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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 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
NASA NTRS1975

Diagonalization and simultaneous symmetrization of the gas-dynamic matrices

The hyperbolic nature of the unsteady, inviscid, gas-dynamic equations implies the existence of a similarity transformation for diagonalizing an arbitrary linear combination of coefficient matrices. It is shown that the individual matrices are simultaneously symmetrized by the similarity transformation. The transformations and their norms can be applied to the well-posedness of the Cauchy problem, linear stability theory for finite-difference approximations, and simplification of block-tridiagonal systems that arise in implicit time-split algorithms.

Warming, R. F.↗
NASA NTRS1975

Computation of transform domain covariance matrices

It is often of interest in applications to compute the covariance matrix of a random process transformed by a fast unitary transform. Here, the recursive definition of fast unitary transforms is used to derive recursive relations for the covariance matrices of the transformed process. These relations lead to fast methods of computation of covariance matrices and to substantial reductions of the number of arithmetic operations required.

Fino, B. J.↗
NASA NTRS1978

DYGABCD: A program for calculating linear A, B, C, and D matrices from a nonlinear dynamic engine simulation

A digital computer program, DYGABCD, was developed that generates linearized, dynamic models of simulated turbofan and turbojet engines. DYGABCD is based on an earlier computer program, DYNGEN, that is capable of calculating simulated nonlinear steady-state and transient performance of one- and two-spool turbojet engines or two- and three-spool turbofan engines. Most control design techniques require linear system descriptions. For multiple-input/multiple-output systems such as turbine engines, state space matrix descriptions of the system are often desirable. DYGABCD computes the state space matrices commonly referred to as the A, B, C, and D matrices required for a linear system description. The report discusses the analytical approach and provides a users manual, FORTRAN listings, and a sample case.

Geyser, L. C.↗
NASA NTRS1978

Coefficient matrices for implicit finite difference solution of the inviscid fluid conservation law equations

Although the Navier-Stokes equations describe most flows of interest in aerodynamics, the inviscid conservation law equations may be used for small regions with viscous forces. Thus, Euler equations and several time-accurate finite difference procedures, explicit and implicit, are discussed. Although implicit techniques require more computational work, they permit larger time steps to be taken without instability. It is noted that the Jacobian matrices for Euler equations in conservation-law form have certain eigenvalue-eigenvector properties which may be used to construct conservative-form coefficient matrices. This reduces the computation time of several implicit and semiimplicit schemes. Extensions of the basic approach to other areas are suggested.

Steger, J. L.↗
NASA NTRS1979

A program for calculating load coefficient matrices utilizing the force summation method, L218 (LOADS). Volume 2: Supplemental system design and maintenance document

The LOADS computer program L218 which calculates dynamic load coefficient matrices utilizing the force summation method is described. The load equations are derived for a flight vehicle in straight and level flight and excited by gusts and/or control motions. In addition, sensor equations are calculated for use with an active control system. The load coefficient matrices are calculated for the following types of loads: (1) translational and rotational accelerations, velocities, and displacements; (2) panel aerodynamic forces; (3) net panel forces; and (4) shears, bending moments, and torsions.

Anderson, L. R.↗
NASA NTRS1979

A program for calculating load coefficient matrices utilizing the force summation method, L218 (LOADS). Volume 1: Engineering and usage

The LOADS program L218, a digital computer program that calculates dynamic load coefficient matrices utilizing the force summation method, is described. The load equations are derived for a flight vehicle in straight and level flight and excited by gusts and/or control motions. In addition, sensor equations are calculated for use with an active control system. The load coefficient matrices are calculated for the following types of loads: translational and rotational accelerations, velocities, and displacements; panel aerodynamic forces; net panel forces; shears and moments. Program usage and a brief description of the analysis used are presented. A description of the design and structure of the program to aid those who will maintain and/or modify the program in the future is included.

Miller, R. D.↗
NASA NTRS1980

Performance properties of graphite reinforced composites with advanced resin matrices

The contribution of the resin matrix to the performance of the composite is studied with particular emphasis on the flammability, and thermal and mechanical properties. Of the several thermoset and thermoplastic matrices examined, the lowest fire-resistant properties of the composite have been observed with epoxy matrices. Bismaleimide A composites exhibit high fire-resistant properties, low moisture absorption, and good mechanical properties at 23 C. Bismaleimide B and phenolic retain their mechanical properties at elevated temperatures but have lower mechanical properties than the epoxy composites at ambient temperatures. Phenolic-novolac, polyethersulfone, and polyphenylsulfone composites exhibit high oxygen index and low smoke evolution.

Kourtides, D. A.↗
NASA NTRS1981

Evaluation of ceramic packed-rod regenerator matrices

An extensive evaluation of a modified cryocooler with various regenerator matrices is reported. The matrices examined are 0.015 in. diam. Pb spheres and 0.008, 0.015, and 0.030 in. diam. rods of a 0.2% SnCl2 doped ceramic labelled LS-8A. Specific heat and thermal conductivity data on these rod materials are also reported. The chronic pulverization/dusting problem common to Pb spheres was investigated. During a 1000 hr life test with 0.0008 in. diam. rods there was no degradation of the refrigerator performance, and a subsequent examination of the rods themselves revealed no evidence of breakage or pulverization. The load temperature characteristics for the rod packed regenerators were inferior to that for the Pb spheres, the effect being to shift the Pb spheres load curve up in temperature. This temperature shift was 5.0, 7.4, and 11.6K for the 0.0008, 0.015, and 0.030 in. diam. rods, respectively.

Lawless, W. N.↗
NASA NTRS1980

Structures and textures of the Murchison and Mighei carbonaceous chondrite matrices

High-resolution transmission electron microscopy has confirmed earlier observations that the character of the Murchison and Mighei fine-grained matrices is complex in mineralogy and texture. Layer structure minerals occur as planar laths, rounded grains or subhedral grains, and range in size from less than 100 A to about 1 micrometer. Serpentine-type and brucite-type structures predominate in the CM matrices. The occurrence of Povlen chrysolite and a vein of disordered mixed-layer and brucite-type material cutting a large lizardite-type grain suggests that at least some of the matrix materials were formed by alteration of preexisting material.

Mackinnon, I. D. R.↗
NASA NTRS1982

Oligonucleotide formation catalyzed by mononucleotide matrices

Pb(2+)-containing precipitates of mononucleotides form matrices which catalyze the self-condensation of nucleotide 5-prime-phosphorimidazolides and their condensation with nucleosides. The reactions exhibit base-pairing specificity between matrix nucleotide and substrate, and usually follow the Watson-Crick pairing rules. Although purine polynucleotides do not facilitate the oligomerization of pyrimidine nucleotide monomers in solution, it is interesting that purine-containing matrices do catalyze such a reaction. The significance of the results in the context of the prebiotic evolution of polynucleotides is discussed.

Lohrmann, R.↗
NASA NTRS1981

The algebraic theory of latent projectors in lambda matrices

Multivariable systems such as a finite-element model of vibrating structures, control systems, and large-scale systems are often formulated in terms of differential equations which give rise to lambda matrices. The present investigation is concerned with the formulation of the algebraic theory of lambda matrices and the relationship of latent roots, latent vectors, and latent projectors to the eigenvalues, eigenvectors, and eigenprojectors of the companion form. The chain rule for latent projectors and eigenprojectors for the repeated latent root or eigenvalues is given.

Denman, E. D.↗
NASA NTRS1985

Differentiating matrices for arbitrarily spaced grid points

Differentiating matrices allow the numerical differentiation of functions defined at points of a discrete grid. A type of differentiating matrix based on local approximation on a sequence of sliding subgrids is considered. Previous derivations of this type of matrix have been restricted to grids with uniformly spaced points, and the resulting derivative approximations have lacked precision, especially at endpoints. The new formulation allows grids which have arbitrarily space points. It is shown that high accuracy can be achieved through use of differentiating matrices on non-uniform grids which include near-boundary points. Use of the differentiating matrix as an operator to solve eigenvalue problems involving ordinary differential equations is also considered.

Lakin, W. D.↗
NASA NTRS1983

Transformation matrices between non-linear and linear differential equations

In the linearization of systems of non-linear differential equations, those systems which can be exactly transformed into the second order linear differential equation Y"-AY'-BY=0 where Y, Y', and Y" are n x 1 vectors and A and B are constant n x n matrices of real numbers were considered. The 2n x 2n matrix was used to transform the above matrix equation into the first order matrix equation X' = MX. Specially the matrix M and the conditions which will diagonalize or triangularize M were studied. Transformation matrices P and P sub -1 were used to accomplish this diagonalization or triangularization to return to the solution of the second order matrix differential equation system from the first order system.

Sartain, R. L.↗
NASA NTRS1987

Errors in plate rotations as described by covariance matrices and their combination in reconstructions

The use of covariance matrices to describe the errors in plate rotations and to combine the contributions of individual plate pairs for plate reconstructions is discussed. Particular attention is given to finite rotations and the combination of covariance matrices for a circuit of successive plate pair rotations. Examples of errors in plate reconstructions in which the position of the Pacific plate relative to North America is reconstructed are presented.

Jurdy, Donna M.↗
NASA NTRS1988

An O(N squared) method for computing the eigensystem of N by N symmetric tridiagonal matrices by the divide and conquer approach

An efficient method is proposed to solve the eigenproblem of N by N Symmetric Tridiagonal (ST) matrices. Unlike the standard eigensolvers which necessitate O(N cubed) operations to compute the eigenvectors of such ST matrices, the proposed method computes both the eigenvalues and eigenvectors with only O(N squared) operations. The method is based on serial implementation of the recently introduced Divide and Conquer (DC) algorithm. It exploits the fact that by O(N squared) of DC operations, one can compute the eigenvalues of N by N ST matrix and a finite number of pairs of successive rows of its eigenvector matrix. The rest of the eigenvectors--all of them or one at a time--are computed by linear three-term recurrence relations. Numerical examples are presented which demonstrate the superiority of the proposed method by saving an order of magnitude in execution time at the expense of sacrificing a few orders of accuracy.

Gill, Doron↗
NASA NTRS1988

Eigenvalue computation of large symmetric tridiagonal matrices on concurrent processors

Symmetric tridiagonal eigenvalue problems may arise indirectly in structural dynamic analysis. An algorithm for eigenvalue computation of large symmetric tridiagonal matrices on concurrent processors to meet the challenge of the new emerging computer hardware technology is presented. A standard bisection method in conjunction with Sylvester's Theorem is chosen to be converted into a parallel N-section algorithm. This parallel algorithm takes advantage of the multi-processor environment by carrying out N (number of processors) triangular factorizations of chosen shifted matrices in all processors concurrently and by minimizing communication between processors. The algorithm is designed for local-memory concurrent processors, i.e. message passing type processors. The efficiency and speed-up are given in terms of problem and machine parameters. The algorithm is very efficient when both the number of processors and the number of eigenvalues to be extracted are much smaller than the order of the tridiagonal matrix.

Chang, H. Y.↗
NASA NTRS1989

Factorization Of Positive Definite, Banded Hermitian Matrices

Report discusses application of Cholesky factorization algorithm to positive definite, banded Hermitian matrices. Begins by extending Cholesky factorization algorithm to cover uniformly-partitioned, banded, positive definite matrices of rank n that is real symmetric or Hermitian. Then two stratagems given for use of algorithm in concurrent-processing system in which N less than it has to be to enable factorization of matrix in as few serial steps as possible and where uniformly high efficiency expected from all processing elements. One of major purposes of this and related studies to maximize speedup and efficiency in system of concurrent-data-processing elements.

Salama, Moktar A.↗
NASA NTRS1988

Generalized Eigenvalues for pairs on heritian matrices

A study was made of certain special cases of a generalized eigenvalue problem. Let A and B be nxn matrics. One may construct a certain polynomial, P(A,B, lambda) which specializes to the characteristic polynomial of B when A equals I. In particular, when B is hermitian, that characteristic polynomial, P(I,B, lambda) has real roots, and one can ask: are the roots of P(A,B, lambda) real when B is hermitian. We consider the case where A is positive definite and show that when N equals 3, the roots are indeed real. The basic tools needed in the proof are Shur's theorem on majorization for eigenvalues of hermitian matrices and the interlacing theorem for the eigenvalues of a positive definite hermitian matrix and one of its principal (n-1)x(n-1) minors. The method of proof first reduces the general problem to one where the diagonal of B has a certain structure: either diag (B) = diag (1,1,1) or diag (1,1,-1), or else the 2 x 2 principal minors of B are all 1. According as B has one of these three structures, we use an appropriate method to replace A by a positive diagonal matrix. Since it can be easily verified that P(D,B, lambda) has real roots, the result follows. For other configurations of B, a scaling and a continuity argument are used to prove the result in general.

Rublein, George↗