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At least 793 records · Page 44

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NASA NTRS1972

Numerical stability in problems of linear algebra.

Mathematical problems are introduced as mappings from the space of input data to that of the desired output information. Then a numerical process is defined as a prescribed recurrence of elementary operations creating the mapping of the underlying mathematical problem. The ratio of the error committed by executing the operations of the numerical process (the roundoff errors) to the error introduced by perturbations of the input data (initial error) gives rise to the concept of lambda-stability. As examples, several processes are analyzed from this point of view, including, especially, old and new processes for solving systems of linear algebraic equations with tridiagonal matrices. In particular, it is shown how such a priori information can be utilized as, for instance, a knowledge of the row sums of the matrix. Information of this type is frequently available where the system arises in connection with the numerical solution of differential equations.

Babuska, I.↗

NASA NTRS1972

Study of X-ray diffraction on aging alloys with different degrees of volume discrepancy between the precipitation phase and the matrix

Study of the diffraction patterns of X rays diffracted by dispersion-hardened alloys with various degrees of difference between the specific atomic volumes of their precipitation phases and matrices. Experiments were performed on aging alloys KhN77TIuR (nimonic) and KhN67VMTIuO, which have the same types of gamma solid solutions and precipitating gamma prime phases, but differ considerably with respect to the volume factor. It is found that in the decay of supersaturated solid solutions for which the difference between the specific atomic volumes of the precipitation phase and the matrix is small (alloy KhN67VMTIuO) the nature of the intensity distribution of the diffraction lines remains practically unchanged regardless of the aging, while in cases where the volume discrepancy is large (alloy KhN77TIuR) significant changes in the appearance of the diffraction lines are recorded.-

Gitgarts, M. I.↗

NASA NTRS1972

Eigenvalues of singular differential operators by finite difference methods. II.

Note is made of an earlier paper which defined finite difference operators for the Hilbert space L2(m), and gave the eigenvalues for these operators. The present work examines eigenvalues for higher order singular differential operators by using finite difference methods. The two self-adjoint operators investigated are defined by a particular value in the same Hilbert space, L2(m), and are strictly positive with compact inverses. A class of finite difference operators is considered, with the idea of application to the theory of Toeplitz matrices. The approximating operators consist of a good approximation plus a perturbing operator.

Baxley, J. V.↗

NASA NTRS1972

Thin film fuel cell electrodes.

Earlier work shows that fuel cell electrodes prepared by sputtering thin films of platinum on porous vycor substrates avoid diffusion limitations even at high current densities. The presented study shows that the specific activity of sputtered platinum is not unusually high. Performance limitations are found to be controlled by physical processes, even at low loadings. Catalyst activity is strongly influenced by platinum sputtering parameters, which seemingly change the surface area of the catalyst layer. The use of porous nickel as a substrate shows that pore size of the substrate is an important parameter. It is noted that electrode performance increases with increasing loading for catalyst layers up to two microns thick, thus showing the physical properties of the sputtered layer to be different from platinum foil. Electrode performance is also sensitive to changing differential pressure across the electrode. The application of sputtered catalyst layers to fuel cell matrices for the purpose of obtaining thin total cells appears feasible.

Asher, W. J.↗

NASA NTRS1972

System theory on group manifolds and coset spaces.

The purpose of this paper is to study questions regarding controllability, observability, and realization theory for a particular class of systems for which the state space is a differentiable manifold which is simultaneously a group or, more generally, a coset space. We show that it is possible to give rather explicit expressions for the reachable set and the set of indistinguishable states in the case of autonomous systems. We also establish a type of state space isomorphism theorem. Our objective is to reduce all questions about the system to questions about Lie algebras generated from the coefficient matrices entering in the description of the system and in that way arrive at conditions which are easily visualized and tested.

Brockett, R. W.↗

NASA NTRS1972

Spectral factorization in periodically time-varying systems and application to navigation problems.

Spectral factorization has been used previously to derive the steady-state solution of Kalman filtering equations without iteration for constant coefficient systems. The present work extends the spectral factorization algorithm to time-varying systems having periodic coefficient matrices for cases of both discrete and continuous systems. Time-consuming, expensive iterations of sequential covariance equations are not required to reach the final solution since this is an algebraic algorithm employing existing eigenvalue, eigenvector subroutines. The computer program incorporating the algorithm is suitable for sensitivity studies in formulating navigation and guidance strategies of low-thrust interplanetary missions. The determination of an optimum tracking pattern from an earth station is examined as an example.

Nishimura, T.↗

NASA NTRS1972

Stability of distributed parameter systems.

A theorem is derived for the stability of solutions of general linear partial differential equations. A norm of the state space in the form of multiple integrals over the spatial domain is used for the Liapunov functional. Theorems and lemmas are also given for linear time-invariant constant coefficient distributed parameter systems, a class of nonlinear distributed parameter systems and for others with a Lure-type nonlinearity. The theorem conditions are similar to those known for corresponding ordinary differential equations but with operators replacing matrices.

Park, K. E.↗

NASA NTRS1973

Eigenvalue routine by Sturm sequence method

Computer program has been generated for efficient solution of certain broad classes of eigenvalue problems. Procedure fully exploits banded nature of associated matrices and further enables user to compute either all roots or any specific ones desired. Special storage options enable storing only nonzero elements of associated main matrix of eigenvalue problem.

Gupta, K. K.↗

NASA NTRS1974

The static nonlinear analysis of shells of revolution (SNASOR II)

Utilizing stiffness matrices and supplying as input the loading and boundary conditions, program generates equilibrium equations for structure. Nonlinear strain energy terms result in pseudogeneralized forces which are combined with applied generalized forces. Resulting set of nonlinear algebraic equilibrium equations is solved by one of several methods.

Stricklin, J. A.↗

NASA NTRS1972

DORCA 2 computer program. Volume 2: Programmer's manual

A guide for coding the Dynamic Operational Requirements and Cost Analysis Program (DORCA 2) is presented. The manual provides a detailed operation of every subroutine, the layout in core of the major matrices and arrays, and the meaning of all program values. Flow charts are included.

Gold, B. J.↗

NASA NTRS1972

An experimental and theoretical evaluation of increased thermal diffusivity phase change devices

This study was to experimentally evaluate and mathematically model the performance of phase change thermal control devices containing high thermal conductivity metal matrices. Three aluminum honeycomb filters were evaluated at five different heat flux levels using n-oct-adecane as the test material. The system was mathematically modeled by approximating the partial differential equations with a three-dimensional implicit alternating direction technique. The mathematical model predicts the system quite well. All of the phase change times are predicted. The heating of solid phase is predicted exactly while there is some variation between theoretical and experimental results in the liquid phase. This variation in the liquid phase could be accounted for by the fact that there are some heat losses in the cell and there could be some convection in the experimental system.

White, S. P.↗

NASA NTRS1973

Finite aperture waveguide laser resonators

A general theory of finite aperture waveguide laser resonators is developed which represents the external reflectors by matrices which couple linearly polarized waveguide modes having the same azimuthal symmetry. The theory allows the determination of resonator efficiency, resonator frequencies, and laser near and far field patterns. Computations of the coupling loss for the fundamental waveguide mode as a function of mirror curvature, separation, and aperture are in agreement with recent infinite aperture calculations in the limit of large apertures and indicate three low-loss configurations: large radius of curvature mirrors close to the guide; large radius of curvature mirrors centered at the guide entrance; and generally smaller curvature mirrors separated by half their curvature from the guide entrance. Design guidelines for construction of high efficiency CO2, CO and He-Ne waveguide laser resonators are summarized in tabular form.

Degnan, J. J.↗

NASA NTRS1972

Study of propellant dynamics in a shuttle type launch vehicle

A method and an associated digital computer program for evaluating the vibrational characteristics of large liquid-filled rigid wall tanks of general shape are presented. A solution procedure was developed in which slosh modes and frequencies are computed for systems mathematically modeled as assemblages of liquid finite elements. To retain sparsity in the assembled system mass and stiffness matrices, a compressible liquid element formulation was incorporated in the program. The approach taken in the liquid finite element formulation is compatible with triangular and quadrilateral structural finite elements so that the analysis of liquid motion can be coupled with flexible tank wall motion at some future time. The liquid element repertoire developed during the course of this study consists of a two-dimensional triangular element and a three-dimensional tetrahedral element.

Jones, C. E.↗

NASA NTRS1973

Development of polyphenylquinoxaline graphite composites

The potential of polyphenylquinoxaline (PPQ)/graphite composites to serve as structural material at 316 C (600 F)has been demonstrated using a block copolymer, BlCo(13), PPQ derivative. Initially, thirteen polyphenylquinoxalines were evaluated. From this work, four candidate polymers were selected for preliminary evaluation as matrices for HMS graphite fiber reinforced composites. The preliminary composite evaluation enabled selection of one of the four polymers for advanced composite preparation and testing. Using an experimentally established cure schedule for each of the four polymers, preliminary laminates of 50% resin volume content, prepared without postcure, were tested for flexure strength and modulus, interlaminar shear strength (short beam), and tensile strength and modulus at ambient temperature. A block copolymer (Bl Co 13) derived from one mole p-bis (phenylglyoxalyl) benzene, one fourth mole 3,3'-diaminobenzidine and three-fourths mole 3,3', 4,4'-tetraminobenzophenone was selected for extensive study. Tensile, flexural, and interlaminar shear values were obtained after aging and testing postcured BlCo(13) laminates at 316 C (600 F). The potential of PPQ/graphite laminates to serve as short term structural materials at temperatures up to 371 C (700 F) was demonstrated through weight loss experiments.

Hoggatt, J. T.↗

NASA NTRS1973

Control of a flexible space shuttle vehicle

The application of optimal control technology to the design of a controller for the space shuttle descent was studied using weighting matrices adjusted through iteration to reduce response peaks, which are defined as mean magnitude plus sigma values. The synthesis techniques, and optimal controller design are discussed along with simplified controller design. Quantitative characteristics of the optimal controller, effects of variation of sample rate, and simplified controller data are included.

Harvey, C. A.↗

NASA NTRS1972

A parametric study of planform and aeroelastic effects on aerodynamic center, alpha- and q- stability derivatives. Appendix D: Procedures used to determine the mass distribution for idealized low aspect ratio two spar fighter wings

The procedures used to establish the mass matrices characteristics for the fighter type wings studied are given. A description of the procedure used to find the mass associated with a specific aerodynamic panel is presented and some examples of the application of the procedure are included.

Roskam, J.↗

NASA NTRS1973

Feasibility of producing cast-refractory metal-fiber superalloy composites

A study was conducted to evaluate the feasibility of direct casting as a practical method for producing cast superalloy tungsten or columbium alloy fiber composites while retaining a high percentage of fiber strength. Fourteen nickel base, four cobalt, and three iron based matrices were surveyed for their degree of reaction with the metal fibers. Some stress-rupture results were obtained at temperatures of 760, 816, 871, and 1093 C for a few composite systems. The feasibility of producing acceptable composites of some cast nickel, cobalt, and iron matrix alloys with tungsten or columbium alloy fibers was demonstrated.

Mcintyre, R. D.↗

NASA NTRS1973

Ion optical design with applications to a solar wind mass spectrometer

The design of charged particle beam transport systems at lower energies is discussed. Topics discussed include: index of refraction, photometry, phase space, matrices, lenses and imaging, charged particle trajectories in crossed electric and magnetic fields, design parameters for the Wien filter, and electrostatic energy analyzer design, an annotated bibliography is presented.

Coplan, M.↗