Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “MATRICES”

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

Stochastically estimated covariance matrices for independent and cumulative fission yields in the ENDF/B-VIII.0 and JEFF-3.3 evaluations

A Monte-Carlo method for the generation of correlation and covariance matrices for independent and cumulative fission yields has been developed. The method uses a constrained Monte-Carlo resampling structure in order to vary evaluated fission yield libraries in a way that meets basic conservation principles. This results in the generation of correlation/covariance matrices with limited model bias and uncertainty; the matrices are primarily reflective of the evaluated fission yield uncertainties and correlations that arise from the evaluation process. This method has been applied to generate correlation and covariance matrices for all of the fissioning systems of the ENDF/B-VIII.0 and JEFF-3.3 evaluations, marking the first time such matrices have been generated for all of these systems. These covariance matrices have been published online for immediate public use. These correlation and covariance matrices can be used to improve uncertainty estimation in calculations of reactor antineutrino emission rates, decay heat problems, and nuclear forensics.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

Fast truncated SVD of sparse and dense matrices on graphics processors

We investigate the solution of low-rank matrix approximation problems using the truncated singular value decomposition (SVD). For this purpose, we develop and optimize graphics processing unit (GPU) implementations for the randomized SVD and a blocked variant of the Lanczos approach. Our work takes advantage of the fact that the two methods are composed of very similar linear algebra building blocks, which can be assembled using numerical kernels from existing high-performance linear algebra libraries. Furthermore, the experiments with several sparse matrices arising in representative real-world applications and synthetic dense test matrices reveal a performance advantage of the block Lanczos algorithm when targeting the same approximation accuracy.

Computer Science↗
NASA NTRS1991

The asymptotic spectra of banded Toeplitz and quasi-Toeplitz matrices

Toeplitz matrices occur in many mathematical, as well as, scientific and engineering investigations. This paper considers the spectra of banded Toeplitz and quasi-Toeplitz matrices with emphasis on non-normal matrices of arbitrarily large order and relatively small bandwidth. These are the type of matrices that appear in the investigation of stability and convergence of difference approximations to partial differential equations. Quasi-Toeplitz matrices are the result of non-Dirichlet boundary conditions for the difference approximations. The eigenvalue problem for a banded Toeplitz or quasi-Toeplitz matrix of large order is, in general, analytically intractable and (for non-normal matrices) numerically unreliable. An asymptotic (matrix order approaches infinity) approach partitions the eigenvalue analysis of a quasi-Toeplitz matrix into two parts, namely the analysis for the boundary condition independent spectrum and the analysis for the boundary condition dependent spectrum. The boundary condition independent spectrum is the same as the pure Toeplitz matrix spectrum. Algorithms for computing both parts of the spectrum are presented. Examples are used to demonstrate the utility of the algorithms, to present some interesting spectra, and to point out some of the numerical difficulties encountered when conventional matrix eigenvalue routines are employed for non-normal matrices of large order. The analysis for the Toeplitz spectrum also leads to a diagonal similarity transformation that improves conventional numerical eigenvalue computations. Finally, the algorithm for the asymptotic spectrum is extended to the Toeplitz generalized eigenvalue problem which occurs, for example, in the stability of Pade type difference approximations to differential equations.

Beam, Richard M.↗
DOE OSTI2024

Symmetry-Based Structured Matrices for Efficient Approximately Equivariant Networks

There has been much recent interest in designing symmetry-aware neural networks (NNs) exhibiting relaxed equivariance. Such NNs aim to interpolate between being exactly equivariant and being fully flexible, affording consistent performance benefits. In a separate line of work, certain structured parameter matrices -- those with displacement structure, characterized by low displacement rank (LDR) -- have been used to design small-footprint NNs. Displacement structure enables fast function and gradient evaluation, but permits accurate approximations via compression primarily to classical convolutional neural networks (CNNs). In this work, we propose a general framework -- based on a novel construction of symmetry-based structured matrices -- to build approximately equivariant NNs with significantly reduced parameter counts. Our framework integrates the two aforementioned lines of work via the use of so-called Group Matrices (GMs), a forgotten precursor to the modern notion of regular representations of finite groups. GMs allow the design of structured matrices -- resembling LDR matrices -- which generalize the linear operations of a classical CNN from cyclic groups to general finite groups and their homogeneous spaces. We show that GMs can be employed to extend all the elementary operations of CNNs to general discrete groups. Further, the theory of structured matrices based on GMs provides a generalization of LDR theory focussed on matrices with cyclic structure, providing a tool for implementing approximate equivariance for discrete groups. We test GM-based architectures on a variety of tasks in the presence of relaxed symmetry. We report that our framework consistently performs competitively compared to approximately equivariant NNs, and other structured matrix-based compression frameworks, sometimes with a one or two orders of magnitude lower parameter count.

Samudre, Ashwin↗
DOE OSTI2020

Measuring Intelligence with the Sandia Matrices: Psychometric Review and Recommendations for Free Raven-Like Item Sets

The Sandia Matrices are a free alternative to the Raven’s Progressive Matrices (RPMs). This study offers a psychometric review of Sandia Matrices items focused on two of the most commonly investigated issues regarding the RPMs: (a) dimensionality and (b) sex differences. Model-data fit of three alternative factor structures are compared using confirmatory multidimensional item response theory (IRT) analyses, and measurement equivalence analyses are conducted to evaluate potential sex bias. Although results are somewhat inconclusive regarding factor structure, results do not show evidence of bias or mean differences by sex. Finally, although the Sandia Matrices software can generate infinite items, editing and validating items may be infeasible for many researchers. Further, to aide implementation of the Sandia Matrices, we provide scoring materials for two brief static tests and a computer adaptive test. Implications and suggestions for future research using the Sandia Matrices are discussed.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2022

Raw tensiometer soil matric potential data, from Oct 2017-Jun 2020 in Manaus, Brazil

This data package contains raw output from two Campbell Scientific CR1000 data loggers each connected to three UMS T4e tensiometer sensors in Manaus, Brazil. Tensiometers at each data logger location were installed to depths of 10 cm, 20 cm and 50 cm below the ground surface for the purpose of measuring soil matric potential at each depth. “Station 3” tensiometers were installed at approximately 2°36'31.68"S, 60°12'34.70"W. “Station 4” tensiometers were installed at approximately 2°36'32.46"S, 60°12'34.92"W. The files “tensio3.edit.202109.csv” and “tensio4.edit.202109.csv” contain raw data (with invalid data removed). A text editor will be required to view the raw files in .csv (comma-separated values) format. Data processing was limited to: 1) Editing column headers for clarity; 2) Applying a correction that converts voltage read by the data loggers to pressure units (kPa); 3) removing all data greater than 50 kPa and less than -115 kPa; 4) Adding columns entitled “Caution.10cm”, “Caution.20cm” and “Caution.50cm” that contains values of either “NA” or “Caution”, the latter of which is applied when data exceeds the manufacturer reported data validity range of less than -85 kPa to suggest use of these data with caution; 5) Adding columns entitled “Invalid.10cm”, “Invalid.20cm”, and “Invalid.50cm” that contains values of either “NA” or “Invalid”, the latter of which is applied when data accuracy is deemed compromised due to the introduction of air bubbles into the instrument. Data marked “Invalid” may still indicate general trends of wet/high matric potential and dry/low matric potential, but values are inaccurate and dry/low matric potential values are likely not low enough. Wet/high matric potential values are likely to be more accurate than dry/low matric potential values; 6) Data format changed from .dat to .csv. This research was performed as a part of the NGEE Tropics project, which aims to advance model predictions of tropical forest carbon cycle responses to a changing climate over the 21st Century.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS2019

Development and Characterization of Hot-Pressed Matrices for Engineered Ceramic Matrix Composites (E-CMCs)

The present research effort was undertaken to develop a new generation of SiC fiber-reinforced engineered ceramic matrix composites (E-CMCs). In contrast to traditional CMCs with a brittle SiC matrix, an E-CMC is designed to consist of a matrix engineered to possess sufficient high temperature plasticity to minimize crack propagation, relatively high fracture toughness, and self-healing capabilities to prevent oxygen ingress to the BN-coated fibers through surface-connected cracks. The present paper discusses the bend strength, isothermal oxidation, microstructures and self-healing properties of several silicide-behaved engineered matrices. Based on the oxidation tests, where it was observed that some of the matrices exhibited either catastrophic oxidation ("pesting") or spalling of the oxide scale, two engineered matrices, CrSi2/SiC/Si3N4 and CrMoSi/SiC/Si3N4, were down-selected for further investigation. Four-point bend tests were conducted on these two engineered matrices between room temperature and 1698 degrees Kelvin. Although these matrices were brittle at low temperatures, it was observed that the bend strengths and bend ductility increased at high temperatures as the silicide particles became more ductile, which was qualitatively consistent with the theoretically expected behavior that crack blunting at these particles should increase the matrix strength. Additional studies were conducted to study the effects of different additives on the self-healing properties of the engineered matrices, which helped to identify the most effective additives.

Composite Materials↗
DOE OSTI2021

Selective penetration behavior of microgels in superpermeable channels and reservoir matrices

Gel treatment is an effective way to attack excessive water production in many mature oilfields around the world. Selective penetration is desired for successful gel treatments. That is, gel materials should easily penetrate the target zones (i.e., channeling features such as superpermeable channels) without entering/damaging the nontarget zones (i.e., reservoir matrices or oil zones). This study revealed that presence of threshold penetration pressure (ΔP th ) was responsible for selective penetration behavior of tested microgels. The concept of ΔP th was utilized to figure out favorable working conditions for effective gel treatments. Microgel dispersions were injected into superpermeable (super-k) sandpacks (mimicking super-k channels in reservoirs, 60–221 darcies), heterogeneous models with super-k channels (79–230 darcies), and sandstone cores (mimicking reservoir matrices, 50–5000 md). The results demonstrated that a minimum differential driving pressure (i.e., threshold penetration pressure, ΔP th ) was required to push microgel particles to penetrate channels or matrices. The critical penetration behavior was closely related to the particle/pore size ratio. Low ΔP th at smaller particle/pore ratios was beneficial to allow easy penetration of gel materials into the channeling zones. On the contrary, high ΔPth at larger particle/pore ratios was desirable to prevent gel materials from massively invading and damaging the matrices. Instead, the gel particles accumulated at the inlet surface, and a gel cake was gradually formed. The cake further prevented the invasion of the gels. The cake could be removed by chemical breakers to resume the injectivity/productivity of the matrices. Correlations were developed to describe the relationship between ΔP th and particle/pore ratio. A distinct transition was identified at the particle/pore ratio of about 3. This research could help identify the favorable conditions to achieve successful gel treatments. In an effective conformance treatment, the particle/pore ratio in the channel should be sufficiently low to allow easy penetration of gel materials into the channel (e.g., particle/pore ratio<2 in this study). Meanwhile, the particle/pore ratio in the matrix should be large enough to support a high ΔP th and thus prevent massive gel invasion into the matrix. This study advances the current pore scale studies (a single particle passing through a single channel) to Darcy-scale characterization.

02 PETROLEUM↗
DOE OSTI2023

Generating accurate density matrices on the tangent space of a Grassmann manifold

Interpolating a density matrix from a set of known density matrices is not a trivial task. This is because a linear combination of density matrices does not necessarily correspond to another density matrix. In this Communication, density matrices are examined as objects of a Grassmann manifold. Although this manifold is not a vector space, its tangent space is a vector space. As a result, one can map the density matrices on this manifold to their corresponding vectors in the tangent space and then perform interpolations on that tangent space. The resulting interpolated vector can be mapped back to the Grassmann manifold, which can then be utilized (1) as an optimal initial guess for a self-consistent field (SCF) calculation or (2) to derive energy directly without time-consuming SCF iterations. Such a promising approach is denoted as Grassmann interpolation (G-Int). The hydrogen molecule has been used to illustrate that the described interpolated method in this work preserves the essential attributes of a density matrix. For phosphorus mononitride and ferrocene, it was demonstrated numerically that reference points for the definition of the corresponding tangent spaces can be chosen arbitrarily. In addition, the interpolated density matrices provide a superior and essentially converged initial guess for an SCF calculation to make the SCF procedure itself unnecessary. Finally, this accurate, efficient, robust, and systematically improved G-Int strategy has been used for the first time to generate highly accurate potential energy surfaces with fine details for the difficult case, ferrocene.

Chemistry↗
NASA NTRS1989

Efficient computer algebra algorithms for polynomial matrices in control design

The theory of polynomial matrices plays a key role in the design and analysis of multi-input multi-output control and communications systems using frequency domain methods. Examples include coprime factorizations of transfer functions, cannonical realizations from matrix fraction descriptions, and the transfer function design of feedback compensators. Typically, such problems abstract in a natural way to the need to solve systems of Diophantine equations or systems of linear equations over polynomials. These and other problems involving polynomial matrices can in turn be reduced to polynomial matrix triangularization procedures, a result which is not surprising given the importance of matrix triangularization techniques in numerical linear algebra. Matrices with entries from a field and Gaussian elimination play a fundamental role in understanding the triangularization process. In the case of polynomial matrices, matrices with entries from a ring for which Gaussian elimination is not defined and triangularization is accomplished by what is quite properly called Euclidean elimination. Unfortunately, the numerical stability and sensitivity issues which accompany floating point approaches to Euclidean elimination are not very well understood. New algorithms are presented which circumvent entirely such numerical issues through the use of exact, symbolic methods in computer algebra. The use of such error-free algorithms guarantees that the results are accurate to within the precision of the model data--the best that can be hoped for. Care must be taken in the design of such algorithms due to the phenomenon of intermediate expressions swell.

Baras, J. S.↗
DOE OSTI2022

On the effect of scalar flux weighing of linearly anisotropic scattering matrices in few-group transport calculations

The majority of the codes available for homogenized group constant generation for deterministic transport calculations apply the approximation of scalar flux weighting during energy group condensation of higher-order anisotropic scattering matrices. In this paper, we discuss the effect of scalar flux weighting of the linearly anisotropic scattering matrices in the frame of S P{sub 3} and S{sub 12} calculations performed for a two-dimensional VVER-440 reactor benchmark. To compare group constants generated for two neutron energy groups, an infinite pin cell was homogenized with Serpent 2 and ERANOS ECCO. Serpent 2 applies scalar flux, while ERANOS ECCO performs current weighting of the linearly anisotropic scattering matrices during energy group condensation. For analyzing the effect of the various weighting options, three simple reactor models were built assuming different core sizes using standard rectangular assemblies with 15*15 fuel pins. Diffusion, SP{sub 3} and S{sub 12} calculations were performed for the 3 models using group constants generated with Serpent 2 and ERANOS ECCO. The effect of scalar flux weighting of linearly anisotropic scattering matrices is shown by comparing the decrease in reactivity due to the decreased reactor size, as well as the assembly power distribution to reference results obtained with Serpent 2 Monte Carlo calculations. Neglecting higher than linearly anisotropic scattering and indirect application of diffusion coefficients in higher-order transport calculations is advised if angular flux-moment spectra weighted higher-order scattering matrices cannot be generated. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2024

What is the gradient of a scalar function defined on a subspace of square matrices?

We illustrate a technique to calculate the gradient of scalar functions that are defined on any arbitrary matrix subspace. It generalizes our earlier work titled “What is the gradient of a scalar function of a symmetric matrix ?”(Indian Journal of Pure and Applied Mathematics (2022), https://doi.org/10.1007/s13226-022-00313-x), in which we considered the special case of the subspace of symmetric matrices. Extant methods to calculate the gradient in such cases have an inherent flaw which leads to spurious results that populate several publications, as well as respected textbooks and handbooks on matrix calculus. Here, we examine these sources and results in a rigorous and concrete mathematical setting of a finite-dimensional inner-product space and discover the inherent flaw and also a remedy. We demonstrate two ways to calculate the derivative/gradient and second derivative for scalar functions of matrices defined over an arbitrary matrix subspace; the first method is by considering any (differentiable) extension to the space of square matrices and projection of its gradient onto the given subspace. The second method utilizes an ordered basis and computes each component of the gradient through evaluation of the directional derivative. All the ideas presented are illustrated by non-trivial examples, namely, considering the subspace of 3 x 3 circulant and Toeplitz matrices and presenting the results of gradient-descent with both the spurious and correct gradients. Moreover, our bibliography makes it clear that a rigorous approach to matrix calculus is not common in practice, and our presentation of matrix calculus in the language of inner-product spaces will be significant and meaningful for applied mathematicians, engineers and researchers working in inter-disciplinary fields to avoid the conceptual pitfalls that exist.

97 MATHEMATICS AND COMPUTING↗