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At least 379 records · Page 21

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NASA NTRS1984

MAGSAT correlations with geoid anomalies

A digital data library of MAGSAT data is described and its applications and capabilities are reviewed. Polynomial trends were removed from each half-orbit in order to estimate and remove ring current effects from the data. The MAGSAT data in the Gulf of Mexico region was analyzed to define better the possible relation of the negative MAGSAT anomaly there to the negative residual geoid anomaly in the western Gulf of Mexico. Since the shape and location of the negative magnetic anomaly are variable depending upon the particular polynomial surface and curve orders used, no definitive conclusion as to the degree of correspondance between the residual geoid and MAGSAT lithosphere anomalies is offered.

Bowin, C. O.↗

NASA NTRS1983

Radar image registration and rectification

Two techniques for radar image registration and rectification are presented. In the registration method, a general 2-D polynomial transform is defined to accomplish the geometric mapping from one image into the other. The degree and coefficients of the polynomial are obtained using an a priori found tiepoint data set. In the second part of the paper, a rectification procedure is developed that models the distortion present in the radar image in terms of the radar sensor's platform parameters and the topographic variations of the imaged scene. This model, the ephemeris data and the digital topographic data are then used in rectifying the radar image. The two techniques are then used in registering and rectifying two examples of radar imagery. Each method is discussed as to its benefits, shortcomings and registration accuracy.

Naraghi, M.↗

NASA NTRS1984

Failure analysis for composite laminates

A discussion of the tensor polynomial failure criterion is presented together with a description of a biaxial compression test procedure used in the evaluation of the interaction strength parameters. In addition, a formulation for predicting the fatigue life of laminates is given based on the experimental evaluation of fatigue functions which are also utilized in a form of the tensor polynomial failure criterion as well. Experimental results are provided to compare with the fatigue life predictions and to demonstrate the effect of flaws and environment. Both bond-line defects in sandwich beam construction and inter-laminar disbond flaws are studied. Up to present, compressive strength test data have been obtained for ambient and elevated temperature, moisture-saturated conditions, including results from thermal-spike cycling simulating supersonic flight.

Tennyson, R. C.↗

NASA NTRS1984

Non-nulling seven-hole probes for high angle flow measurement

This paper illustrates a method for calibrating seven-hole probes to measure local total and static pressures and relative flow angles of up to 70 degrees in subsonic compressible flows. The method of Latin Squares was used to statistically sample a large and otherwise unmanageable data set, thereby reducing to a minimum the number of data points required to construct a polynomial curve fit to the data. Calibration produces three-variable third order polynomials which permit all of the desired flow properties to be found explicitly from probe measured pressures. This method determines the flow angles to within 2 degrees and Mach number to within 0.04 with 95 percent certainty.

Gerner, A. A.↗

NASA NTRS1984

Performance of the h, p and h-p versions

There are three basic versions of the finite element method, called the h, p and h-p versions. They are characterized by the way in which the finite element meshes and polynomial degree of elements are chosen. They differ in computer implementation (program architecture) and mathematical analysis. The manner in which the meshes and polynomial degree of the elements affect the accuracy of finite element solutions is examined. The approach is to fix certain parameters and increase the number of degrees of freedom so that the finie element solutions converge to the exact solution. Such a systematic increase of the number of degrees of freedom is called extension because it can be interpreted as a systematic extension of finite element spaces.

Babuska, I.↗

NASA NTRS1984

Periodic binary sequence generators: VLSI circuits considerations

Feedback shift registers are efficient periodic binary sequence generators. Polynomials of degree r over a Galois field characteristic 2(GF(2)) characterize the behavior of shift registers with linear logic feedback. The algorithmic determination of the trinomial of lowest degree, when it exists, that contains a given irreducible polynomial over GF(2) as a factor is presented. This corresponds to embedding the behavior of an r-stage shift register with linear logic feedback into that of an n-stage shift register with a single two-input modulo 2 summer (i.e., Exclusive-OR gate) in its feedback. This leads to Very Large Scale Integrated (VLSI) circuit architecture of maximal regularity (i.e., identical cells) with intercell communications serialized to a maximal degree.

Perlman, M.↗

NASA NTRS1985

Crystallinity determination by curvefit procedure for a semi-crystalline polymer

Wide angle X-ray scattering (WAXS) data from poly(etheretherketone) (PEEK) was resolved into a crystalline contribution represented as four reflections and an amorphous contribution represented as a broad, smoothly varying curve. The crystalline scatter is described as a linear combination of Cauchy and Gaussian functions while that of the amorphous halo is expressed as a cubic polynomial. Statistical analysis of the measured scattered intensity from an amorphous specimen with that calculated from the cubic polynomial, as a function of the combination parameter (fraction of Cauchy and Gaussian functions), suggests that the crystalline fraction of the polymer specimen studied is about 0.39.

Wakelyn, N. T.↗

NASA NTRS1984

Separation of large-scale photospheric Doppler patterns

Mount Wilson solar Doppler data covering the period from January 1967 to March 1984 are refit using polynomials appropriate to the rotation, limbshift, and meridional flow motion fields identified by LaBonte and Howard (1982). No 'ear' terms are included, and additional degrees of freedom are allowed in the limbshift and meridional flow fluctions. An examination of the residuals shows this fit to be a slight improvement over that of the above workers, and the new residuals are used to tighten the limits on photospheric giant signatures to about 1 m/s per wavenumber. The focus of the paper is on polynomial functions and their fit-determined coefficients, with particular emphasis on the problem of crosstalk as the coefficients are tracked over time.

Snodgrass, H. B.↗

NASA NTRS1985

Axisymmetric solid elements by a rational hybrid stress method

Four-node axisymmetric solid elements are derived by a new version of hybrid method for which the assumed stresses are expressed in complete polynomials in natural coordinates. The stress equilibrium conditions are introduced through the use of additional displacements as Lagrange multipliers. A rational procedure is to choose the displacement terms such that the resulting strains are also of complete polynomials of the same order. Example problems all indicate that elements obtained by this procedure lead to better results in displacements and stresses than that by other finite elements.

Tian, Z.↗

NASA NTRS1986

Transfer function analysis of thermospheric perturbations

Applying perturbation theory, a spectral model in terms of vectors spherical harmonics (Legendre polynomials) is used to describe the short term thermospheric perturbations originating in the auroral regions. The source may be Joule heating, particle precipitation or ExB ion drift-momentum coupling. A multiconstituent atmosphere is considered, allowing for the collisional momentum exchange between species including Ar, O2, N2, O, He and H. The coupled equations of energy, mass and momentum conservation are solved simultaneously for the major species N2 and O. Applying homogeneous boundary conditions, the integration is carred out from the Earth's surface up to 700 km. In the analysis, the spherical harmonics are treated as eigenfunctions, assuming that the Earth's rotation (and prevailing circulation) do not significantly affect perturbations with periods which are typically much less than one day. Under these simplifying assumptions, and given a particular source distribution in the vertical, a two dimensional transfer function is constructed to describe the three dimensional response of the atmosphere. In the order of increasing horizontal wave numbers (order of polynomials), this transfer function reveals five components. To compile the transfer function, the numerical computations are very time consuming (about 100 hours on a VAX for one particular vertical source distribution). However, given the transfer function, the atmospheric response in space and time (using Fourier integral representation) can be constructed with a few seconds of a central processing unit. This model is applied in a case study of wind and temperature measurements on the Dynamics Explorer B, which show features characteristic of a ringlike excitation source in the auroral oval. The data can be interpreted as gravity waves which are focused (and amplified) in the polar region and then are reflected to propagate toward lower latitudes.

Mayr, H. G.↗

NASA NTRS1987

FPT Algorithm for Two-Dimensional Cyclic Convolutions

Fast-polynomial-transform (FPT) algorithm computes two-dimensional cyclic convolution of two-dimensional arrays of complex numbers. New algorithm uses cyclic polynomial convolutions of same length. Algorithm regular, modular, and expandable.

Truong, Trieu-Kie↗

NASA NTRS1987

AKPLOT: A plotter routine for IBM PC, XT and AT

The AKPLOT software for the IBM PC, XT, and AT is an efficient and versatile tool that allows X-Y plotting of quantitative information. Features include IBM four-color graphics, which combined with 10 different symbols allows 40 different curves on the same grid, shrink or expansion of the graph size, any combination of log and linear X and Y axes, selective plotting from multiple curves of a previous run, interpolation and polynomial least-squares fit with any degree polynomial, and a 90-degree tilt of the entire graph. These options are independent, and can be invoked individually.

Kantak, Anil↗

NASA NTRS1987

Elastic interaction of a crack with a microcrack array. I - Formulation of the problem and general form of the solution. II - Elastic solution for two crack configurations (piecewise constant and linear approximations)

The elastic interactions of a two-dimensional configuration consisting of a crack with an array of microcracks located near the tip are studied. The general form of the solution is based on the potential representations and approximations of tractions on the microcracks by polynomials. In the second part, the technique is applied to two simple two-dimensional configurations involving one and two microcracks. The problems of stress shielding and stress amplification (the reduction or increase of the effective stress intensity factor due to the presence of microcracks) are discussed, and the refinements introduced by higher order polynomial approximations are illustrated.

Chudnovsky, A.↗

NASA NTRS1988

Free vibration of rectangular plates with a small initial curvature

The method of matched asymptotic expansions is used to solve the transverse free vibration of a slightly curved, thin rectangular plate. Analytical results for natural frequencies and mode shapes are presented in the limit when the dimensionless bending rigidity, epsilon, is small compared with in-plane forces. Results for different boundary conditions are obtained when the initial deflection is: (1) a polynomial in both directions, and (2) the product of a polynomial and a trigonometric function, and arbitrary. For the arbitrary initial deflection case, the Fourier series technique is used to define the initial deflection. The results obtained show that the natural frequencies of vibration of slightly curved plates are coincident with those of perfectly flat, prestressed rectangular plates. However, the eigenmodes are very different from those of initially flat prestressed rectangular plates. The total deflection is found to be the sum of the initial deflection, the deflection resulting from the solution of the flat plate problem, and the deflection resulting from the static problem.

Adeniji-Fashola, A. A.↗

NASA NTRS1988

Convergence acceleration for vector sequences and applications to computational fluid dynamics

Some recent developments in acceleration of convergence methods for vector sequences are reviewed. The methods considered are the minimal polynomial extrapolation, the reduced rank extrapolation, and the modified minimal polynomial extrapolation. The vector sequences to be accelerated are those that are obtained from the iterative solution of linear or nonlinear systems of equations. The convergence and stability properties of these methods as well as different ways of numerical implementation are discussed in detail. Based on the convergence and stability results, strategies that are useful in practical applications are suggested. Two applications to computational fluid mechanics involving the three dimensional Euler equations for ducted and external flows are considered. The numerical results demonstrate the usefulness of the methods in accelerating the convergence of the time marching techniques in the solution of steady state problems.

Sidi, Avram↗

NASA NTRS1987

Boundary layer stability calculations

In this paper numerical calculation of the spatial stability of disturbances in the parallel and nonparallel Blasius boundary layers is considered. Chebyshev polynomials are used for discretization. The problem with the boundary condition at infinity is overcome, and the resulting nonlinear matrix eigenvalue problem is attacked directly. The secondary eigenvalue problem for three-dimensional disturbances is shown to be uniformly stable, and particular solutions of this problem generated by the Orr-Sommerfeld equation are shown. A numerical solution of the nonparallel problem is considered using Chebyshev polynomials. The matrix equations are analyzed directly and the problem of uniqueness of the nonparallel correction is settled by careful application of the Fredholm alternative. Nonparallel corrections to the streamwise eigenfunction are shown.

Bridges, Thomas J.↗

NASA NTRS1988

Recursive algorithms for vector extrapolation methods

Three classes of recursion relations are devised for implementing some extrapolation methods for vector sequences. One class of recursion relations can be used to implement methods like the modified minimal polynomial extrapolation and the topological epsilon algorithm; another allows implementation of methods like minimal polynomial and reduced rank extrapolation; while the remaining class can be employed in the implementation of the vector E-algorithm. Operation counts and storage requirements for these methods are also discussed, and some related techniques for special applications are also presented. Included are methods for the rapid evaluations of the vector E-algorithm.

Ford, William F.↗

NASA NTRS1989

Minimal inversion, command matching and disturbance decoupling in multivariable systems

The present treatment of the related problems of minimal inversion and perfect output control in linear multivariable systems uses a simple analytical expression for the inverse of a square multivariate system's transfer-function matrix to construct a minimal-order inverse of the system. Because the poles of the minimal-order inverse are the transmission zeros of the system, necessary and sufficient conditions for the inverse system's stability are simply stated in terms of the zero polynomial of the original system. A necessary and sufficient condition for the existence of the required controllers is that the plant zero polynomial be neither identical to zero nor unstable.

Seraji, H.↗