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NASA NTRS1989

Theoretical analysis of compatibility of several reinforcement materials with NiAl and FeAl matrices

Several potential reinforcement materials were assessed for their chemical, coefficient of thermal expansion (CTE), and mechanical compatibility with the intermetallic matrices based on NiAl and FeAl. Among the ceramic reinforcement materials, Al2O3, TiC, and TiB2, appear to be the optimum choices for NiAl and FeAl matrices. However, the problem of CTE mismatch with the matrix needs to be solved for these three reinforcement materials. Beryllium-rich intermetallic compounds can be considered as potential reinforcement materials provided suitable reaction barrier coatings can be developed for these. Based on preliminary thermodynamic calculations, Sc2O3 and TiC appear to be suitable as reaction barrier coatings for the beryllides. Several reaction barrier coatings are also suggested for the currently available SiC fibers.

Misra, Ajay K.↗

NASA NTRS1990

Computer-Access-Code Matrices

Authorized users respond to changing challenges with changing passwords. Scheme for controlling access to computers defeats eavesdroppers and "hackers". Based on password system of challenge and password or sign, challenge, and countersign correlated with random alphanumeric codes in matrices of two or more dimensions. Codes stored on floppy disk or plug-in card and changed frequently. For even higher security, matrices of four or more dimensions used, just as cubes compounded into hypercubes in concurrent processing.

Collins, Earl R., Jr.↗

NASA NTRS1990

Flux Jacobian Matrices For Equilibrium Real Gases

Improved formulation includes generalized Roe average and extension to three dimensions. Flux Jacobian matrices derived for use in numerical solutions of conservation-law differential equations of inviscid flows of ideal gases extended to real gases. Real-gas formulation of these matrices retains simplifying assumptions of thermodynamic and chemical equilibrium, but adds effects of vibrational excitation, dissociation, and ionization of gas molecules via general equation of state.

Vinokur, Marcel↗

NASA NTRS1989

A restricted signature normal form for Hermitian matrices, quasi-spectral decompositions, and applications

In recent years, a number of results on the relationships between the inertias of Hermitian matrices and the inertias of their principal submatrices appeared in the literature. We study restricted congruence transformation of Hermitian matrices M which, at the same time, induce a congruence transformation of a given principal submatrix A of M. Such transformations lead to concept of the restricted signature normal form of M. In particular, by means of this normal form, we obtain short proofs of most of the known inertia theorems and also derive some new results of this type. For some applications, a special class of almost unitary restricted congruence transformations turns out to be useful. We show that, with such transformations, M can be reduced to a quasi-diagonal form which, in particular, displays the eigenvalues of A. Finally, applications of this quasi-spectral decomposition to generalize inverses and Hermitian matrix pencils are discussed.

Freund, Roland W.↗

NASA NTRS1989

Conjugate gradient type methods for linear systems with complex symmetric coefficient matrices

We consider conjugate gradient type methods for the solution of large sparse linear system Ax equals b with complex symmetric coefficient matrices A equals A(T). Such linear systems arise in important applications, such as the numerical solution of the complex Helmholtz equation. Furthermore, most complex non-Hermitian linear systems which occur in practice are actually complex symmetric. We investigate conjugate gradient type iterations which are based on a variant of the nonsymmetric Lanczos algorithm for complex symmetric matrices. We propose a new approach with iterates defined by a quasi-minimal residual property. The resulting algorithm presents several advantages over the standard biconjugate gradient method. We also include some remarks on the obvious approach to general complex linear systems by solving equivalent real linear systems for the real and imaginary parts of x. Finally, numerical experiments for linear systems arising from the complex Helmholtz equation are reported.

Freund, Roland↗

NASA NTRS1993

Computing Vibration-Mode Matrices From Finite-Element Output

Postprocessing algorithms devised to facilitate vibrational-mode analyses of dynamics of complicated structures. Yields inertia matrices and elastic/rigid-coupling matrices. Such analyses important in simulation and control in active suppression of vibrations in large building or in precise aiming of large antenna.

Levy, Roy↗

NASA NTRS1993

Model updating based on sensitivities of system matrices

A new approach, which allows the physical parameters to be adjusted and preserves the structural connectivity condition, is developed in this paper. This approach is based on the sensitivities of the mass and stiffness matrices with respect to physical parameters in an attempt to use test data to correct the analytical model. The analytical mass and stiffness matrices can be corrected simultaneously. The modal data of the updated model dramatically converges to that of the test model. A numerical example is presented to illustrate the feasibility of this approach. Comparisons with the other methods are also given.

Huang, Hsin-Hsen↗

NASA NTRS1993

Chemical stability of titanium diboride reinforcement in nickel aluminide matrices

Chemical stability of TiB2 reinforcement in NiAl (45 at percent Al) and Ni3Al (24 at percent Al) matrices has been theoretically and experimentally investigated. Calculations were made using thermodynamic properties of the systems to predict behavior at temperatures between 1173 and 1573 K. Experimental investigation of hot-press consolidated TiB2 particulate/prealloyed matrix powder blends were conducted using energy dispersive X-ray analysis, XRD, AES, and TEM. The theoretical and experimental analyses suggest that TiB2 is chemically stable in both matrices up to 1573 K; however, TiB2 was found to be less active in NiAl than in Ni3Al due to lower nickel activity in NiAl.

Rigney, J. D.↗

NASA NTRS1995

Asymptotic Spectra Of Banded Quasi-Toeplitz Matrices

Paper presents theoretical and numerical study of asymptotic spectra of eigenvalues of banded Toeplitz and quasi-Toeplitz matrices. Emphasis in study on non-normal banded Toeplitz and quasi-Toeplitz matrices of arbitrarily large order and relatively small bandwidth.

Beam, Richard↗

NASA NTRS1995

The detector response matrices of the burst and transient source experiment (BATSE) on the Compton Gamma Ray Observatory

The detector response matrices for the Burst And Transient Source Experiment (BATSE) on board the Compton Gamma Ray Observatory (CGRO) are described, including their creation and operation in data analysis. These response matrices are a detailed abstract representation of the gamma-ray detectors' operating characteristics that are needed for data analysis. They are constructed from an extensive set of calibration data coupled with a complex geometry electromagnetic cascade Monte Carlo simulation code. The calibration tests and simulation algorithm optimization are described. The characteristics of the BATSE detectors in the spacecraft environment are also described.

Pendleton, Geoffrey N.↗

NASA NTRS1992

Sparse Matrices in MATLAB: Design and Implementation

The matrix computation language and environment MATLAB is extended to include sparse matrix storage and operations. The only change to the outward appearance of the MATLAB language is a pair of commands to create full or sparse matrices. Nearly all the operations of MATLAB now apply equally to full or sparse matrices, without any explicit action by the user. The sparse data structure represents a matrix in space proportional to the number of nonzero entries, and most of the operations compute sparse results in time proportional to the number of arithmetic operations on nonzeros.

Gilbert, John R.↗

NASA NTRS1999

The Production of Polycyclic Aromatic Hydrocarbon Anions in Inert Gas Matrices Doped with Alkali Metals. Electronic Absorption Spectra of the Pentacene Anion (C22H14(-))

The absorption spectra of pentacene (C22H14) and its radical cation (C22H14(+)) and anion (C22H14(-)) isolated in inert-gas matrices of Ne, Ar, and Kr are reported from the ultraviolet to the near-infrared. The associated vibronic band systems and their spectroscopic assignments are discussed together with the physical and chemical conditions governing ion (and counterion) production in the solid matrix. In particular, the formation of isolated pentacene anions is found to be optimized in matrices doped with alkali metal (Na and K).

Halasinski, Thomas M.↗

NASA NTRS1994

Perceptual Optimization of DCT Color Quantization Matrices

Many image compression schemes employ a block Discrete Cosine Transform (DCT) and uniform quantization. Acceptable rate/distortion performance depends upon proper design of the quantization matrix. In previous work, we showed how to use a model of the visibility of DCT basis functions to design quantization matrices for arbitrary display resolutions and color spaces. Subsequently, we showed how to optimize greyscale quantization matrices for individual images, for optimal rate/perceptual distortion performance. Here we describe extensions of this optimization algorithm to color images.

Watson, Andrew B.↗

NASA NTRS2001

Spectroscopy of Cosmic Carbon Analogs in Inert-Gas Matrices and in the Gas-Phase: Comparative Results and Perspectives for Astrophysics

Recent studies of the spectroscopy of large (up to approx. 50 carbon atoms) neutral and Ionized polycyclic aromatic hydrocarbons (PAHs) and Fullerenes isolated in inert gas matrices will be presented. The advantages and the limitations of matrix isolation spectroscopy for the study of the molecular spectroscopy of interstellar dust analogs will be discussed. The laboratory data will be compared to the astronomical spectra (the interstellar extinction, the diffuse interstellar bands). Finally, the spectra of PAH ions isolated in neon/argon matrices will be compared to the spectra obtained for PAH ion seeded in a supersonic expansion. The astrophysical implications and future perspectives will be discussed.

Salama, Farid↗

NASA NTRS2004

Characteristic Matrices for Spherical Shell Photonic Systems

We establish a parallel between the transfer matrix used in the study of plane-parallel photonic structures and the matrix characterizing transfer of partial waves in concentric spheres. We derive explicit expressions for the elements of the transfer matrix for concentric spherical layers, and from those expressions derive the scattering coefficients of a multilayered sphere. The transfer matrices are 4x4 block diagonal with only four independent elements. Matrix elements for the case of TM waves are related to those for the case of TE waves through simple interchange and multiplicative constants. In analogy with plane parallel layers, the transfer matrix for concentric multilayers is simply the product of the transfer matrices of the individual layers.

Fuller, Kirk A.↗

NASA NTRS1997

On the Possibility of Ill-Conditioned Covariance Matrices in the First-Order Two-Step Estimator

The first-order two-step nonlinear estimator, when applied to a problem of orbital navigation, is found to occasionally produce first step covariance matrices with very low eigenvalues at certain trajectory points. This anomaly is the result of the linear approximation to the first step covariance propagation. The study of this anomaly begins with expressing the propagation of the first and second step covariance matrices in terms of a single matrix. This matrix is shown to have a rank equal to the difference between the number of first step states and the number of second step states. Furthermore, under some simplifying assumptions, it is found that the basis of the column space of this matrix remains fixed once the filter has removed the large initial state error. A test matrix containing the basis of this column space and the partial derivative matrix relating first and second step states is derived. This square test matrix, which has dimensions equal to the number of first step states, numerically drops rank at the same locations that the first step covariance does. It is formulated in terms of a set of constant vectors (the basis) and a matrix which can be computed from a reference trajectory (the partial derivative matrix). A simple example problem involving dynamics which are described by two states and a range measurement illustrate the cause of this anomaly and the application of the aforementioned numerical test in more detail.

Garrison, James L.↗

NASA NTRS2005

Porous media matric potential and water content measurements during parabolic flight

Control of water and air in the root zone of plants remains a challenge in the microgravity environment of space. Due to limited flight opportunities, research aimed at resolving microgravity porous media fluid dynamics must often be conducted on Earth. The NASA KC-135 reduced gravity flight program offers an opportunity for Earth-based researchers to study physical processes in a variable gravity environment. The objectives of this study were to obtain measurements of water content and matric potential during the parabolic profile flown by the KC-135 aircraft. The flight profile provided 20-25 s of microgravity at the top of the parabola, while pulling 1.8 g at the bottom. The soil moisture sensors (Temperature and Moisture Acquisition System: Orbital Technologies, Madison, WI) used a heat-pulse method to indirectly estimate water content from heat dissipation. Tensiometers were constructed using a stainless steel porous cup with a pressure transducer and were used to measure the matric potential of the medium. The two types of sensors were placed at different depths in a substrate compartment filled with 1-2 mm Turface (calcined clay). The ability of the heat-pulse sensors to monitor overall changes in water content in the substrate compartment decreased with water content. Differences in measured water content data recorded at 0, 1, and 1.8 g were not significant. Tensiometer readings tracked pressure differences due to the hydrostatic force changes with variable gravity. The readings may have been affected by changes in cabin air pressure that occurred during each parabola. Tensiometer porous membrane conductivity (function of pore size) and fluid volume both influence response time. Porous media sample height and water content influence time-to-equilibrium, where shorter samples and higher water content achieve faster equilibrium. Further testing is needed to develop these sensors for space flight applications.

Parabolic Flight↗

NASA NTRS2009

Subspace Iteration Method for Complex Eigenvalue Problems with Nonsymmetric Matrices in Aeroelastic System

Modern airplane design is a multidisciplinary task which combines several disciplines such as structures, aerodynamics, flight controls, and sometimes heat transfer. Historically, analytical and experimental investigations concerning the interaction of the elastic airframe with aerodynamic and in retia loads have been conducted during the design phase to determine the existence of aeroelastic instabilities, so called flutter .With the advent and increased usage of flight control systems, there is also a likelihood of instabilities caused by the interaction of the flight control system and the aeroelastic response of the airplane, known as aeroservoelastic instabilities. An in -house code MPASES (Ref. 1), modified from PASES (Ref. 2), is a general purpose digital computer program for the analysis of the closed-loop stability problem. This program used subroutines given in the International Mathematical and Statistical Library (IMSL) (Ref. 3) to compute all of the real and/or complex conjugate pairs of eigenvalues of the Hessenberg matrix. For high fidelity configuration, these aeroelastic system matrices are large and compute all eigenvalues will be time consuming. A subspace iteration method (Ref. 4) for complex eigenvalues problems with nonsymmetric matrices has been formulated and incorporated into the modified program for aeroservoelastic stability (MPASES code). Subspace iteration method only solve for the lowest p eigenvalues and corresponding eigenvectors for aeroelastic and aeroservoelastic analysis. In general, the selection of p is ranging from 10 for wing flutter analysis to 50 for an entire aircraft flutter analysis. The application of this newly incorporated code is an experiment known as the Aerostructures Test Wing (ATW) which was designed by the National Aeronautic and Space Administration (NASA) Dryden Flight Research Center, Edwards, California to research aeroelastic instabilities. Specifically, this experiment was used to study an instability known as flutter. ATW was a small-scale airplane wing comprised of an airfoil and wing tip boom. This wing was formulated based on a NACA-65A004 airfoil shape with a 3.28 aspect ratio. The wing had a span of 18 inch with root chord length of 13.2 inch and tip chord length of 8.7 inch. The total area of this wing was 197 square inch. The wing tip boom was a 1 inch diameter hollow tube of length 21.5 inch. The total weight of the wing was 2.66 lbs.

Pak, Chan-gi↗