SEARCH · Engineering Papers

Results for “Matrix factorization”

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.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 775 records · Page 43

All sources NASA NTRS DOE OSTI

NASA NTRS1976

A numerical comparison of discrete Kalman filtering algorithms - An orbit determination case study

An improved Kalman filter algorithm based on a modified Givens matrix triangularization technique is proposed for solving a nonstationary discrete-time linear filtering problem. The proposed U-D covariance factorization filter uses orthogonal transformation technique; measurement and time updating of the U-D factors involve separate application of Gentleman's fast square-root-free Givens rotations. Numerical stability and accuracy of the algorithm are compared with those of the conventional and stabilized Kalman filters and the Potter-Schmidt square-root filter, by applying these techniques to a realistic planetary navigation problem (orbit determination for the Saturn approach phase of the Mariner Jupiter-Saturn Mission, 1977). The new algorithm is shown to combine the numerical precision of square root filtering with the efficiency of the original Kalman algorithm.

Thornton, C. L.↗

NASA NTRS1982

Refraction at a curved dielectric interface - Geometrical optics solution

The transmission of a spherical or plane wave through an arbitrarily curved dielectric interface is solved by the geometrical optics theory. The transmitted field is proportional to the product of the conventional Fresnel's transmission coefficient and a divergence factor (DF), which describes the cross-sectional variation (convergence or divergence) of a ray pencil as the latter propagates in the transmitted region. The factor DF depends on the incident wavefront, the curvatures of the interface, and the relative indices of the two media. Explicit matrix formulas for calculating DF are given, and its physical significance is illustrated via examples.

Lee, S.-W.↗

NASA NTRS1988

Structural analysis and design of multivariable control systems: An algebraic approach

The application of algebraic system theory to the design of controllers for multivariable (MV) systems is explored analytically using an approach based on state-space representations and matrix-fraction descriptions. Chapters are devoted to characteristic lambda matrices and canonical descriptions of MIMO systems; spectral analysis, divisors, and spectral factors of nonsingular lambda matrices; feedback control of MV systems; and structural decomposition theories and their application to MV control systems.

Tsay, Yih Tsong↗

NASA NTRS1988

Krylov subspace methods on supercomputers

A short survey of recent research on Krylov subspace methods with emphasis on implementation on vector and parallel computers is presented. Conjugate gradient methods have proven very useful on traditional scalar computers, and their popularity is likely to increase as three-dimensional models gain importance. A conservative approach to derive effective iterative techniques for supercomputers has been to find efficient parallel/vector implementations of the standard algorithms. The main source of difficulty in the incomplete factorization preconditionings is in the solution of the triangular systems at each step. A few approaches consisting of implementing efficient forward and backward triangular solutions are described in detail. Polynomial preconditioning as an alternative to standard incomplete factorization techniques is also discussed. Another efficient approach is to reorder the equations so as to improve the structure of the matrix to achieve better parallelism or vectorization. An overview of these and other ideas and their effectiveness or potential for different types of architectures is given.

Saad, Youcef↗

DOE OSTI2020

FLAG Review 2019: Flavour Lattice Averaging Group (FLAG)

Abstract We review lattice results related to pion, kaon, D -meson, B -meson, and nucleon physics with the aim of making them easily accessible to the nuclear and particle physics communities. More specifically, we report on the determination of the light-quark masses, the form factor $$f_+(0)$$ f + ( 0 ) arising in the semileptonic $$K \rightarrow \pi $$ K → π transition at zero momentum transfer, as well as the decay constant ratio $$f_K/f_\pi $$ f K / f π and its consequences for the CKM matrix elements $$V_{us}$$ V us and $$V_{ud}$$ V ud . Furthermore, we describe the results obtained on the lattice for some of the low-energy constants of $$SU(2)_L\times SU(2)_R$$ S U ( 2 ) L × S U ( 2 ) R and $$SU(3)_L\times SU(3)_R$$ S U ( 3 ) L × S U ( 3 ) R Chiral Perturbation Theory. We review the determination of the $$B_K$$ B K parameter of neutral kaon mixing as well as the additional four B parameters that arise in theories of physics beyond the Standard Model. For the heavy-quark sector, we provide results for $$m_c$$ m c and $$m_b$$ m b as well as those for D - and B -meson decay constants, form factors, and mixing parameters. These are the heavy-quark quantities most relevant for the determination of CKM matrix elements and the global CKM unitarity-triangle fit. We review the status of lattice determinations of the strong coupling constant $$\alpha _s$$ α s . Finally, in this review we have added a new section reviewing results for nucleon matrix elements of the axial, scalar and tensor bilinears, both isovector and flavor diagonal.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2020

Pattern-matching indexing of Laue and monochromatic serial crystallography data for applications in materials science

Serial crystallography data can be challenging to index, as each frame is processed individually, rather than being processed as a whole like in conventional X-ray single-crystal crystallography. An algorithm has been developed to index still diffraction patterns arising from small-unit-cell samples. The algorithm is based on the matching of reciprocal-lattice vector pairs, as developed for Laue microdiffraction data indexing, combined with three-dimensional pattern matching using a nearest-neighbors approach. As a result, large-bandpass data (e.g. 5–24 keV energy range) and monochromatic data can be processed, the main requirement being prior knowledge of the unit cell. Furthermore, angles calculated in the vicinity of a few theoretical and experimental reciprocal-lattice vectors are compared, and only vectors with the highest number of common angles are selected as candidates to obtain the orientation matrix. Global matching on the entire pattern is then checked. Four indexing options are available, two for the ranking of the theoretical reciprocal-lattice vectors and two for reducing the number of possible candidates. Furthermore, the algorithm has been used to index several data sets collected under different experimental conditions on a series of model samples. Additionally, knowing the crystallographic structure of the sample and using this information to rank the theoretical reflections based on the structure factors helps the indexing of large-bandpass data for the largest-unit-cell samples. For small-bandpass data, shortening the candidate list to determine the orientation matrix should be based on matching pairs of reciprocal-lattice vectors instead of triplet matching.

36 MATERIALS SCIENCE↗

NASA NTRS2010

Cellular reflectarray antenna and method of making same

A method of manufacturing a cellular reflectarray antenna arranged in an m by n matrix of radiating elements for communication with a satellite includes steps of determining a delay .phi.m,n for each of said m by n matrix of elements of said cellular reflectarray antenna using sub-steps of: determining the longitude and latitude of operation, determining elevation and azimuth angles of the reflectarray with respect to the satellite and converting theta.sub.0 (.theta..sub.0) and phi.sub.0 (.phi..sub.0), determining .DELTA..beta..sub.m,n, the pointing vector correction, for a given inter-element spacing and wavelength, determining .DELTA..phi..sub.m,n, the spherical wave front correction factor, for a given radius from the central element and/or from measured data from the feed horn; and, determining a delay .phi.m,n for each of said m by n matrix of elements as a function of .DELTA..beta..sub.m,n and .DELTA..phi..sub.m,n..

Romanofsky, Robert R↗

NASA NTRS2011

Cellular reflectarray antenna and method of making same

Romanofsky, Robert R↗

DOE OSTI2024

A Measurement-Based Adaptive Voltage Regulation Method Considering Topology Changes

This paper proposes an online adaptive data-driven distributed energy resource (DER) dispatch optimization method for voltage control considering topology changes. By using a local sensitivity factor (LSF)-enabled voltage control, traditional DER control can be reformulated into a linear programming (LP) problem, leading to faster computation speeds. Power injection alteration and topology changes are two common operational changes in the distribution network that can affect the LSF and voltage control performance. To address this issue, a robust estimation method is developed to adjust the sensitivity matrix at each time step for the time-varying power injection changes. When topology changes occur, only the allocated predominant LSF submatrices are updated based on measurement data, allowing for a fast adaptation to the system reconfiguration. Results obtained from a real distribution feeder in Southern California demonstrate its robustness as compared to traditional volt-var control and constant LSF matrix dispatch control methods.

DERs↗

DOE OSTI2024

Denoising of imaginary time response functions with Hankel projections

Imaginary-time response functions of finite-temperature quantum systems are often obtained with methods that exhibit stochastic or systematic errors. Reducing these errors comes at a large computational cost—in quantum Monte Carlo simulations, the reduction of noise by a factor of two incurs a simulation cost of a factor of four. In this paper, we relate certain imaginary-time response functions to an inner product on the space of linear operators on Fock space. We then show that data with noise typically does not respect the positive definiteness of its associated Gramian. The Gramian has the structure of a Hankel matrix. As a method for denoising noisy data, we introduce an alternating projection algorithm that finds the closest positive definite Hankel matrix consistent with noisy data. We test our methodology at the example of fermion Green's functions for continuous-time quantum Monte Carlo data and show remarkable improvements of the error, reducing noise by a factor of up to 20 in practical examples. We argue that Hankel projections should be used whenever finite-temperature imaginary-time data of response functions with errors is analyzed, be it in the context of quantum Monte Carlo, quantum computing, or in approximate semianalytic methodologies. Published by the American Physical Society 2024

Yu, Yang (ORCID:0000000186178878)↗

NASA NTRS2002

Fracture Mechanisms For SiC Fibers And SiC/SiC Composites Under Stress-Rupture Conditions at High Temperatures

The successful application of SiC/SiC ceramic matrix composites as high-temperature structural materials depends strongly on maximizing the fracture or rupture life of the load-bearing fiber and matrix constituents. Using high-temperature data measured under stress-rupture test conditions, this study examines in a mechanistic manner the effects of various intrinsic and extrinsic factors on the creep and fracture behavior of a variety of SiC fiber types. It is shown that although some fiber types fracture during a large primary creep stage, the fiber creep rate just prior to fracture plays a key role in determining fiber rupture time (Monkman-Grant theory). If it is assumed that SiC matrices rupture in a similar manner as fibers with the same microstructures, one can develop simple mechanistic models to analyze and optimize the stress-rupture behavior of SiC/SiC composites for applied stresses that are initially below matrix cracking.

DiCarlo, James A.↗

DOE OSTI2023

Generalized Mercier stability criterion for stellarators

The Mercier criterion is a well-known stability criterion for tokamaks. It is derived from a 2 × 2 matrix eigenvalue problem arising from the expansion of resonant solutions about a singular surface where m−nq=0, with m and n being the poloidal and toroidal mode numbers, respectively, and q being the safety factor. The stability criterion is that the eigenvalues must be real, otherwise, the solution oscillates, violating the Newcomb crossing criterion. Because of the non-axisymmetry of stellarators, different toroidal as well as poloidal harmonics couple to each other. It follows that each singular surface can have multiple resonant harmonics, with multiplicity M≥1. The corresponding matrix eigenvalue problem involves a 2M×2M matrix, resulting in M pairs of positive and negative eigenvalues. The generalized stability criterion is that all eigenvalues must be real. While the original Mercier criterion can be expressed in terms of quadratures of equilibrium quantities over the singular surface, which can be evaluated anywhere, the generalized Mercier criterion can only be evaluated on rational q surfaces with a given set of resonant harmonics.

Physics↗

DOE OSTI2020

ELSI — An open infrastructure for electronic structure solvers

Routine applications of electronic structure theory to molecules and periodic systems need to compute the electron density from given Hamiltonian and, in case of non-orthogonal basis sets, overlap matrices. System sizes can range from few to thousands or, in some examples, millions of atoms. Different discretization schemes (basis sets) and different system geometries (finite non-periodic vs. infinite periodic boundary conditions) yield matrices with different structures. The ELectronic Structure Infrastructure (ELSI) project provides an open-source software interface to facilitate the implementation and optimal use of high-performance solver libraries covering cubic scaling eigensolvers, linear scaling density-matrix-based algorithms, and other reduced scaling methods in between. In this paper, we present recent improvements and developments inside ELSI, mainly covering (1) new solvers connected to the interface, (2) matrix layout and communication adapted for parallel calculations of periodic and/or spin-polarized systems, (3) routines for density matrix extrapolation in geometry optimization and molecular dynamics calculations, and (4) general utilities such as parallel matrix I/O and JSON output. The ELSI interface has been integrated into four electronic structure code projects (DFTB+, DGDFT, FHI-aims, SIESTA), allowing us to rigorously benchmark the performance of the solvers on an equal footing. Based on results of a systematic set of large-scale benchmarks performed with Kohn–Sham density-functional theory and density-functional tight-binding theory, we identify factors that strongly affect the efficiency of the solvers, and propose a decision layer that assists with the solver selection process. As a result, we describe a reverse communication interface encoding matrix-free iterative solver strategies that are amenable, e.g., for use with planewave basis sets.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Effect of nickel on the kinematic stability of retained austenite in carburized bearing steels – In-situ neutron diffraction and crystal plasticity modeling of uniaxial tension tests in AISI 8620, 4320 and 3310 steels

The presence of kinematically metastable retained austenite in the microstructure of bearing components can significantly affect the macro and micro-mechanical material response. In the present work, the influence of Ni on the stability of the retained austenite within three different grades of high carbon bearing steel using in-situ neutron diffraction is investigated. For the first time, the results show that presence of Ni increases the stability of the austenite in the elastic regime whereas the transformation rate remains unaffected. Crystal plasticity finite element (CPFE) modeling was used to study the deformation in these three steels and shows that the predominant factor causing the difference in mechanical behavior of these steels is the austenite stability. Finally, the elastic and plastic response of the matrix martensite was found to be identical among all specimens while the austenite demonstrates similar elastic behavior but remarkably different stabilities under monotonic loading.

36 MATERIALS SCIENCE↗

DOE OSTI2022

How to Get the Best Gas Separation Membranes from State-of-the-Art Glassy Polymers

Herein we focus on fundamental polymer science factors in membrane-based gas separation to open another chapter on this important topic. Realistically thinking about nano and angstrom scale matrix attributes that are translatable into higher performance thin glassy polymer asymmetric membrane layers in practical large-scale devices is crucial. Such thinking should be guided by expertise in both polymer and membrane communities to advance the state of the art. Polymer structures, membrane morphologies and effects of operating conditions are discussed here, using specific examples to illustrate key issues. Rubbery polymers are not the focus of this discussion, since they lack diffusive discrimination for size-similar penetrants, which glassy polymers provide and make them the focus here. Four scalable subtopics guide necessary thinking: (i) plasticization; (ii) anti-plasticization†2; (iii) dual-mode transport involving saturation of unrelaxed free volume, and (iv) non-uniform free volume and stress profiles in thin skin glassy polymer asymmetric or composite membranes. Furthermore, using these subtopics in the context of macromolecular science we discuss issues needed to expand the state-of-the-art in gas separation membranes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2020

A Multidimensional Operando Study Showing the Importance of the Electrode Macrostructure in Lithium Sulfur Batteries

Lithium sulfur batteries are one of the most promising next-generation energy storage technologies, because of their impressive theoretical energy density, low materials cost, and relative safety. However, incomplete understanding of their underlying operation mechanisms has hindered their further development and commercialization. In this work, to gain a better understanding of the operation mechanisms in the lithium sulfur battery, three macroscopically different (woven and nonwoven) and microscopically similar (made from the same carbon fibers) free-standing carbon felts are used as the conductive matrices to show how the macrostructure influences the redox reactions and the electrochemical performance. Additionally, an operando radiography and simultaneous in situ electrochemical impedance spectroscopy study are performed to highlight the differences of the carbon hosts and how they compare electrochemically in a lithium sulfur battery. The electrochemical results show that the carbon host with a more open structure results in increased capacity as well as a higher diffusion coefficient. The operando radiography shows that the open structures are more conducive to efficient redox reactivity in forming solid sulfur species, mostly in the form of elongated needlelike structures identified as β-S8, near the end of charge, which is corroborated by the impedance data. The data also reveal a “breathing” mechanism, where the polysulfides are pushed to the edges during discharge and pulled back during charge. Furthermore, it is also revealed that the “breathing” process is a limiting factor in the high rate performance. Overall, this study shows that there is a close relationship between the macrostructure of the carbon matrix and the electrochemical performance of the sulfur cathode.

25 ENERGY STORAGE↗

DOE OSTI2023

Averages of b -hadron, c -hadron, and τ -lepton properties as of 2021

Not Available

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

NASA NTRS1985

Development of a heterogeneous laminating resin system

The factors which effect the impact resistance of laminating resin systems and yet retain equivalent performance with the conventional 450 K curing epoxy matrix systems in other areas were studied. Formulation work was conducted on two systems, an all-epoxy and an epoxy/bismaleimide, to gain fundamental information on the effect formulation changes have upon neat resin and composite properties. The all-epoxy work involved formulations with various amounts and combinations of eight different epoxy resins, four different hardeners, fifteen different toughening agents, a filler, and a catalyst. The epoxy/bismaleimide effort improved formulations with various amounts and combinations of nine different resins, four different hardeners, eight different toughening agents, four different catalysts, and a filler. When a formulation appeared to offer the proper combination of properties required for a laminating resin Celion 3K-70P fabric was prepregged. Initial screening tests on composites primarily involved Gardner type impact and measurement of short beam shear strengths under dry and hot/wet conditions.

Biermann, T. F.↗