Engineering Papers⌕ Search

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.

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

At least 217 records · Page 12
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Potential molecular targets for intervention in pelvic organ prolapse

Pelvic organ prolapse (POP) is a concerning gynecological benign illness in middle-aged and senior women. Its etiology is complex, the incidence rate is high, symptoms are clinically subjective, and its influence tends to be polarized. At present, for those who need medical treatment, whether surgical or non-surgical, complications cannot be ignored, and treatment effect needs to be optimized. However, there is a lack of accurate molecular biological interventions for the prevention, diagnosis, progression delay, and treatment of POP. Here, we reviewed the current state of understanding of the molecular mechanisms and factors associated with POP etiology. These factors include cyclins, matrix metal peptidases/tissue inhibitors of metalloproteinases, microRNAs, homeobox A11, transforming growth factor β1, insulin-like growth factor 1, fibulin 5, lysyl oxidase-like 1, oxidative stress, inflammatory response, estrogen, and other potential biomarkers associated with POP. In addition, relevant molecular targets that may be used to intervene in POP are summarized. The aim of this review was to provide more information to identify accurate potential biomarkers and/or molecular targets for the prevention, diagnosis, progression delay, and treatment of POP, with the goal of improving medical treatment for patients at-risk for POP or having POP. Continued research is needed to identify additional details of currently accepted molecular mechanisms and to identify additional mechanisms that contribute to POP.

Wu, Xia↗
NASA NTRS1997

Stress Intensity Factor Solutions for Multiple Edge Cracks in Ceramic Matrix Composites

NASA Lewis Research Center conducted a study to determine the stress intensity factor solutions for periodic arrays of bridged cracks for various crack spacings and crack lengths. Initially, the stress intensity factor of an array of unbridged multiple edge cracks was determined under constant global displacement as well as at a point load along the crack wake. These solutions are expected to contribute toward the development of a damage-based life-prediction methodology for CMC engine components.

Ghosn, Louis↗
NASA NTRS2002

Mechanical signaling and the cellular response to extracellular matrix in angiogenesis and cardiovascular physiology

Great advances have been made in the identification of the soluble angiogenic factors, insoluble extracellular matrix (ECM) molecules, and receptor signaling pathways that mediate control of angiogenesis--the growth of blood capillaries. This review focuses on work that explores how endothelial cells integrate these chemical signals with mechanical cues from their local tissue microenvironment so as to produce functional capillary networks that exhibit specialized form as well as function. These studies have revealed that ECM governs whether an endothelial cell will switch between growth, differentiation, motility, or apoptosis programs in response to a soluble stimulus based on its ability to mechanically resist cell tractional forces and thereby produce cell and cytoskeletal distortion. Transmembrane integrin receptors play a key role in this mechanochemical transduction process because they both organize a cytoskeletal signaling complex within the focal adhesion and preferentially focus mechanical forces on this site. Molecular filaments within the internal cytoskeleton--microfilaments, microtubules, and intermediate filaments--also contribute to the cell's structural and functional response to mechanical stress through their role as discrete support elements within a tensegrity-stabilized cytoskeletal array. Importantly, a similar form of mechanical control also has been shown to be involved in the regulation of contractility in vascular smooth muscle cells and cardiac myocytes. Thus, the mechanism by which cells perform mechanochemical transduction and the implications of these findings for morphogenetic control are discussed in the wider context of vascular development and cardiovascular physiology.

Non-NASA Center↗
NASA NTRS1983

Design for temperature and thermal buckling constraints employing a noneigenvalue formulation

A numerical procedure for simultaneous consideration of structural/thermal interactions during aircraft design is presented, with an emphasis on reentry vehicles such as the Orbiter. It has been shown that sequential design is inappropriate for reentry vehicles, due to the degradation of the material properties at elevated reentry temperatures. Attention is focused on thermal buckling, using an analytical technique that involves requiring that the stability matrix be positive definite, with the diagonal terms on the Gauss-Doolittle factor of the matrix also constrained to be positive. A finite element method is employed to calculate the derivative of the diagonal matrix, with optimization achieved by minimization of the mass of the structure and thermal protection system. Sample calculations are presented in terms of the aluminum structure and insulation for a section of the Orbiter wing bay.

Haftka, R. T.↗
NASA NTRS1991

A globally well-posed finite element algorithm for aerodynamics applications

A finite element CFD algorithm is developed for Euler and Navier-Stokes aerodynamic applications. For the linear basis, the resultant approximation is at least second-order-accurate in time and space for synergistic use of three procedures: (1) a Taylor weak statement, which provides for derivation of companion conservation law systems with embedded dispersion-error control mechanisms; (2) a stiffly stable second-order-accurate implicit Rosenbrock-Runge-Kutta temporal algorithm; and (3) a matrix tensor product factorization that permits efficient numerical linear algebra handling of the terminal large-matrix statement. Thorough analyses are presented regarding well-posed boundary conditions for inviscid and viscous flow specifications. Numerical solutions are generated and compared for critical evaluation of quasi-one- and two-dimensional Euler and Navier-Stokes benchmark test problems.

Iannelli, G. S.↗
NASA NTRS1976

Triangular covariance factorizations for

An improved computational form of the discrete Kalman filter is derived using an upper triangular factorization of the error covariance matrix. The covariance P is factored such that P = UDUT where U is unit upper triangular and D is diagonal. Recursions are developed for propagating the U-D covariance factors together with the corresponding state estimate. The resulting algorithm, referred to as the U-D filter, combines the superior numerical precision of square root filtering techniques with an efficiency comparable to that of Kalman's original formula. Moreover, this method is easily implemented and involves no more computer storage than the Kalman algorithm. These characteristics make the U-D method an attractive realtime filtering technique. A new covariance error analysis technique is obtained from an extension of the U-D filter equations. This evaluation method is flexible and efficient and may provide significantly improved numerical results. Cost comparisons show that for a large class of problems the U-D evaluation algorithm is noticeably less expensive than conventional error analysis methods.

Thornton, C. L.↗
DOE OSTI2020

Low synchronization Gram–Schmidt and generalized minimal residual algorithms

The Gram–Schmidt process uses orthogonal projection to construct the A = QR factorization of a matrix. When Q has linearly independent columns, the operator P = I - Q(QTQ)-1QT defines an orthogonal projection onto Q⊥. In finite precision, Q loses orthogonality as the factorization progresses. A family of approximate projections is derived with the form P = I - QTQT, with correction matrix T. When T = (QTQ)-1, and T is triangular, it is postulated that the best achievable orthogonality is $\mathcal{O}(ε)\mathcal{K}(A)$. We present new variants of modified (MGS) and classical Gram–Schmidt algorithms that require one global reduction step. An interesting form of the projector leads to a compact WY representation for MGS. In particular, the inverse compact WY MGS algorithm is equivalent to a lower triangular solve. Our main contribution is to introduce a backward normalization lag into the compact WY representation, resulting in a $\mathcal{O}(ε)\mathcal{K}[r_0, AV_m])$ stable Generalized Minimal Residual Method (GMRES) algorithm that requires only one global reduce per iteration. Finally, further improvements in performance are achieved by accelerating GMRES on GPUs.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1997

Tensegrity: the architectural basis of cellular mechanotransduction

Physical forces of gravity, hemodynamic stresses, and movement play a critical role in tissue development. Yet, little is known about how cells convert these mechanical signals into a chemical response. This review attempts to place the potential molecular mediators of mechanotransduction (e.g. stretch-sensitive ion channels, signaling molecules, cytoskeleton, integrins) within the context of the structural complexity of living cells. The model presented relies on recent experimental findings, which suggests that cells use tensegrity architecture for their organization. Tensegrity predicts that cells are hard-wired to respond immediately to mechanical stresses transmitted over cell surface receptors that physically couple the cytoskeleton to extracellular matrix (e.g. integrins) or to other cells (cadherins, selectins, CAMs). Many signal transducing molecules that are activated by cell binding to growth factors and extracellular matrix associate with cytoskeletal scaffolds within focal adhesion complexes. Mechanical signals, therefore, may be integrated with other environmental signals and transduced into a biochemical response through force-dependent changes in scaffold geometry or molecular mechanics. Tensegrity also provides a mechanism to focus mechanical energy on molecular transducers and to orchestrate and tune the cellular response.

Review↗
DOE OSTI2022

Fibrous anisotropy and mineral gradients within the radula stylus of chiton: Controlled stiffness and damage tolerance in a flexible biological composite

Over hundreds of millions of years, organisms have evolved architected structures via precise control over hierarchically assembled components, including the integration of dissimilar materials. One such example is found in the radula system of chitons, intertidal mollusks that feed on algae growing on the rock. Their radula consists of multiple rows of ultrahard teeth, each integrated with a foldable belt-like substrate via a stiff, yet flexible stylus, which is essential for efficient rasping during the feeding process. Here, we investigate the nano and micro-scale components and architectures as well as regional mechanical properties of the stylus, and their subsequent role during the rasping of Cryptochiton stelleri. Three important factors were determined to contribute to the regio-specific stiffness of the stylus: the presence of mineral components, highly oriented chitinous fibers, and a chemically cross-linked protein matrix. All these factors are varied throughout the stylus. There is a high mineral content on the trailing edge close to the tooth and a cross-linked matrix on the leading edge, both with orientational specific oriented chitin fibers that provide force transduction to the tooth. Conversely, there is a significant lack of mineral or cross-linked matrix in the proximal end as well as a low degree of fiber orientation, resulting in a flexible region that can accommodate torsion and flexure during rasping. Understanding the graded composite structure of the stylus and applying this unique design to various engineering fields such as soft robotics, biotechnology, and the medical industry, can inspire the production of high-performance materials.

Lee, Jung-Eun↗
NASA NTRS1994

Tensor-GMRES method for large sparse systems of nonlinear equations

This paper introduces a tensor-Krylov method, the tensor-GMRES method, for large sparse systems of nonlinear equations. This method is a coupling of tensor model formation and solution techniques for nonlinear equations with Krylov subspace projection techniques for unsymmetric systems of linear equations. Traditional tensor methods for nonlinear equations are based on a quadratic model of the nonlinear function, a standard linear model augmented by a simple second order term. These methods are shown to be significantly more efficient than standard methods both on nonsingular problems and on problems where the Jacobian matrix at the solution is singular. A major disadvantage of the traditional tensor methods is that the solution of the tensor model requires the factorization of the Jacobian matrix, which may not be suitable for problems where the Jacobian matrix is large and has a 'bad' sparsity structure for an efficient factorization. We overcome this difficulty by forming and solving the tensor model using an extension of a Newton-GMRES scheme. Like traditional tensor methods, we show that the new tensor method has significant computational advantages over the analogous Newton counterpart. Consistent with Krylov subspace based methods, the new tensor method does not depend on the factorization of the Jacobian matrix. As a matter of fact, the Jacobian matrix is never needed explicitly.

Feng, Dan↗
NASA NTRS1989

Strain intensity factor approach for predicting the strength of continuously reinforced metal matrix composites

A method was previously developed to predict the fracture toughness (stress intensity factor at failure) of composites in terms of the elastic constants and the tensile failing strain of the fibers. The method was applied to boron/aluminum composites made with various proportions of 0 deg and +/- 45 deg plies. Predicted values of fracture toughness were in gross error because widespread yielding of the aluminum matrix made the compliance very nonlinear. An alternate method was develolped to predict the strain intensity factor at failure rather than the stress intensity factor because the singular strain field was not affected by yielding as much as the stress field. Far-field strains at failure were calculated from the strain intensity factor, and then strengths were calculated from the far-field strains using uniaxial stress-strain curves. The predicted strengths were in good agreement with experimental values, even for the very nonlinear laminates that contained only +/- 45 deg plies. This approach should be valid for other metal matrix composites that have continuous fibers.

Poe, Clarence C., Jr.↗
NASA NTRS1988

Strain intensity factor approach for predicting the strength of continuously reinforced metal matrix composites

A method was previously developed to predict the fracture toughness (stress intensity factor at failure) of composites in terms of the elastic constants and the tensile failing strain of the fibers. The method was applied to boron/aluminum composites made with various proportions of 0 to + or - 45 deg plies. Predicted values of fracture toughness were in gross error because widespread yielding of the aluminum matrix made the compliance very nonlinear. An alternate method was developed to predict the strain intensity factor at failure rather than the stress intensity factor because the singular strain field was not affected by yielding as much as the stress field. Strengths of specimens containing crack-like slits were calculated from predicted failing strains using uniaxial stress-strain curves. Predicted strengths were in good agreement with experimental values, even for the very nonlinear laminates that contained only + or - 45 deg plies. This approach should be valid for other metal matrix composites that have continuous fibers.

Poe, C. C., Jr.↗
NASA NTRS2000

User's Manual for PCSMS (Parallel Complex Sparse Matrix Solver)

PCSMS (Parallel Complex Sparse Matrix Solver) is a computer code written to make use of the existing real sparse direct solvers to solve complex, sparse matrix linear equations. PCSMS converts complex matrices into real matrices and use real, sparse direct matrix solvers to factor and solve the real matrices. The solution vector is reconverted to complex numbers. Though, this utility is written for Silicon Graphics (SGI) real sparse matrix solution routines, it is general in nature and can be easily modified to work with any real sparse matrix solver. The User's Manual is written to make the user acquainted with the installation and operation of the code. Driver routines are given to aid the users to integrate PCSMS routines in their own codes.

Reddy, C. J.↗
NASA NTRS2011

A Multiple Sphere T-Matrix Fortran Code for Use on Parallel Computer Clusters

A general-purpose Fortran-90 code for calculation of the electromagnetic scattering and absorption properties of multiple sphere clusters is described. The code can calculate the efficiency factors and scattering matrix elements of the cluster for either fixed or random orientation with respect to the incident beam and for plane wave or localized- approximation Gaussian incident fields. In addition, the code can calculate maps of the electric field both interior and exterior to the spheres.The code is written with message passing interface instructions to enable the use on distributed memory compute clusters, and for such platforms the code can make feasible the calculation of absorption, scattering, and general EM characteristics of systems containing several thousand spheres.

Mackowski, D. W.↗
DOE OSTI2020

Finite Element Modeling of the Fiber-Matrix Interface in Polymer Composites

Polymer composites are used in numerous industries due to their high specific strength and high specific stiffness. Composites have markedly different properties than both the reinforcement and the matrix. Of the several factors that govern the final properties of the composite, the interface is an important factor that influences the stress transfer between the fiber and matrix. The present study is an effort to characterize and model the fiber-matrix interface in polymer matrix composites. Finite element models were developed to study the interfacial behavior during pull-out of a single fiber in continuous fiber-reinforced polymer composites. A three-dimensional (3D) unit-cell cohesive damage model (CDM) for the fiber/matrix interface debonding was employed to investigate the effect of interface/sizing coverage on the fiber. Furthermore, a two-dimensional (2D) axisymmetric model was used to (a) analyze the sensitivity of interface stiffness, interface strength, friction coefficient, and fiber length via a parametric study; and (b) study the shear stress distribution across the fiber-interface-matrix zone. It was determined that the force required to debond a single fiber from the matrix is three times higher if there is adequate distribution of the sizing on the fiber. The parametric study indicated that cohesive strength was the most influential factor in debonding. Moreover, the stress distribution model showed the debonding mechanism of the interface. It was observed that the interface debonded first from the matrix and remained in contact with the fiber even when the fiber was completely pulled out.

36 MATERIALS SCIENCE↗
NASA NTRS2003

Multilineage differentiation of rhesus monkey embryonic stem cells in three-dimensional culture systems

In the course of normal embryogenesis, embryonic stem (ES) cells differentiate along different lineages in the context of complex three-dimensional (3D) tissue structures. In order to study this phenomenon in vitro under controlled conditions, 3D culture systems are necessary. Here, we studied in vitro differentiation of rhesus monkey ES cells in 3D collagen matrixes (collagen gels and porous collagen sponges). Differentiation of ES cells in these 3D systems was different from that in monolayers. ES cells differentiated in collagen matrixes into neural, epithelial, and endothelial lineages. The abilities of ES cells to form various structures in two chemically similar but topologically different matrixes were different. In particular, in collagen gels ES cells formed gland-like circular structures, whereas in collagen sponges ES cells were scattered through the matrix or formed aggregates. Soluble factors produced by feeder cells or added to the culture medium facilitated ES cell differentiation into particular lineages. Coculture with fibroblasts in collagen gel facilitated ES cell differentiation into cells of a neural lineage expressing nestin, neural cell adhesion molecule, and class III beta-tubulin. In collagen sponges, keratinocytes facilitated ES cell differentiation into cells of an endothelial lineage expressing factor VIII. Exogenous granulocyte-macrophage colony-stimulating factor further enhanced endothelial differentiation. Thus, both soluble factors and the type of extracellular matrix seem to be critical in directing differentiation of ES cells and the formation of tissue-like structures. Three-dimensional culture systems are a valuable tool for studying the mechanisms of these phenomena.

Pluripotent Stem Cells/cytology/physiology↗