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At least 1,171 records · Page 65

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NASA NTRS1975

A three-parameter analytic phase function for multiple scattering calculations

A very simple procedure has been developed to fit the first three moments of an actual phase function with a three-parameter analytic phase function. The exact Legendre polynomial decomposition of this function is known which makes it quite suitable for multiple scattering calculations. The use of this function can be expected to yield excellent flux values at all depths within a medium. Since it is capable of reproducing the glory, it can be used in synthetic spectra computations from planetary atmospheres. Accurate asymptotic radiance values can also be achieved as long as the single scattering albedo is not less than 0.9.

Kattawar, G. W.↗

NASA NTRS1977

Development of a transfer function method for dynamic stability measurement

Flutter testing method based on transfer function measurements is developed. The error statistics of several dynamic stability measurement methods are reviewed. It is shown that the transfer function measurement controls the error level by averaging the data and correlating the input and output. The method also gives a direct estimate of the error in the response measurement. An algorithm is developed for obtaining the natural frequency and damping ratio of low damped modes of the system, using integrals of the transfer function in the vicinity of a resonant peak. Guidelines are given for selecting the parameters in the transfer function measurement. Finally, the dynamic stability measurement technique is applied to data from a wind tunnel test of a proprotor and wing model.

Johnson, W.↗

NASA NTRS1977

Symbolic Laplace transforms of special functions

A MACSYMA implementation of the Laplace transform for special functions is described. The generalized hypergeometric functions are used as a basis for the representation of approximately fifty special functions. Only a relatively small number of formulas that generally involve generalized hypergeometric functions are utilized for the integration stage. A sample of actual examples and their timing is provided.

Avgoustis, Y.↗

NASA NTRS1977

The velocity correlation function in cosmic-ray diffusion theory

It is shown that Earl's (1973) eigenvalue sum for the cosmic-ray spatial diffusion coefficient parallel to the mean magnetic field is precisely equivalent to the time integral of the particle-velocity correlation function parallel to the mean field. A derivation due to Kubo (1957) is applied to cosmic-ray pitch-angle scattering, and it is proven that all nine components of the cosmic-ray diffusion tensor can be expressed as integrals over the velocity correlation function. A pitch-angle correlation function is derived, and the effect of long-wavelength turbulence on the velocity correlation function and spatial diffusion coefficients is examined. Application of the velocity-correlation method to a realistic case involving both pitch-angle scattering and appreciable fluctuation in the direction of the local field indicates that long-wavelength turbulence in the local field reduces the parallel diffusion coefficient and places an upper limit on the ratio of the perpendicular to parallel diffusion coefficients.

Forman, M. A.↗

NASA NTRS1978

Adding stress plot function to NASTRAN

Stress plot function was developed and added to the NASTRAN level 15.5. Computed stress distribution can be displayed by this function, with vectors showing the principal stresses of the finite elements over the specified portions of the structure. NASTRAN is reviewed in the aspect of plotting capabilities. Stress tensor field is examined in preparation of stress display. Then the stress plot function as added to the NASTRAN is described. A sample plotout by this function is shown.

Katoh, S.↗

NASA NTRS1978

Two dimensional eye tracking: Sampling rate of forcing function

A study was conducted to determine the minimum update rate of a forcing function display required for the operator to approximate the tracking performance obtained on a continuous display. In this study, frequency analysis was used to determine whether there was an associated change in the transfer function characteristics of the operator. It was expected that as the forcing function display update rate was reduced, from 120 to 15 samples per second, the operator's response to the high frequency components of the forcing function would show a decrease in gain, an increase in phase lag, and a decrease in coherence.

Hornseth, J. P.↗

NASA NTRS1980

Catecholamines and myocardial contractile function during hypodynamia and with an altered thyroid hormone balance

The dynamics of catecholamine content and myocardial contractile function during hypodynamia were studied in 109 white rats whose motor activity was severely restricted for up to 30 days. During the first five days myocardial catecholamine content, contractile function, and physical load tolerance decreased. Small doses of thyroidin counteracted this tendency. After 15 days, noradrenalin content and other indices approached normal levels and, after 30 days, were the same as control levels, although cardiac functional reserve was decreased. Thyroidin administration after 15 days had no noticeable effect. A detailed table shows changes in 17 indices of myocardial contractile function during hypodynamia.

Pruss, G. M.↗

NASA NTRS1980

Application of functional analysis to perturbation theory of differential equations

The deviation of the solution of the differential equation y' = f(t, y), y(O) = y sub O from the solution of the perturbed system z' = f(t, z) + g(t, z), z(O) = z sub O was investigated for the case where f and g are continuous functions on I x R sup n into R sup n, where I = (o, a) or I = (o, infinity). These functions are assumed to satisfy the Lipschitz condition in the variable z. The space Lip(I) of all such functions with suitable norms forms a Banach space. By introducing a suitable norm in the space of continuous functions C(I), introducing the problem can be reduced to an equivalent problem in terminology of operators in such spaces. A theorem on existence and uniqueness of the solution is presented by means of Banach space technique. Norm estimates on the rate of growth of such solutions are found. As a consequence, estimates of deviation of a solution due to perturbation are obtained. Continuity of the solution on the initial data and on the perturbation is established. A nonlinear perturbation of the harmonic oscillator is considered a perturbation of equations of the restricted three body problem linearized at libration point.

Bogdan, V. M.↗

NASA NTRS1979

Imaging performance of annular apertures. III - Apodization and modulation transfer functions

Apodization functions with decreasing transmission and their opposite, functions with increasing transmission, are investigated for various central obstruction ratios. The resultant modulation transfer functions are presented for various transmission functions and central obstruction ratios. Conclusions applicable to the improvement of imaging performance are discussed.

Tschunko, H. F. A.↗

NASA NTRS1980

To develop behavioral tests of vestibular functioning in the Wistar rat

Two tests of vestibular functioning in the rat were developed. The first test was the water maze. In the water maze the rat does not have the normal proprioceptive feedback from its limbs to help it maintain its orientation, and must rely primarily on the sensory input from its visual and vestibular systems. By altering lighting conditions and visual cues the vestibular functioning without visual cues was assessed. Whether there was visual compensation for some vestibular dysfunction was determined. The second test measured vestibular functioning of the rat's behavior on a parallel swing. In this test the rat's postural adjustments while swinging on the swing with the otoliths being stimulated were assessed. Less success was achieved in developing the parallel swing as a test of vestibular functioning than with the water maze. The major problem was incorrect initial assumptions of what the rat's probable behavior on the parallel swing would be.

Nielson, H. C.↗

NASA NTRS1980

Convolution of a Doppler line by a Gaussian instrument function

A simple and direct method is obtained for assessing the distortion of a Doppler line by a Gaussian instrument function. It is suggested that a close approximation to the width of a Gaussian instrument function, or an almost Gaussian function, may be obtained by measuring a line with a Doppler absorption coefficient. The method is applicable to diode laser measurements, and may be used whenever a Gaussian instrument function is a reasonable approximation to real conditions

Fridovich, B.↗

NASA NTRS1980

The luminosity functions of the 1969 Perseid and Orionid meteor showers

Observations of the 1969 Perseid and Orionid meteor showers are presented and used to derive luminosity functions for the 288 Perseids and 56 Orionids detected. Visual counts were performed under very good to excellent seeing conditions at the times of peak activities, and the brightnesses of the meteors were estimated to the nearest magnitude by comparison with the magnitudes of known objects. Maximum likelihood estimates of the power law index of the luminosity function of 1.56 + or - 0.06 for the Perseids and of 1.85 + or - 0.1 for the Orionids are obtained which are lower than the values found by other investigators. Under the assumption that the luminosity of visual meteors is proportional to their mass, the luminosity function power law may also be used to characterize the mass function.

Krisciunas, K.↗

NASA NTRS1981

Asymptotic form of the longitudinal correlation function for isotropic homogeneous turbulence

An asymptotic form is derived for the longitudinal correlation function for isotropic homogeneous turbulence in an incompressible fluid governed by the Navier-Stokes equation. The result is obtained from an analysis of the algebraic-differential structure of the two-point correlation tensor contained in the complex-valued Fourier transform of the probability measure over the turbulence ensemble, which reveals that the Hopf characteristic functional (the complex-valued Fourier transform of the probability measure) satisfies the Fourier interference inequality. Consequences of the expression obtained, in which the correlation function is a positive definite function of the inverse cube of the spatial coordinate as it approaches infinity, are shown to include the nonexistence of the Loitsianskii invariant, and the solution is shown to be consistent with empirical formulas.

Rosen, G.↗

NASA NTRS1981

Use of global functions for improvement in efficiency of nonlinear analysis

A method for improving the efficiency of nonlinear structural analysis by the use of global displacement functions is presented. The computer programs include options to define the global functions as input or let the program automatically select and update these functions. The program was applied to a number of structures: (1) 'pear-shaped cylinder' in compression, (2) bending of a long cylinder, (3) spherical shell subjected to point force, (4) panel with initial imperfections, (5) cylinder with cutouts. The sample cases indicate the usefulness of the procedure in the solution of nonlinear structural shell problems by the finite element method. It is concluded that the use of global functions for extrapolation will lead to savings in computer time.

Almroth, B. O.↗

NASA NTRS1981

Correlation function studies for snow and ice

The random medium model is used to characterize snow and ice fields in the interpretation of active and passive microwave remote sensing data. A correlation function is used to describe the random permittivity fluctuations with the associated mean and variance and correlation lengths; and several samples are investigated to determine typical correlation functions for snow and ice. It is shown that correlation functions are extracted directly from appropriate ground truth data, and an exponential correlation function is observed for snow and ice with lengths corresponding to the actual size of ice particles or air bubbles. Thus, given that a medium has spatially stationary statistics and a small medium, the random medium model can interpret remote sensing data where theoretical parameters correspond to actual physical parameters of the terrain.

Vallese, F.↗

NASA NTRS1982

Development of low-frequency kernel-function aerodynamics for comparison with time-dependent finite-difference methods

Finite difference methods for unsteady transonic flow frequency use simplified equations in which certain of the time dependent terms are omitted from the governing equations. Kernel functions are derived for two dimensional subsonic flow, and provide accurate solutions of the linearized potential equation with the same time dependent terms omitted. These solutions make possible a direct evaluation of the finite difference codes for the linear problem. Calculations with two of these low frequency kernel functions verify the accuracy of the LTRAN2 and HYTRAN2 finite difference codes. Comparisons of the low frequency kernel function results with the Possio kernel function solution of the complete linear equations indicate the adequacy of the HYTRAN approximation for frequencies in the range of interest for flutter calculations.

Bland, S. R.↗

NASA NTRS1982

An efficient sampling technique for sums of bandpass functions

A well known sampling theorem states that a bandlimited function can be completely determined by its values at a uniformly placed set of points whose density is at least twice the highest frequency component of the function (Nyquist rate). A less familiar but important sampling theorem states that a bandlimited narrowband function can be completely determined by its values at a properly chosen, nonuniformly placed set of points whose density is at least twice the passband width. This allows for efficient digital demodulation of narrowband signals, which are common in sonar, radar and radio interferometry, without the side effect of signal group delay from an analog demodulator. This theorem was extended by developing a technique which allows a finite sum of bandlimited narrowband functions to be determined by its values at a properly chosen, nonuniformly placed set of points whose density can be made arbitrarily close to the sum of the passband widths.

Lawton, W. M.↗

NASA NTRS1982

Expansion series of integral functions occurring in unsteady aerodynamics

Attention is given to two real integral functions which occur in the kernel of singular integral equations for subsonic unsteady lifting surfaces. The arguments k, r, and X of the functions correspond to the reduced frequency, spanwise distance, and modified coordinate in the flow direction, respectively. The value of the parameter nu in the functions depends on geometrical conditions. The considered investigation has the objective to present a series for general values of the nonnegative integer nu in order to compute efficiently the integral functions. The approach makes it possible to avoid any approximation or numerical quadrature.

Ueda, T.↗