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NASA NTRS1986

The statistics of peaks of Gaussian random fields

A set of new mathematical results on the theory of Gaussian random fields is presented, and the application of such calculations in cosmology to treat questions of structure formation from small-amplitude initial density fluctuations is addressed. The point process equation is discussed, giving the general formula for the average number density of peaks. The problem of the proper conditional probability constraints appropriate to maxima are examined using a one-dimensional illustration. The average density of maxima of a general three-dimensional Gaussian field is calculated as a function of heights of the maxima, and the average density of 'upcrossing' points on density contour surfaces is computed. The number density of peaks subject to the constraint that the large-scale density field be fixed is determined and used to discuss the segregation of high peaks from the underlying mass distribution. The machinery to calculate n-point peak-peak correlation functions is determined, as are the shapes of the profiles about maxima.

Bardeen, J. M.↗

NASA NTRS1985

Optimum search strategy for randomly distributed CW transmitters

The relative probability of detecting randomly distributed CW transmitters as a function of the fraction of the sky which is searched (in a fixed time interval) is given. It is shown that the probability of detecting such a class of transmitters with a given receiving system is a maximum if the entire sky is searched, provided that the receiving system is sufficiently sensitive to detect the nearest transmitter in the allocated time and that the integration time - bandwidth product in a specified direction is greater than 8.

Gulkis, S.↗

NASA NTRS1986

Radiative transfer in multilayered random medium with laminar structure - Green's function approach

For a multilayered random medium with a laminar structure a Green's function approach is introduced to obtain the emitted intensity due to an arbitrary point source. It is then shown that the approach is applicable to both active and passive remote sensing. In active remote sensing, the computed radar backscattering cross section for the multilayered medium includes the effects of both volume multiple scattering and surface multiple scattering at the layer boundaries. In passive remote sensing, the brightness temperature is obtained for arbitrary temperature profiles in the layers. As an illustration the brightness temperature and reflectivity are calculated for a bounded layer and compared with results in the literature.

Karam, M. A.↗

NASA NTRS1986

Visibility and aerosol measurement by diode-laser random-modulation CW lidar

Examples of diode laser (DL) random-modulation continuous wave (RM-CW) lidar measurements are reported. The ability of the measurement of the visibility, vertical aerosol profile, and the cloud ceiling height is demonstrated. Although the data shown here were all measured at night time, the daytime measurement is, of course, possible. For that purpose, accurate control of the laser frequency to the center frequency of a narrow band filter is required. Now a new system with a frequency control is under construction.

Takeuchi, N.↗

NASA NTRS1987

Component response to random vibratory motion of the carrier vehicle

Two physical models of component plus supporting substructure are considered. Each model consists of a rigid body attached to a moving base by means of linear springs and viscous dampers. The second model differs from the first in that its dampers are elastically supported. The first model receives the more extensive treatment. Base motion, assumed a random translational motion parallel to a fixed axis, is prescribed only to the extent that the power spectral density (PSD) of its acceleration is given; and, as given, its plot on log-log graph paper is a series of straight line segments, each segment having an extremity in common with the adjacent segment. Closed expressions are given for the mean squares of base acceleration, base velocity, and base displacement. The component is restricted to planar motion and allowed two degrees of freedom, one translational and one rotational. Integral expressions are given for the mean squares of component response variables, the transfer functions essential to mean square computation being available via the equations of motion. Closed expressions are given for mean squares of certain of the response variables for the case wherein the base acceleration PSD is constant.

Tuell, L. P.↗

NASA NTRS1987

Influence of large deflection and transverse shear on random response of rectangular symmetric composite laminates to acoustic loads

Nonlinear equations of motion of symmetrically laminated anisotropic plates are derived accounting for von Karman strains. The effect of transverse shear is included in the formulation and the rotatory inertia effect is ignored. Using a single-mode Galerkin procedure the nonlinear modal equation is obtained. Direct equivalent linearization is employed. The response of acoustic excitation on moderately thick composite panels is studied. Further, the effects of transverse shear on large deflection vibration of laminates under random excitation are studied. Mean-square deflection and mean-square inplane stresses are obtained for some symmetric graphite-epoxy laminates. Using equilibrium equations and the continuity requirements, the mean-square transverse shear stresses are calculated. The results obtained will be useful in the sonic fatigue design of composite aircraft panels. The analysis is presented in detail for simply supported plate. The analogous equations for a clamped case are given in the appendix.

Mei, Chuh↗

NASA NTRS1987

Integration of altitude and airspeed information into a primary flight display via moving-tape formats: Evaluation during random tracking task

A ground-based aircraft simulation study was conducted to determine the effects on pilot preference and performance of integrating airspeed and altitude information into an advanced electronic primary flight display via moving-tape (linear moving scale) formats. Several key issues relating to the implementation of moving-tape formats were examined in this study: tape centering, tape orientation, and trend information. The factor of centering refers to whether the tape was centered about the actual airspeed or altitude or about some other defined reference value. Tape orientation refers to whether the represented values are arranged in descending or ascending order. Two pilots participated in this study, with each performing 32 runs along seemingly random, previously unknown flight profiles. The data taken, analyzed, and presented consisted of path performance parameters, pilot-control inputs, and electrical brain response measurements.

Abbott, Terence S.↗

NASA NTRS1986

Vector solution for the mean electromagnetic fields in a layer of random particles

The mean electromagnetic fields are found in a layer of randomly oriented particles lying over a half space. A matrix-dyadic formulation of Maxwell's equations is employed in conjunction with the Foldy-Lax approximation to obtain equations for the mean fields. A two variable perturbation procedure, valid in the limit of small fractional volume, is then used to derive uncoupled equations for the slowly varying amplitudes of the mean wave. These equations are solved to obtain explicit expressions for the mean electromagnetic fields in the slab region in the general case of arbitrarily oriented particles and arbitrary polarization of the incident radiation. Numerical examples are given for the application to remote sensing of vegetation.

Lang, R. H.↗

NASA NTRS1987

Effective propagation constants in dense random media under effective medium approximation

The effective medium approximation is applied to study the effective propagation constants in a dense random medium. The dyadic Green's function is introduced to establish the effective medium approximation formalism for electromagnetic waves. The multiple scattering equations and the Lippmann-Schwinger equations for the transition operator are obtained in the configuration average form. The dispersion equations of multiple scattering is derived by using a standard method in quantum mechanics. To obtain an expression for the effective propagation constants the matrix elements of the configuration average dyadic transiton operator are calculated in momentum representation. Numerical illustations are carried out to demonstrate the difference in the effective propagation constants between the use of this approximation and the well-known quasi-crystalline approximation. A comparison is made with measured loss tangent in dry snow.

Zhu, P. Y.↗

NASA NTRS1988

Random vibration (stress screening) of printed wiring assemblies

The results of a random vibration test screening (RVSS) study of the determination of the upper and lower vibration limits on printed wiring assemblies (PWA) are summarized. The study results are intended to serve as a guide for engineers and designers who make decisions on PWA features that need to withstand the stresses of dynamic testing and screening. The maximum allowable PWA deflection, G levels, and PSD levels are compared to the expected or actual levels to determine if deleterious effects will occur.

Bastien, Gilbert J.↗

NASA NTRS1987

Multiple-mode large deflection random response of beams with nonlinear damping subjected to acoustic excitation

Multiple-mode nonlinear analysis is carried out for beams subjected to acoustic excitation. Effects of both nonlinear damping and large-deflection are included in the analysis in an attempt to explain the experimental phenomena of aircraft panels excited at high sound pressure levels; that is the broadening of the strain response peaks and the increase of modal frequency. An amplitude dependent nonlinear damping model is used in the anlaysis to study the effects and interactions of multiple modes, nonlinear stiffness and nonlinear damping on the random response of beams. Mean square maximum deflection, mean square maximum strain, and spectral density function of maximum strain for simple supported and clamped beams are obtained. It is shown analytically that nonlinear damping contributes significantly to the broadening of the response peak and to the mean square deflection and strain.

Prasad, C. B.↗

NASA NTRS1987

The effect of decay of the amplitude of oscillation on random process models for QPO X-ray stars

Random process models provide a useful mathematical framework for analysis of the quasi-periodic oscillations (QPO) recently discovered in the X-ray emission from certain luminous Galactic X-ray stars. In this paper, consideration is given to the effects of the power spectrum of the decay of the amplitude of oscillation that is expected in some physical models for the QPO phenomena. The resulting changes in the power spectrum depend on the ratio of the decay time of the amplitude of oscillation to the lifetime of the shot envelope. For values of this ratio less than about 10, it is found that incoherent QPO peaks in the power spectrum are significantly reduced in height and total power and are broadened in width, making them more difficult to detect. Coherent terms in the power spectrum, if present, are reduced in height and total power, but their width is unaffected. The red noise component remains unchanged. The present results are applied to the beat-frequency modulated accretion model in order to set constraints on the physical properties of the boundary layer between the inner edge of the accretion disk and the neutron star magnetosphere.

Shibazaki, N.↗

NASA NTRS1987

A scattering model for perfectly conducting random surfaces. I - Model development. II - Range of validity

The surface current on a perfectly conducting randomly rough surface is estimated by solving iteratively a standard integral equation, and the estimate is then used to compute the far-zone scattered fields and the backscattering coefficients for vertical, horizontal and cross polarizations. The model developed here yields a simple backscattering coefficient expression in terms of the surface parameters. The expression reduces analytically to the Kirchhoff and the first-order small-perturbation model in the high- and low-frequency regions, respectively. The range of validity of the model is determined.

Fung, A. K.↗

NASA NTRS1987

Effects of intensity modulations on the power spectra of random processes

Intensity-modulated random processes (IMRPs), defined as the products of (1) deterministic modulating functions or processes and (2) stationary modulated processes statistically independent of (1), are investigated analytically. Instantaneous power spectra are derived for IMRPs with different classes of (1), and a spectrum series expansion with a known locally stationary approximation as its first term is obtained. Numerical results for sample IMRPs with known (deterministic), stationary, nonstationary, ergodic, onset, and bell-shaped types of (1) are presented graphically and briefly characterized.

Mark, W. D.↗

NASA NTRS1988

Time domain simulation of the response of geometrically nonlinear panels subjected to random loading

The response of composite panels subjected to random pressure loads large enough to cause geometrically nonlinear responses is studied. A time domain simulation is employed to solve the equations of motion. An adaptive time stepping algorithm is employed to minimize intermittent transients. A modified algorithm for the prediction of response spectral density is presented which predicts smooth spectral peaks for discrete time histories. Results are presented for a number of input pressure levels and damping coefficients. Response distributions are calculated and compared with the analytical solution of the Fokker-Planck equations. RMS response is reported as a function of input pressure level and damping coefficient. Spectral densities are calculated for a number of examples.

Moyer, E. Thomas, Jr.↗

NASA NTRS1988

Modified radiative transfer theory for a two-layer anisotropic random medium

The modified radiative transfer (MRT) equations which describe propagation and scattering of the electromagnetic field intensity in a layered anisotropic random medium are derived from the Bethe-Salpeter equation with the ladder approximation and the Dyson equation with the nonlinear approximation. The extinction matrices and scattering phase matrices for both mean and incoherent field intensities are obtained. Backscattering enhancement is observed due to the spatial coherent effect between upward and downward propagating waves. It also occurs for the half-space case, because of coupling between ordinary and extraordinary waves. The depolarization effect is predicted in the first-order renormalization approximation to the MRT equation.

Lee, J. K.↗

NASA NTRS1988

Electromagnetic scattering from a layer of finite length, randomly oriented, dielectric, circular cylinders over a rough interface with application to vegetation

A scattering model for defoliated vegetation is developed by treating a layer of defoliated vegetation as a collection of randomly oriented dielectric cylinders of finite length over an irregular ground surface. Both polarized and depolarized backscattering are computed and their behavior versus the volume fraction, the incidence angle, the frequency, the angular distribution and the cylinder size are illustrated. It is found that both the angular distribution and the cylinder size have significant effects on the backscattered signal. The present theory is compared with measurements from defoliated vegetations.

Karam, M. A.↗

NASA NTRS1988

Non-random cratering flux in recent time

Proposed periodic cycles of mass mortality have been linked to periodic changes in the impact flux on Earth. Such changes in the impact flux, however, also should be recorded on the Moon. Previous studies have concluded that the impact flux on the Moon over the last 1 to 2 billion years has been reasonably constant, but sudden changes in the impact flux over time intervals as short as 30 my could not be detected in these studies unless the added crater population greatly exceeded the cumulative cratering record. Consequently this study focuses only on bright-rayed craters larger than 1 km thereby not only limiting the study to recent craters but also largely eliminating contamination by secondary craters. Preservation of ray patterns and other fine-scale surface textures in the ejecta provides first-order culling of craters younger than Tycho, i.e., about 100 my. Although a periodic change in the impact flux in the Earth-Moon system cannot yet be confirmed from the data, a non-random component appears to exist with an increased flux around 7 and 15 my. The concentrations in different quadrants of the lunar hemisphere would be consistent with a shower of debris generally smaller than 0.5 km.

Schultz, P. H.↗