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At least 73 records · Page 4

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NASA NTRS1980

Improvements in sparse matrix operations of NASTRAN

A "nontransmit" packing routine was added to NASTRAN to allow matrix data to be refered to directly from the input/output buffer. Use of the packing routine permits various routines for matrix handling to perform a direct reference to the input/output buffer if data addresses have once been received. The packing routine offers a buffer by buffer backspace feature for efficient backspacing in sequential access. Unlike a conventional backspacing that needs twice back record for a single read of one record (one column), this feature omits overlapping of READ operation and back record. It eliminates the necessity of writing, in decomposition of a symmetric matrix, of a portion of the matrix to its upper triangular matrix from the last to the first columns of the symmetric matrix, thus saving time for generating the upper triangular matrix. Only a lower triangular matrix must be written onto the secondary storage device, bringing 10 to 30% reduction in use of the disk space of the storage device.

Harano, S.↗

NASA NTRS1982

Dynamic switch matrix for the TDMA satellite switching system

Future high capacity satellite communication systems require signal processing on board satellites. The on-board signal processing includes switching of RF signals between multiple antennas to provide interconnection between the uplink and downlink beams. This paper describes the development of a dynamic switch matrix for a TDMA satellite switching system to be used in the next generation communications satellites. In this paper, a dynamic switch matrix, which includes the microwave switch matrix, the distribution control unit and the timing source, will be described. Several different microwave switch matrix architectures and switching devices were evaluated and compared. A unique coupler crossbar switch matrix architecture with dual-gate field effect transistor as switching element was developed. Experimental results of both microwave switch matrix (MSM) and distribution control unit (DCU) are presented. These test results verify the MSM with coupler crossbar architecture and dual-gate FET as switching element will meet the future SS-TDMA system requirements. Finally, the reliability of the dynamic switch matrix is addressed. The analysis shows reliability of 0.9981 for 7 year space operation can be achieved for the designed dynamic switch matrix.

Ho, P. T.↗

NASA NTRS1988

Fast polar decomposition of an arbitrary matrix

The polar decomposition of an m x n matrix A of full rank, where m is greater than or equal to n, can be computed using a quadratically convergent algorithm. The algorithm is based on a Newton iteration involving a matrix inverse. With the use of a preliminary complete orthogonal decomposition the algorithm can be extended to arbitrary A. How to use the algorithm to compute the positive semi-definite square root of a Hermitian positive semi-definite matrix is described. A hybrid algorithm which adaptively switches from the matrix inversion based iteration to a matrix multiplication based iteration due to Kovarik, and to Bjorck and Bowie is formulated. The decision when to switch is made using a condition estimator. This matrix multiplication rich algorithm is shown to be more efficient on machines for which matrix multiplication can be executed 1.5 times faster than matrix inversion.

Higham, Nicholas J.↗

NASA NTRS1989

Metal matrix composite micromechanics: In-situ behavior influence on composite properties

Recent efforts in computational mechanics methods for simulating the nonlinear behavior of metal matrix composites have culminated in the implementation of the Metal Matrix Composite Analyzer (METCAN) computer code. In METCAN material nonlinearity is treated at the constituent (fiber, matrix, and interphase) level where the current material model describes a time-temperature-stress dependency of the constituent properties in a material behavior space. The composite properties are synthesized from the constituent instantaneous properties by virtue of composite micromechanics and macromechanics models. The behavior of metal matrix composites depends on fabrication process variables, in situ fiber and matrix properties, bonding between the fiber and matrix, and/or the properties of an interphase between the fiber and matrix. Specifically, the influence of in situ matrix strength and the interphase degradation on the unidirectional composite stress-strain behavior is examined. These types of studies provide insight into micromechanical behavior that may be helpful in resolving discrepancies between experimentally observed composite behavior and predicted response.

Murthy, P. L. N.↗

NASA NTRS1989

The interface in tungsten fiber reinforced niobium metal-matrix composites

The creep resistance of tungsten fiber reinforced niobium metal-matrix composites was evaluated. The interface region between the fiber and matrix was characterized by microhardness and electron probe microanalysis measurements which indicated that its properties were between those of fiber and matrix. However, the measured properties of the composite exceeded those calculated by the rule of mixtures even when the interface zone was assumed to retain all the strength of the fiber. The composite structure appeared to enhance the strengths of both the fibers and the matrix above what they exhibited in stand-alone tests. The effect of fiber orientation and matrix alloy composition on the fiber/matrix interface were also evaluated. Small alloying additions of zirconium and tungsten to the niobium matrix affected the creep resistance of the composites only slightly. A decrease in the creep resistance of the composite with increasing zirconium content in the matrix was ascribed to an increase in the diffusion rate of the fiber/matrix interdiffusion reaction, and a slight increase in the creep resistance of the composite was observed with an addition of 9 w percent tungsten to the matrix. In addition, Kirkendall void formation was observed at the fiber/matrix interface; the void distribution differed depending on the fiber orientation relative to the stress axis.

Grobstein, Toni L.↗

NASA NTRS1990

Eigenvalue computations with the QUAD4 consistent-mass matrix

The NASTRAN user has the option of using either a lumped-mass matrix or a consistent- (coupled-) mass matrix with the QUAD4 shell finite element. At the Sixteenth NASTRAN Users' Colloquium (1988), Melvyn Marcus and associates of the David Taylor Research Center summarized a study comparing the results of the QUAD4 element with results of other NASTRAN shell elements for a cylindrical-shell modal analysis. Results of this study, in which both the lumped-and consistent-mass matrix formulations were used, implied that the consistent-mass matrix yielded poor results. In an effort to further evaluate the consistent-mass matrix, a study was performed using both a cylindrical-shell geometry and a flat-plate geometry. Modal parameters were extracted for several modes for both geometries leading to some significant conclusions. First, there do not appear to be any fundamental errors associated with the consistent-mass matrix. However, its accuracy is quite different for the two different geometries studied. The consistent-mass matrix yields better results for the flat-plate geometry and the lumped-mass matrix seems to be the better choice for cylindrical-shell geometries.

Butler, Thomas A.↗

NASA NTRS1992

A micromechanics-based strength prediction methodology for notched metal matrix composites

An analytical micromechanics based strength prediction methodology was developed to predict failure of notched metal matrix composites. The stress-strain behavior and notched strength of two metal matrix composites, boron/aluminum (B/Al) and silicon-carbide/titanium (SCS-6/Ti-15-3), were predicted. The prediction methodology combines analytical techniques ranging from a three dimensional finite element analysis of a notched specimen to a micromechanical model of a single fiber. In the B/Al laminates, a fiber failure criteria based on the axial and shear stress in the fiber accurately predicted laminate failure for a variety of layups and notch-length to specimen-width ratios with both circular holes and sharp notches when matrix plasticity was included in the analysis. For the SCS-6/Ti-15-3 laminates, a fiber failure based on the axial stress in the fiber correlated well with experimental results for static and post fatigue residual strengths when fiber matrix debonding and matrix cracking were included in the analysis. The micromechanics based strength prediction methodology offers a direct approach to strength prediction by modeling behavior and damage on a constituent level, thus, explicitly including matrix nonlinearity, fiber matrix debonding, and matrix cracking.

Bigelow, C. A.↗

NASA NTRS1990

Intermetallic matrix composites; Proceedings of the MRS Symposium, San Francisco, CA, Apr. 18-20, 1990

The present volume on intermetallic matrix composites discusses the modeling, processing, microstructure/property relationships, and compatibility of intermetallic matrix composites. Attention is given to models for the strength of ductile matrix composites, innovative processing techniques for intermetallic matrix composites, ductile phase toughening of brittle intermetallics, and reactive synthesis of NbAl3 matrix composites. Topics addressed include solidification processing of NbCr2 alloys, Ta and Nb reinforced MoSi2, the microstructure and mechanical behavior of Ni3Al-matrix composites, and ductile-phase toughening of Cr3Si with chromium. Also discussed are dislocation morphologies in TiB2/NiAl, the development of highly impact resistant NiAl matrix composites, the effect of notches on the fatigue life of the SCS-6Ti3Al composite, and the chemical stability of fiber-metal matrix composites.

Anton, D. L.↗

NASA NTRS1993

A micromechanics-based strength prediction methodology for notched metal-matrix composites

An analytical micromechanics-based strength prediction methodology was developed to predict failure of notched metal matrix composites. The stress-strain behavior and notched strength of two metal matrix composites, boron/aluminum (B/Al) and silicon-carbide/titanium (SCS-6/Ti-15-3), were predicted. The prediction methodology combines analytical techniques ranging from a three-dimensional finite element analysis of a notched specimen to a micromechanical model of a single fiber. In the B/Al laminates, a fiber failure criteria based on the axial and shear stress in the fiber accurately predicted laminate failure for a variety of layups and notch-length to specimen-width ratios with both circular holes and sharp notches when matrix plasticity was included in the analysis. For the SCS-6/Ti-15-3 laminates, a fiber failure based on the axial stress in the fiber correlated well with experimental results for static and postfatigue residual strengths when fiber matrix debonding and matrix cracking were included in the analysis. The micromechanics-based strength prediction methodology offers a direct approach to strength prediction by modeling behavior and damage on a constituent level, thus, explicitly including matrix nonlinearity, fiber matrix debonding, and matrix cracking.

Bigelow, C. A.↗

NASA NTRS1995

Time-dependent deformation of titanium metal matrix composites

A three-dimensional finite element program called VISCOPAC was developed and used to conduct a micromechanics analysis of titanium metal matrix composites. The VISCOPAC program uses a modified Eisenberg-Yen thermo-viscoplastic constitutive model to predict matrix behavior under thermomechanical fatigue loading. The analysis incorporated temperature-dependent elastic properties in the fiber and temperature-dependent viscoplastic properties in the matrix. The material model was described and the necessary material constants were determined experimentally. Fiber-matrix interfacial behavior was analyzed using a discrete fiber-matrix model. The thermal residual stresses due to the fabrication cycle were predicted with a failed interface, The failed interface resulted in lower thermal residual stresses in the matrix and fiber. Stresses due to a uniform transverse load were calculated at two temperatures, room temperature and an elevated temperature of 650 C. At both temperatures, a large stress concentration was calculated when the interface had failed. The results indicate the importance of accuracy accounting for fiber-matrix interface failure and the need for a micromechanics-based analytical technique to understand and predict the behavior of titanium metal matrix composites.

Bigelow, C. A.↗

NASA NTRS1997

Micromechanical Modeling of Woven Metal Matrix Composites

This report presents the results of an extensive micromechanical modeling effort for woven metal matrix composites. The model is employed to predict the mechanical response of 8-harness (8H) satin weave carbon/copper (C/Cu) composites. Experimental mechanical results for this novel high thermal conductivity material were recently reported by Bednarcyk et al. along with preliminary model results. The micromechanics model developed herein is based on an embedded approach. A micromechanics model for the local (micro-scale) behavior of the woven composite, the original method of cells (Aboudi), is embedded in a global (macro-scale) micromechanics model (the three-dimensional generalized method of cells (GMC-3D) (Aboudi). This approach allows representation of true repeating unit cells for woven metal matrix composites via GMC-3D, and representation of local effects, such as matrix plasticity, yarn porosity, and imperfect fiber-matrix bonding. In addition, the equations of GMC-3D were reformulated to significantly reduce the number of unknown quantities that characterize the deformation fields at the microlevel in order to make possible the analysis of actual microstructures of woven composites. The resulting micromechanical model (WCGMC) provides an intermediate level of geometric representation, versatility, and computational efficiency with respect to previous analytical and numerical models for woven composites, but surpasses all previous modeling work by allowing the mechanical response of a woven metal matrix composite, with an elastoplastic matrix, to be examined for the first time. WCGMC is employed to examine the effects of composite microstructure, porosity, residual stresses, and imperfect fiber-matrix bonding on the predicted mechanical response of 8H satin C/Cu. The previously reported experimental results are summarized, and the model predictions are compared to monotonic and cyclic tensile and shear test data. By considering appropriate levels of porosity, residual stresses, and imperfect fiber-matrix debonding, reasonably good qualitative and quantitative correlation is achieved between model and experiment.

Bednarcyk, Brett A.↗

DOE OSTI2024

Characterizing the impact of finite matrix block size on conservative particle transport through three-dimensional fracture networks

Mass transfer of solutes between fractures and the surrounding rock matrix exerts a noticeable signature on the tail of travel time distributions. When the width of the matrix is assumed to be infinite and advective transport through the fracture is sufficiently fast, the tails of the travel time distributions exhibit a classically expected slope of ψ(t) ∝ t -3/2 . However, studies have yet to characterize how solute transfer between fractures via diffusion through finite matrix blocks influences the tail’s slope in three-dimensional fractured media. Here, in this study, we assess the impact of finite matrix block size on breakthrough curve shape at different spatio-temporal scales by con ducting particle tracking simulations in three-dimensional discrete fracture networks. We consider a variety of hydrodynamic and geostructural proper ties to determine their relative impact on the resulting travel time distributions. We observe that the impact of matrix diffusion through a finite block on travel time distributions is similar to that of an infinite matrix block when the fracture spacing is sufficiently large, matrix diffusion is relatively weak, or transport is considered at an early control plane distance. We observe that the converse of these conditions, results in deviations from the classical ψ(t) ∝ t -3/2 scaling. These results provide a first step toward developing a metric to assess when finite block size effects are expected to significantly influence transport.

58 GEOSCIENCES↗

DOE OSTI2026

Powers of magnetic graph matrix: Fourier spectrum, walk compression, and applications

Magnetic graphs, originally developed to model quantum systems under magnetic fields, have recently emerged as a powerful framework for analyzing complex directed networks. Existing research has primarily used the spectral properties of the magnetic graph matrix to study global and stationary network features. However, their capacity to model local, nonequilibrium behaviors, often described by matrix powers, remains largely unexplored. We present a combinatorial interpretation of the magnetic graph matrix powers through directed walk profiles—counts of graph walks indexed by the number of edge reversals. Crucially, we establish that walk profiles correspond to a Fourier transform of magnetic matrix powers. The connection allows exact reconstruction of walk profiles from magnetic matrix powers at multiple discrete potentials, and more importantly, an even smaller number of potentials often suffices for accurate approximate reconstruction in real networks. This shows the empirical compressibility of the information captured by the magnetic matrix. This fresh perspective suggests further applications; for example, we illustrate how powers of the magnetic matrix can identify frustrated directed cycles (e.g., feedforward loops) and can be effectively employed for link prediction by encoding local structural details in directed graphs.

complex networks↗

NASA NTRS1994

Al2O3 fiber strength degradation in metal and intermetallic matrix composites

The mechanisms for fiber damage in single crystal Al2O3 fiber-reinforced composites were investigated. Both fiber fragmentation and fiber strength degradation were observed in composites with a variety of matrix compositions. Four mechanisms that may be contributing to the fiber strength loss have been proposed and include matrix reaction, reaction with binders, residual stress-induced damage, and pressure from hot pressing. The effect of matrix reaction was separated from the other three effects by sputter-coating the matrices on cleaned fibers and annealing with a temperature profile that simulates processing conditions. These experiments revealed that Y and Cr in FeCrAlY base alloys and Zr in NiAl alloys reacted with the fiber, and grooves and adherent particles were formed on the fiber surface which were responsible for the strength loss. The effects of the matrix reaction appeared to dominate over the other possible mechanisms, although evidence for reaction with binders was also found. Ridges on the fiber surface, which reflected the grain boundaries of the matrix, were also observed. In order for single-crystal Al2O3 to be used as a fiber in MMC's and IMC's, a matrix or protective coating which minimizes matrix reaction during processing will be necessary. Of the matrices investigated, the Thermo-span(sup TM) alloy was the least damaging to fiber properties.

ALUMINA/IRON CHROMIUM ALUMINUM↗

NASA NTRS1995

Cytoskeletal filament assembly and the control of cell spreading and function by extracellular matrix

This study was undertaken to analyze how cell binding to extracellular matrix produces changes in cell shape. We focused on the initial process of cell spreading that follows cell attachment to matrix and, thus, cell 'shape' changes are defined here in terms of alterations in projected cell areas, as determined by computerized image analysis. Cell spreading kinetics and changes in microtubule and actin microfilament mass were simultaneously quantitated in hepatocytes plated on different extracellular matrix substrata. The initial rate of cell spreading was highly dependent on the matrix coating density and decreased from 740 microns 2/h to 50 microns 2/h as the coating density was lowered from 1000 to 1 ng/cm2. At approximately 4 to 6 hours after plating, this initial rapid spreading rate slowed and became independent of the matrix density regardless of whether laminin, fibronectin, type I collagen or type IV collagen was used for cell attachment. Analysis of F-actin mass revealed that cell adhesion to extracellular matrix resulted in a 20-fold increase in polymerized actin within 30 minutes after plating, before any significant change in cell shape was observed. This was followed by a phase of actin microfilament disassembly which correlated with the most rapid phase of cell extension and ended at about 6 hours; F-actin mass remained relatively constant during the slow matrix-independent spreading phase. Microtubule mass increased more slowly in spreading cells, peaking at 4 hours, the time at which the transition between rapid and slow spreading rates was observed. However, inhibition of this early rise in microtubule mass using either nocodazole or cycloheximide did not prevent this transition. Use of cytochalasin D revealed that microfilament integrity was absolutely required for hepatocyte spreading whereas interference with microtubule assembly (using nocodazole or taxol) or protein synthesis (using cycloheximide) only partially suppressed cell extension. In contrast, cell spreading could be completely inhibited by combining suboptimal doses of cytochalasin D and nocodazole, suggesting that intact microtubules can stabilize cell form when the microfilament lattice is partially compromised. The physiological relevance of the cytoskeleton and cell shape in hepatocyte physiology was highlighted by the finding that a short exposure (6 hour) of cells to nocodazole resulted in production of smaller cells 42 hours later that exhibited enhanced production of a liver-specific product (albumin). These data demonstrate that spreading and flattening of the entire cell body is not driven directly by net polymerization of either microfilaments or microtubules.(ABSTRACT TRUNCATED AT 400 WORDS).

NASA Discipline Cell Biology↗

DOE OSTI2025

Communication Lower Bounds and Optimal Algorithms for Symmetric Matrix Computations

In this article, we focus on the communication costs of three symmetric matrix computations: (i) multiplying a matrix with its transpose, known as a symmetric rank-k update (SYRK) (ii) adding the result of the multiplication of a matrix with the transpose of another matrix and the transpose of that result, known as a symmetric rank-2k update (SYR2K) (iii) performing matrix multiplication with a symmetric input matrix (SYMM). All three computations appear in the Level 3 Basic Linear Algebra Subroutines (BLAS) and have wide use in applications involving symmetric matrices. We establish communication lower bounds for these kernels using sequential and distributed-memory parallel computational models, and we show that our bounds are tight by presenting communication-optimal algorithms for each setting. Our lower bound proofs rely on applying a geometric inequality for symmetric computations and analytically solving constrained nonlinear optimization problems. As a result, the symmetric matrix and its corresponding computations are accessed and performed according to a triangular block partitioning scheme in the optimal algorithms.

Al Daas, Hussam [Rutherford Appleton Laboratory, D↗

NASA NTRS1984

Chondrule rims and interchondrule matrix in UOC

Opaque rims around chondrules and clasts were distinguished from opaque, interchondrule matrix apparently unrelated spatially to chondrules and clasts. Microprobe and electron microscope techniques were used. The mean chemical composition for dark rim and matrix in Bishunpur and Tieschitz are similar to the opaque matrix of Huss, et al. However, the mean dark rim compositions in Bishunpur have significantly higher Fe, and lower Na, K, Al and Si than opaque interchondrule matrix. The opaque matrix of Huss, et al, essentially lies between these compositions. In Tieschitz only rim material was observed. In Tieschitz the rims are Si-poor and dominated by normative olivine (Fo50). Again there is an Na, K, Al component but is often nepheline normative rather than albitic. It too is probably present as glass, Ashworth (pers.comm.). In Bishunpur rims as well as the silicate-FeS, FeNi layering described by Allen, et al, discontinuous layering was observed within the silicate portion. This is apparently due to variations in the proportions of the components, particularly in the glassy phase. In Bishunpur there is a strong genetic link between matrix and rims, although rims seem to have formed under different, possibly more oxidizing, conditions. Also the presence of the same component in rims, matrix chondrules, and clasts suggests a common source.

Alexander, C.↗

NASA NTRS1984

Matrix material in type 3 chondrites - Occurrence, heterogeneity and relationship with chondrules

Variations between mean matrix compositions of individual type 3 ordinary chondrites are nearly fivefold, and partly reflect systematic differences between H, L, and LL matrices. Such variations are probably the result of a nebular separation of feldspathic material and ferromagnesian silicates. While compositions of chondrules and their matrix rims are normally unrelated, rim compositions are correlated with those of matrix lumps inside chondrules. Matrix lumps are as heterogeneous as chondrules, but mean chondrule and matrix compositions differ. Since bulk compositions of matrix lumps and rims have probably not changed significantly since their formation, the present matrix samples cannot represent typical chondrule precursor materials.

Scott, E. R. D.↗