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At least 451 records · Page 25

All sources NASA NTRS DOE OSTI

NASA NTRS1993

Proposed framework for thermomechanical life modeling of metal matrix composites

The framework of a mechanics of materials model is proposed for thermomechanical fatigue (TMF) life prediction of unidirectional, continuous-fiber metal matrix composites (MMC's). Axially loaded MMC test samples are analyzed as structural components whose fatigue lives are governed by local stress-strain conditions resulting from combined interactions of the matrix, interfacial layer, and fiber constituents. The metallic matrix is identified as the vehicle for tracking fatigue crack initiation and propagation. The proposed framework has three major elements. First, TMF flow and failure characteristics of in situ matrix material are approximated from tests of unreinforced matrix material, and matrix TMF life prediction equations are numerically calibrated. The macrocrack initiation fatigue life of the matrix material is divided into microcrack initiation and microcrack propagation phases. Second, the influencing factors created by the presence of fibers and interfaces are analyzed, characterized, and documented in equation form. Some of the influences act on the microcrack initiation portion of the matrix fatigue life, others on the microcrack propagation life, while some affect both. Influencing factors include coefficient of thermal expansion mismatch strains, residual (mean) stresses, multiaxial stress states, off-axis fibers, internal stress concentrations, multiple initiation sites, nonuniform fiber spacing, fiber debonding, interfacial layers and cracking, fractured fibers, fiber deflections of crack fronts, fiber bridging of matrix cracks, and internal oxidation along internal interfaces. Equations exist for some, but not all, of the currently identified influencing factors. The third element is the inclusion of overriding influences such as maximum tensile strain limits of brittle fibers that could cause local fractures and ensuing catastrophic failure of surrounding matrix material. Some experimental data exist for assessing the plausibility of the proposed framework.

Halford, Gary R.↗

NASA NTRS1996

Some Experiences with Nonoverlapping Schur Complement Parallel Preconditioning for CFD Calculations

In this work we consider solving matrices which arise from the discretization of advection-diffusion field equations on arbitrary triangulated domains using stabilized numerical methods. The talk will discuss several candidate matrix preconditioning algorithms based on the 2 x 2 block factorization induced by an apriori partitioning of the triangulated domain. Application of the 2 x 2 block preconditioner requires the formation and inversion of the Schur complement submatrix. We consider several strategies for simplifying this task: incomplete Schur complement factorizations, drop tolerance element filling, Schur complement probing, and localized Schur complement inversion. Numerical results will be shown comparing performance and efficiency of these approximations. The matrix preconditioner has also been embedded into a Newton algorithm for solving the nonlinear Euler and Navier-Stokes equations governing compressible flow. The remainder of the talk will show numerous examples in CFD to demonstrate the efficiency and robustness of the techniques.

Barth, Timothy J.↗

DOE OSTI2025

Towards excitations and dynamical quantities in correlated lattices with density matrix embedding theory

Density matrix embedding theory (DMET) provides a framework to describe ground-state expectation values in strongly correlated systems, but its extension to dynamical quantities is still an open problem. We show one route to obtaining excitations and dynamical spectral functions by using the techniques of DMET to approximate the matrix elements that arise in a single-mode inspired excitation ansatz. We demonstrate this approach in the one-dimensional Hubbard model, comparing the neutral excitations, single-particle density of states, charge, and spin dynamical structure factors to benchmarks from the Bethe ansatz and density matrix renormalization group. Finally, our work highlights the potential of these ideas in building computationally efficient approaches for dynamical quantities.

1-dimensional systems↗

DOE OSTI2021

Analysis Report for Determination of pH Correction Factors for Brines under AP-157 Rev.1

This Analysis Report (AR) documents the determination of pH correction factors for the observed pH readings. The correction factor converts the observed pH reading recorded from the brines used in geochemical studies in support of the Waste Isolation Pilot Plant (WIPP) to a corrected pH value. The data analysis in this AR falls under AP-157 Rev. 1 Analysis Plan for Determination of pH Correction Factors in Brines (Kirkes et al, 2021). Measurement of pH in some solutions can be challenging due to numerous factors such as high ionic strength, elevated or lowered temperature, complex matrix composition, etc. (Knauss et al., 1990; and Rai et al., 1995). The measured pH can be corrected by applying the correction factor, empirically obtained from a specific test solution.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

A new upper bound for the growth factor in Gaussian elimination with complete pivoting

Abstract The growth factor in Gaussian elimination measures how large the entries of an LU factorization can be relative to the entries of the original matrix. It is a key parameter in error estimates, and one of the most fundamental topics in numerical analysis. We produce an upper bound of for the growth factor in Gaussian elimination with complete pivoting — the first improvement upon Wilkinson's original 1961 bound of .

Bisain, Ankit [Department of Mathematics Massachus↗

NASA NTRS1997

Effect of Cyclic Thermal Loads on Fatigue Reliability in Polymer Matrix Composites

Technological solutions that will ensure the economic viability and environmental compatibility of a future High Speed Civil Transport plane are currently being sought. Lighter structural materials for both airframe primary structures and engine structure components are being investigated. We believe that such objectives can be achieved through the use of high-temperature composites as well as other conventional, lighter weight alloys. One of the prime issues for these structural components is assured long-term behavior with a specified reliability. An investigation was conducted to describe a computational simulation methodology for predicting fatigue life, reliability, and probabilistic long-term behavior of polymer matrix composites. A unified time-, stress-, and load-dependent Multi- Factor Interaction Equation (MFIE) model developed at the NASA Lewis Research Center was used to simulate the long-term behavior of polymer matrix composites.

Chamis, Christos C.↗

NASA NTRS1990

Identification of thermodynamically stable ceramic reinforcement materials for iron aluminide matrices

Aluminide-base intermetallic matrix composites are currently being considered as potential high-temperature materials. One of the key factors in the selection of a reinforcement material is its chemical stability in the matrix. In this study, chemical interactions between iron aluminides and several potential reinforcement materials, which include carbides, oxides, borides, and nitrides, are analyzed from thermodynamic considerations. Several chemically compatible reinforcement materials are identified for the iron aluminides with Al concentrations ranging from 40 to 50 at. pct.

Misra, Ajay K.↗

NASA NTRS1993

Interface considerations in Al2O3/NiAl composite

The fiber-matrix interface requirements in an Al2O3/NiAl composite were examined from theoretical considerations. Several factors that influence the interface bonding requirements were analyzed. These include: (1) residual stresses due to fiber-matrix coefficient of thermal expansion (CTE) mismatch; (2) matrix cracking stress at room temperature; (3) fracture toughness at room temperature; (4) load transfer from the matrix to the fiber and ultimate tensile strength at the use temperature; and (5) creep resistance at high temperature. A relatively weak fiber-matrix bond, with an interfacial shear strength of approximately 15-20 MPa, might be sufficient for attaining the desired mechanical properties in the fiber direction at the use temperature. A weak fiber-matrix bond is also beneficial for increasing the fracture toughness of the composite at room temperature. In contrast, a strong fiber-matrix bond is required to withstand some of the residual stresses resulting from the fiber-matrix CTE mismatch, which are not likely to be reduced significantly by interface coatings. A relatively strong bond is also beneficial in increasing the matrix cracking stress at room temperature. Various interface coating options to accommodate the conflicting bonding requirements were reviewed. One viable coating option is to incorporate a thick, ductile interface layer well bonded to both the fiber and the matrix.

Misra, Ajay K.↗

NASA NTRS2000

Growth and differentiation of human lens epithelial cells in vitro on matrix

PURPOSE: To characterize the growth and maturation of nonimmortalized human lens epithelial (HLE) cells grown in vitro. METHODS: HLE cells, established from 18-week prenatal lenses, were maintained on bovine corneal endothelial (BCE) extracellular matrix (ECM) in medium supplemented with basic fibroblast growth factor (FGF-2). The identity, growth, and differentiation of the cultures were characterized by karyotyping, cell morphology, and growth kinetics studies, reverse transcription-polymerase chain reaction (RT-PCR), immunofluorescence, and Western blot analysis. RESULTS: HLE cells had a male, human diploid (2N = 46) karyotype. The population-doubling time of exponentially growing cells was 24 hours. After 15 days in culture, cell morphology changed, and lentoid formation was evident. Reverse transcription-polymerase chain reaction (RT-PCR) indicated expression of alphaA- and betaB2-crystallin, fibroblast growth factor receptor 1 (FGFR1), and major intrinsic protein (MIP26) in exponential growth. Western analyses of protein extracts show positive expression of three immunologically distinct classes of crystallin proteins (alphaA-, alphaB-, and betaB2-crystallin) with time in culture. By Western blot analysis, expression of p57(KIP2), a known marker of terminally differentiated fiber cells, was detectable in exponential cultures, and levels increased after confluence. MIP26 and gamma-crystallin protein expression was detected in confluent cultures, by using immunofluorescence, but not in exponentially growing cells. CONCLUSIONS: HLE cells can be maintained for up to 4 months on ECM derived from BCE cells in medium containing FGF-2. With time in culture, the cells demonstrate morphologic characteristics of, and express protein markers for, lens fiber cell differentiation. This in vitro model will be useful for investigations of radiation-induced cataractogenesis and other studies of lens toxicity.

Non-NASA Center↗

NASA NTRS1974

Semiclassical S-matrix theory of vibrationally inelastic collisions between two diatomic molecules

We derive a semiclassical S matrix for vibrationally inelastic collisions between two diatomic molecules, assuming a collinear geometry. Our theory incorporates a quantum mechanical superposition principle with classical dynamics and, as such, is an extension of the atom-diatomic molecule theory of Miller. The several approximations to the S matrix differ in the complexity with which the interference between various classical trajectories is treated. We report numerical calculations for H2-D2 and D2-D2 collisions based on two different interaction potentials. The cruder approximations yield transition probabilities which agree with exact quantum mechanical results to within a factor of 2. More sophisticated approximations to the S matrix yield excellent quantitative agreement with the quantum calculations.

Cohen, S. C.↗

NASA NTRS2016

Hydrogen Isotopic Composition of Apatite in Northwest Africa 7034: A Record of the "Intermediate" H-Isotopic Reservoir in the Martian Crust?

Northwest Africa (NWA) 7034 and its pairings comprise a regolith breccia with a basaltic bulk composition [1] that yields a better match than any other martian meteorite to visible-infrared reflectance spectra of the martian surface measured from orbit [2]. The composition of the fine-grained matrix within NWA 7034 bears a striking resemblance to the major element composition estimated for the martian crust, with several exceptions. The NWA 7034 matrix is depleted in Fe, Ti, and Cr and enriched in Al, Na, and P [3]. The differences in Al and Fe are the most substantial, but the Fe content of NWA 7034 matrix falls within the range reported for the southern highlands crust [6]. It was previously suggested by [4] that NWA 7034 was sourced from the southern highlands based on the ancient 4.4 Ga ages recorded in NWA 7034/7533 zircons [4, 5]. In addition, the NWA 7034 matrix material is enriched in incompatible trace elements by a factor of 1.2-1.5 [7] relative to estimates of the bulk martian crust. The La/Yb ratio of the bulk martian crust is estimated to be approximately 3 [7], and the La/Yb of the NWA 7034 matrix materials ranges from approximately 3.9 to 4.4 [3, 8], indicating a higher degree of LREE enrichment in the NWA 7034 matrix materials. This elevated La/Yb ratio and enrichment in incompatible lithophile trace elements is consistent with NWA 7034 representing a more geochemically enriched crustal terrain than is represented by the bulk martian crust, which would be expected if NWA 7034 represents the bulk crust from the southern highlands. Given the similarities between NWA 7034 and the martian crust, NWA 7034 may represent an important sample for constraining the composition of the martian crust, particularly the ancient highlands. In the present study, we seek to constrain the H isotopic composition of the martian crust using Cl-rich apatite in NWA 7034. Usui et al., [9] recently proposed that a H isotopic reservoir exists within the martian crust that has a H-isotopic composition that is intermediate (δD of 1000-2000per mille) between an isotopically light mantle (Delta D is less than 275per mille [10]) and an isotopically heavy atmosphere (δD of 2500-6100per mille [11, 12]). Apatites in NWA 7034 occur in a number of lithologic domains, however apatites across all lithologic domains have been affected by a Pb-loss event at about 1.5 Ga before present [5], so they are unlikely to have retained a primary composition and are more likely to have equilibrated with fluids within the martian crust that may or may not have exchanged with the martian atmosphere. Equilibration of apatite with crustal fluids is further supported by the chlorine-rich compositions exhibited by apatites in NWA 7034 in comparison to apatites from other martian meteorites (Figure 1; [13]). Cl is more hydrophilic than F, which promotes formation of Cl-rich apatite compositions in fluid-rich systems [e.g., 14, 15-17].

McCubbin, F. M.↗

DOE OSTI2026

Extracting $B_s\to D_s^*\ellν_\ell$ form factors

Semileptonic $B_{(s)}$ decays are of great phenomenological interest because they allow to determine e.g. CKM matrix elements or test lepton flavor universality. Taking advantage of already existing lattice data, we demonstrate the analysis steps to extract the four form factors describing exclusive semileptonic $B_s\to D_s^*\ellν_\ell$ decays using the narrow width approximation. Our data are based on RBC/UKQCD's set of 2+1 flavor gauge field ensembles with Shamir domain-wall fermion and Iwasaki gauge field action featuring inverse lattice spacings of $a^{-1}=$1.785, 2.383, and 2.785 GeV as well as pion masses between 268 and 433 MeV. Light, strange and charm quarks are simulated using domain-wall fermions, whereas bottom quarks are generated with the relativistic heavy quark (RHQ) action.

Boushmelev, Anastasia [Siegen U.] (ORCID:000000033↗

NASA NTRS1987

A direct algorithm for solution of incompressible three-dimensional unsteady Navier-Stokes equations

A direct, implicit, numerical solution algorithm, with second-order accuracy in space and time, is constructed for the three-dimensional unsteady incompressible Navier-Stokes equations formulated in terms of velocity and vorticity, using generalized orthogonal coordinates to achieve the accurate solution of complex viscous flow configurations. A numerically stable, efficient, direct inversion procedure is developed for the computationally intensive divergence-curl elliptic velocity problem. This overdetermined partial differential operator is first formulated as a uniquely determined, nonsingular matrix-vector problem; this aspect of the procedure is a unique feature of the present analysis. The three-dimensional vorticity-transport equation is solved by a modified factorization technique which completely eliminates the need for any block-matrix inversions and only scalar tridiagonal matrices need to be inverted. The method is applied to the test problem of the three-dimensional flow within a shear-driven cubical box. Coherent streamwise vortex structures are observed within the steady-state flow at Re = 100.

Osswald, G. A.↗

DOE OSTI2023

Tangent functional connectomes uncover more unique phenotypic traits

Functional connectomes (FCs) containing pairwise estimations of functional couplings between pairs of brain regions are commonly represented by correlation matrices. As symmetric positive definite matrices, FCs can be transformed via tangent space projections, resulting into tangent-FCs. Tangent-FCs have led to more accurate models predicting brain conditions or aging. Motivated by the fact that tangent-FCs seem to be better biomarkers than FCs, we hypothesized that tangent-FCs have also a higher fingerprint. We explored the effects of six factors: fMRI condition, scan length, parcellation granularity, reference matrix, main-diagonal regularization, and distance metric. Our results showed that identification rates are systematically higher when using tangent-FCs across the “fingerprint gradient” (here including test-retest, monozygotic and dizygotic twins). Highest identification rates were achieved when minimally (0.01) regularizing FCs while performing tangent space projection using Riemann reference matrix and using correlation distance to compare the resulting tangent-FCs. Such configuration was validated in a second dataset (resting-state).

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2026

Active operator learning with predictive uncertainty quantification for partial differential equations

With the increased prevalence of neural operators being used to provide rapid solutions to partial differential equations (PDEs), understanding the accuracy of model predictions and the associated error levels is necessary for deploying reliable surrogate models in scientific applications. Existing uncertainty quantification (UQ) frameworks employ ensembles or Bayesian methods, which can incur substantial computational costs during both training and inference. Here, we propose a lightweight predictive UQ method tailored for Deep operator networks (DeepONets) that also generalizes to other operator networks. Numerical experiments on linear and nonlinear PDEs demonstrate that the framework’s uncertainty estimates are unbiased and provide accurate out-of-distribution uncertainty predictions with a sufficiently large training dataset. Our framework provides fast inference and uncertainty estimates that can efficiently drive outer-loop analyses that would be prohibitively expensive with conventional solvers. We demonstrate how predictive uncertainties can be used in the context of Bayesian optimization and active learning problems to yield improvements in accuracy and data-efficiency for outer-loop optimization procedures. In the active learning setup, we extend the framework to Fourier Neural Operators (FNO) and describe a generalized method for other operator networks. To enable real-time deployment, we introduce an inference strategy based on precomputed trunk outputs and a sparse placement matrix, reducing evaluation time by more than a factor of five. Our method provides a practical route to uncertainty-aware operator learning in time-sensitive settings.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1972

Application of the matrix exponential kernel

A point matrix kernel for radiation transport, developed by the transmission matrix method, has been used to develop buildup factors and energy spectra through slab layers of different materials for a point isotropic source. Combinations of lead-water slabs were chosen for examples because of the extreme differences in shielding properties of these two materials.

Rohach, A. F.↗

NASA NTRS1982

Process Research On Polycrystalline Silicon Material (PROPSM)

Performance limiting mechanisms in polycrystalline silicon are investigated by fabricating a matrix of solar cells of various thicknesses from polycrystalline silicon wafers of several bulk resistivities. The analysis of the results for the entire matrix indicates that bulk recombination is the dominant factor limiting the short circuit current in large grain (greater than 1 to 2 mm diameter) polycrystalline silicon, the same mechanism that limits the short circuit current in single crystal silicon. An experiment to investigate the limiting mechanisms of open circuit voltage and fill factor for large grain polycrystalline silicon is designed. Two process sequences to fabricate small cells are investigated.

Culik, J. S.↗

NASA NTRS1986

Global collocation methods for approximation and the solution of partial differential equations

Polynomial interpolation methods are applied both to the approximation of functions and to the numerical solutions of hyperbolic and elliptic partial differential equations. The derivative matrix for a general sequence of the collocation points is constructed. The approximate derivative is then found by a matrix times vector multiply. The effects of several factors on the performance of these methods including the effect of different collocation points are then explored. The resolution of the schemes for both smooth functions and functions with steep gradients or discontinuities in some derivative are also studied. The accuracy when the gradients occur both near the center of the region and in the vicinity of the boundary is investigated. The importance of the aliasing limit on the resolution of the approximation is investigated in detail. Also examined is the effect of boundary treatment on the stability and accuracy of the scheme.

Solomonoff, A.↗