National Aeronautics and Space Administration Headquarters. The conference was attended by 80 scientists, divided by institution almost equally into private industry, research laboratories, and academia. Fifteen attendees came from countries other than the U.S.A. In addition to the fruitful discussions, the most significant factor of the conference was of course the lectures. The lecturers include most of the leaders in the field of multigrid research. The program offered a nice integrated blend of theory, numerical studies, basic research, and applications. Some of the new areas of research that have surfaced since the Koln-Porz conference include: the algebraic multigrid approach; multigrid treatment of Euler equations for inviscid fluid flow problems; 3-D problems; and the application of MG methods on vector and parallel computers.

Mccormick, S.↗
NASA NTRS1991

A rocket tomography measurement of the N2(+) 3914 A emission rates within an auroral arc

A rocket tomography experiment designed to measure the two-dimensional distribution of the N2(+) 3914 A volume emission rates within an auroral arc is described. A simple filter photometer on board a sounding rocket, which was launched during the ARIES auroral campaign, was used to measure the 3914 A aruoral brightnesses at elevation angles ranging from 0 to 360 deg in the plane of the rocket trajectory. The measured auroral brightnesses have been tomographically inverted to recover the local 3914 A volume emissioin rates as a function of both altitude and latitude within the arc. The tomographic inversion procedure, which is based upon a maximum probability algebraic reconstruction approach, is described, and the implications of the results for studies of auroral excitation processes are briefly discussed.

Mcdade, I. C.↗
NASA NTRS1992

Multiple symbol partially coherent detection of MPSK

It is shown that by using the known (or estimated) value of carrier tracking loop signal to noise ratio (SNR) in the decision metric, it is possible to improve the error probability performance of a partially coherent multiple phase-shift-keying (MPSK) system relative to that corresponding to the commonly used ideal coherent decision rule. Using a maximum-likeihood approach, an optimum decision metric is derived and shown to take the form of a weighted sum of the ideal coherent decision metric (i.e., correlation) and the noncoherent decision metric which is optimum for differential detection of MPSK. The performance of a receiver based on this optimum decision rule is derived and shown to provide continued improvement with increasing length of observation interval (data symbol sequence length). Unfortunately, increasing the observation length does not eliminate the error floor associated with the finite loop SNR. Nevertheless, in the limit of infinite observation length, the average error probability performance approaches the algebraic sum of the error floor and the performance of ideal coherent detection, i.e., at any error probability above the error floor, there is no degradation due to the partial coherence. It is shown that this limiting behavior is virtually achievable with practical size observation lengths. Furthermore, the performance is quite insensitive to mismatch between the estimate of loop SNR (e.g., obtained from measurement) fed to the decision metric and its true value. These results may be of use in low-cost Earth-orbiting or deep-space missions employing coded modulations.

Simon, M. K.↗