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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.

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At least 865 records · Page 48
All sourcesNASA NTRSDOE OSTI
NASA NTRS1980

Normal and shear impact of layered composite with a crack - Dynamic stress intensification

The dynamic response of a layered composite under normal and shear impact is analyzed by assuming that the composite contains an initial flaw in the matrix material. One of the objectives was to develop an analytical method for determining dynamic stress solutions which should lead to a numerical method which utilizes Fourier transform for the space variable and Laplace transform for the time variable. The time-dependent angle loading is separated into two parts: a symmetric and a skew-symmetric with reference to the crack plane. By superposition, the transient boundary conditions consist of applying normal and shear tractions to a crack embedded in a layered composite; one phase of the composite could represent the fiber while the other could be the matrix. Mathematically, these conditions reduce the problem to a system of dual integral equations solved in the transform plane for the transform of the dynamic stress-intensity factor.

Sih, G. C.↗
NASA NTRS1986

Efficient solution methods for the Navier-Stokes equations

Implicit finite difference schemes for solving two-dimensional and three-dimensional Euler and thin layer Navier-Stokes equations are addressed. The methods are demonstrated in fully vectorized codes for a Cray type architecture. The Beam and Warming implicit approximate factorization algorithm in generalized coordinates is used. The methods are either time accurate or accelerated non-time accurate steady state schemes. Acceleration and efficiency modifications such as matrix reduction, diagonalization, and flux split schemes are presented. Two dimensional inviscid and viscous calculations (e.g., airfoils with a deflected spoiler, circulation control airfoils, and unsteady buffeting) and of three dimensional viscous elliptical bodies, exhausting boattails, and generic oblique wing computations are discussed.

Pulliam, T. H.↗
NASA NTRS1991

Fatigue life prediction of an intermetallic matrix composite at elevated temperatures

A strain-based fatigue life prediction method is proposed for an intermetallic matrix composite (IMC) under tensile cyclic loadings at elevated temperatures. Styled after the Universal Slopes method, the model utilizes the composite's tensile properties to estimate fatigue life. Factors such as fiber volume ratio, number of plys and temperature dependence are implicitly incorporated into the model through these properties. The model constants are determined by using unidirectional fatigue data at temperatures of 425 and 815 C. Fatigue lives from two independent sources are used to verify the model at temperatures of 650 and 760 C. Cross-ply lives at 760 C are also predicted. It is demonstrated that the correlation between experimental and predicted lives is within a factor of two.

Bartolotta, Paul A.↗
NASA NTRS1991

Fatigue life prediction of an intermetallic matrix composite at elevated temperatures

A strain-based fatigue life prediction method is proposed for an intermetallic matrix composite (IMC) under tensile cyclic loadings at elevated temperatures. Styled after the 'Universal Slopes' method, the model utilizes the composite's tensile properties to estimate fatigue life. Factors such as fiber volume ratio (Vf), number of plys and temperature dependence are implicitly incorporated into the model through these properties. The model constants are determined by using unidirectional fatigue data at temperatures of 425 and 815 C. Fatigue lives from two independent sources are used to verify the model at temperatures of 650 and 760 C. Cross-ply lives at 760 C are also predicted. It is demonstrated that the correlation between experimental and predicted lives is within a factor of two.

Bartolotta, P. A.↗
NASA NTRS1961

Stress Concentrations in Filamentary Structures

Theoretical analyses are made of the stress distributions in a sheet of parallel filaments which carry normal loads and are imbedded in a matrix which carries only shear. In all cases, uniform loading at infinity is assumed and small-deflection elasticity theory is used. Static and dynamic stress-concentration factors due to one or more filaments being broken are determined. Particular attention is paid the dynamic overshoot resulting when the filaments are suddenly broken. The dynamic-response factor increases from 1.15 to 1.27 as the number of broken filaments is increased from one to infinity. A somewhat lower dynamic-response factor is obtained when a hole is suddenly caused in the filament sheet.

Hedgepeth, John M.↗
NASA NTRS2008

An Uncertainty Structure Matrix for Models and Simulations

Software that is used for aerospace flight control and to display information to pilots and crew is expected to be correct and credible at all times. This type of software is typically developed under strict management processes, which are intended to reduce defects in the software product. However, modeling and simulation (M&S) software may exhibit varying degrees of correctness and credibility, depending on a large and complex set of factors. These factors include its intended use, the known physics and numerical approximations within the M&S, and the referent data set against which the M&S correctness is compared. The correctness and credibility of an M&S effort is closely correlated to the uncertainty management (UM) practices that are applied to the M&S effort. This paper describes an uncertainty structure matrix for M&S, which provides a set of objective descriptions for the possible states of UM practices within a given M&S effort. The columns in the uncertainty structure matrix contain UM elements or practices that are common across most M&S efforts, and the rows describe the potential levels of achievement in each of the elements. A practitioner can quickly look at the matrix to determine where an M&S effort falls based on a common set of UM practices that are described in absolute terms that can be applied to virtually any M&S effort. The matrix can also be used to plan those steps and resources that would be needed to improve the UM practices for a given M&S effort.

Green, Lawrence L.↗
NASA NTRS2002

Fluid flow increases mineralized matrix deposition in 3D perfusion culture of marrow stromal osteoblasts in a dose-dependent manner

Bone is a complex highly structured mechanically active 3D tissue composed of cellular and matrix elements. The true biological environment of a bone cell is thus derived from a dynamic interaction between responsively active cells experiencing mechanical forces and a continuously changing 3D matrix architecture. To investigate this phenomenon in vitro, marrow stromal osteoblasts were cultured on 3D scaffolds under flow perfusion with different rates of flow for an extended period to permit osteoblast differentiation and significant matrix production and mineralization. With all flow conditions, mineralized matrix production was dramatically increased over statically cultured constructs with the total calcium content of the cultured scaffolds increasing with increasing flow rate. Flow perfusion induced de novo tissue modeling with the formation of pore-like structures in the scaffolds and enhanced the distribution of cells and matrix throughout the scaffolds. These results represent reporting of the long-term effects of fluid flow on primary differentiating osteoblasts and indicate that fluid flow has far-reaching effects on osteoblast differentiation and phenotypic expression in vitro. Flow perfusion culture permits the generation and study of a 3D, actively modeled, mineralized matrix and can therefore be a valuable tool for both bone biology and tissue engineering.

Non-NASA Center↗
NASA NTRS2005

Determination of Interlaminar Toughness of IM7/977-2 Composites at Temperature Extremes and Different Thicknesses

Composite materials are being used in the aerospace industry as a means of reducing vehicle weight. In particular, polymer matrix composites (PMC) are good candidates due to their high strength-to-weight and high stiffness-to-weight ratios. Future reusable space launch vehicles and space exploration structures will need advanced light weight composites in order to minimize vehicle weight while demonstrating robustness and durability, guaranteeing high factors of safety. In particular, the implementation of composite cryogenic propellant fuel tanks (cryotanks) for future reusable launch vehicles (RLVs) could greatly reduce the vehicle's weight versus identically sized cryotanks constructed of metallic materials. One candidate composite material for future cryotank designs is IM7/977-2, which is a graphite/epoxy system. A successful candidate must demonstrate reasonable structural properties over a wide range of temperatures. Since the matrix material is normally the weak link in the composite, tests that emphasize matrix-dominated behavior need to be conducted. Therefore, the objective of this work is to determine the mode I interlaminar fracture toughness of "unidirectional" 8-ply and 16-ply IM7/977-2 through experimental testing. Tests were performed at -196 degrees Celsius (-320 degrees Fahrenheit), 22 degrees Celsius (72 degrees Fahrenheit), 93 degrees Celsius (200 degrees Fahrenheit) and 160 degrees C (320 degrees Fahrenheit). Low temperature testing was completed while the specimen was submerged in a liquid nitrogen bath. High temperature testing was completed in a temperature-controlled oven.

Johnson, W. S.↗
DOE OSTI2021

Inversion of dynamical Bragg intensities to complex structure factors by iterated projections. For Ultramic. 2020. ("Pico" Festschrift, May 2021)

We discuss a method for recovering complex structure factors from many simultaneously excited Bragg beam intensities is described. The method is applied to simulated transmission electron diffraction data over a wide range of crystal thickness and beam energies. The method is based on iterated projections between structure and scattering matrices, which are related by a matrix unitary transformation, exponential, which we invert. The algorithm removes multiple-scattering perturbations from diffraction data and might be extended to other fields, including X-ray and neutron diffraction and cryo-electron microscopy. Because coherent multiple scattering involves interference between Bragg beams, the method also solves the phase problem. Unlike dynamical inversion from electron microscope images or ptychography data, the method, which starts with Bragg beam intensities, provides complex structure factors unaffected by focusing errors or resolution limitations imposed by lenses. We provide inversions from simulated data with 441 simultaneously excited Bragg beams over a range of thickness and beam energy. We discuss the retrieval of chirality information from enantiomorphs, the efficient incorporation of symmetry information using the irreducible representation of the group of structure matrices, and the effect of HOLZ lines to provide three-dimensional information.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Gapped-filtering for efficient Chebyshev expansion of the density projection operator

In this paper, we develop the gapped-filtering method, whereby a short Chebyshev expansion accurately represents the density-matrix operator. The method optimizes the Chebyshev coefficients to give the correct density matrix at all energies except within the gapped region where there are no eigenstates. Gapped filtering reduces the number of required terms in the Chebyshev expansion compared to traditional expansion methods, as long as one knows or can determine efficiently the HOMO and LUMO positions. The reduction is especially noticeable (factors of 2-3) when high accuracy is sought. To exemplify the method, we use gapped-filtering to increase the efficiency of stochastic-GW calculations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Calcium fluoride as a dominating matrix for quantitative analysis by laser ablation-inductively coupled plasma-mass spectrometry (LA-ICP-MS): A feasibility study

Here, calcium fluoride formed by the reaction between ammonium bifluoride and calcium chloride was investigated as a dominating matrix for quantitative analysis by laser ablation inductively coupled plasma mass spectrometry (LA-ICP-MS). Transformation from a solid sample to the calcium fluoride-based matrix permitted quantitative analysis based on calibration standards made from elemental standards. A low abundance stable calcium isotope, i.e. 44 Ca + , was monitored as the internal standard for quantitative analysis by LA-ICP-MS. Correlation coefficient factors for multiple elements were obtained with values over 0.999. The results for multiple elements in a certified reference material of soil (NIST SRM 2710a) agreed with the certified values in the range of expanded uncertainty, indicating the present method was valid for quantitation of elements in solid samples.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

A flexible class of priors for orthonormal matrices with basis function-specific structure

Statistical modeling of high-dimensional matrix-valued data motivates the use of a low-rank representation that simultaneously summarizes key characteristics of the data and enables dimension reduction. Low-rank representations commonly factor the original data into the product of orthonormal basis functions and weights, where each basis function represents an independent feature of the data. However, the basis functions in these factorizations are typically computed using algorithmic methods that cannot quantify uncertainty or account for basis function correlation structure a priori. While there exist Bayesian methods that allow for a common correlation structure across basis functions, empirical examples motivate the need for basis function-specific dependence structure. We propose a prior distribution for orthonormal matrices that can explicitly model basis function-specific structure. The prior is used within a general probabilistic model for singular value decomposition to conduct posterior inference on the basis functions while accounting for measurement error and fixed effects. We discuss how the prior specification can be used for various scenarios and demonstrate favorable model properties through synthetic data examples. Finally, we apply our method to two-meter air temperature data from the Pacific Northwest, enhancing our understanding of the Earth system’s internal variability.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Nonlocal Effect of Percolated Particle Networks on Viscoelasticity of Polymer–Filler Nanocomposites: A Mesoscale Simulation Study

With nanoparticles (NPs) as fillers, polymer nanocomposites (PNCs) usually exhibit enhanced mechanical properties. However, a direct connection between the microscopic structural relaxation and macroscopic mechanical properties of PNCs remains to be established. To investigate the micro-to-macro connection, we develop a mesoscale model, in which the NPbridging polymer chains are represented by a dynamic bonded interaction between NPs, and the bulk polymer matrix is implicitly modeled by overdamped Langevin dynamics. Extensive equilibrium simulations are performed to quantify the microscopic dynamics of model PNCs. Systematic analyses of modified Rouse dynamics, dynamic structure factor, and relaxation modulus uncover that the microscopic relaxation dynamics of PNCs are significantly decelerated across different length scales because of nonlocal effects of percolated particle networks a phenomenon that has not been adequately captured in prior simulation studies. We find that NPvolume- fraction and NP-bonding-energy barrier are the two critical variables that affect bulk viscoelasticity the most. The proposed mesoscale model is versatile and provides a powerful framework for studying structure−property relations of different PNCs.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Does jackknife scale really matter for accurate large-scale structure covariances?

ABSTRACT The jackknife method gives an internal covariance estimate for large-scale structure surveys and allows model-independent errors on cosmological parameters. Using the SDSS-III BOSS CMASS sample, we study how the jackknife size and number of resamplings impact the precision of the covariance estimate on the correlation function multipoles and the error on the inferred baryon acoustic scale. We compare the measurement with the MultiDark Patchy mock galaxy catalogues, and we also validate it against a set of lognormal mocks with the same survey geometry. We build several jackknife configurations that vary in size and number of resamplings. We introduce the Hartlap factor in the covariance estimate that depends on the number of jackknife resamplings. We also find that it is useful to apply the tapering scheme to estimate the precision matrix from a limited number of resamplings. The results from CMASS and mock catalogues show that the error estimate of the baryon acoustic scale does not depend on the jackknife scale. For the shift parameter α, we find an average error of 1.6 per cent, 2.2 per cent and 1.2 per cent, respectively, from CMASS, Patchy, and lognormal jackknife covariances. Despite these uncertainties fluctuate significantly due to some structural limitations of the jackknife method, our α estimates are in reasonable agreement with published pre-reconstruction analyses. Jackknife methods will provide valuable and complementary covariance estimates for future large-scale structure surveys.

Favole, Ginevra (ORCID:000000028218563X)↗
DOE OSTI2022

Modelling nearest neighbour distributions of biased tracers using hybrid effective field theory

ABSTRACT We investigate the application of hybrid effective field theory (HEFT) – which combines a Lagrangian bias expansion with subsequent particle dynamics from N-body simulations – to the modelling of k-nearest neighbour cumulative distribution functions (kNN-CDFs) of biased tracers of the cosmological matter field. The kNN-CDFs are sensitive to all higher order connected N-point functions in the data, but are computationally cheap to compute. We develop the formalism to predict the kNN-CDFs of discrete tracers of a continuous field from the statistics of the continuous field itself. Using this formalism, we demonstrate how kNN-CDF statistics of a set of biased tracers, such as haloes or galaxies, of the cosmological matter field can be modelled given a set of low-redshift HEFT component fields and bias parameter values. These are the same ingredients needed to predict the two-point clustering. For a specific sample of haloes, we show that both the two-point clustering and the kNN-CDFs can be well-fit on quasi-linear scales (≳ 20h−1Mpc) by the second-order HEFT formalism with the same values of the bias parameters, implying that joint modelling of the two is possible. Finally, using a Fisher matrix analysis, we show that including kNN-CDF measurements over the range of allowed scales in the HEFT framework can improve the constraints on σ8 by roughly a factor of 3, compared to the case where only two-point measurements are considered. Combining the statistical power of kNN measurements with the modelling power of HEFT, therefore, represents an exciting prospect for extracting greater information from small-scale cosmological clustering.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Nonperturbative running of the tensor operator for N f = 3 QCD from the chirally rotated Schrödinger functional

We study the renormalization group (RG) running of the nonsinglet tensor operator, for N f = 3 QCD with Wilson fermions in a mixed action setup, with standard Schrödinger functional (SF) boundary conditions for sea quarks and chirally rotated Schrödinger functional ( χ SF ) boundary conditions for valence quarks. Based on a recursive finite-size scaling technique we compute nonperturbatively the tensor step-scaling function for an energy range between a hadronic scale and an electroweak scale, above which perturbation theory may be safely applied. Our result is expressed as the RG-running factor T RGI / [ T ( μ had ) ] R , where the numerator is the scale independent (renormalization group invariant—RGI) tensor operator and the denominator is its renormalized counterpart at a hadronic scale μ had = 233 ( 8 ) MeV in a given scheme. We determine the step-scaling function in four distinct renormalization schemes. We also compute the renormalization parameters of these schemes at μ had which, combined with the RG-running factor, gives the scheme-independent quantity Z T RGI ( g 0 2 ) in four schemes and for a range of bare gauge couplings in which large volume hadronic matrix element simulations are performed by the CLS consortium in N f = 2 + 1 QCD. All four results are compatible and also agree with a recent determination based on a unitary setup for Wilson quarks with Schrödinger functional boundary conditions [arXiv:2309.04314]. This provides a strong universality test. Published by the American Physical Society 2024

Astronomy & Astrophysics↗
DOE OSTI2025

Homomorphic data compression for real time photon correlation analysis

The construction of highly coherent X-ray sources, combined with next-generation detectors that are larger and faster, has enabled new research opportunities across the scientific landscape. Among the techniques that benefit most from these advancements is X-ray photon correlation spectroscopy (XPCS), where faster acquisition unlocks the ability to study faster dynamics within samples. However, faster acquisition on larger detectors also introduces unprecedented challenges for online data processing and offline data storage. Such challenges are particularly prominent for XPCS, where real time analyses require simultaneous calculation of all the previously acquired data in the time series. We present a homomorphic compression scheme to effectively reduce the computational time and memory space required for XPCS analysis. Leveraging similarities in the mathematical expression between a matrix-based compression algorithm and the correlation calculation, our approach allows direct operation on the compressed data without their decompression. The offline compression scheme extends storage capacity by a factor of 40 while preserving key features in the lossy compressed data. Meanwhile, the online compression scheme reduces the computational time to below 1 ms, enabling real time calculation of the correlation functions at kHz framerate. Our demonstration of a homomorphic compression of scientific data provides an effective solution to the big data challenge at coherent light sources. Beyond the example shown in this work, the framework can be extended to facilitate real-time operations directly on a compressed data stream for other techniques.

36 MATERIALS SCIENCE↗
NASA NTRS1980

Efficient program for decoding the /255, 223/ Reed-Solomon code over GF/2 to the 8th/ with both errors and erasures, using transform decoding

The paper deals with a method developed for decoding a (255, 223) Reed-Solomon code over GF(2 to the 8th) with both errors and erasures. The matrix of decoding times for correcting errors and erasures of the code using a simplified decoder is presented. It is shown that the algorithm proposed is faster by a factor of from three to seven.

Miller, R. L.↗