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NASA NTRS1982

A structure function representation theorem with applications to frequency stability estimation

Random processes with stationary nth differences serve as models for oscillator phase noise. A theorem which obtains the structure function (covariance of the nth differences) of such a process in terms of the differences of a single function of one time variable is proven. In turn, this function can easily be obtained from the spectral density of the process. The theorem is used for computing the variance of two estimators of frequency stability.

Greenhall, C. A.↗

NASA NTRS1981

Predicted star counts in selected fields and photometric bands Applications to galactic structure, the disk luminosity function, and the detection of a massive halo

Tables are presented of predicted star counts in 17 selected directions on the sky as a function of apparent B, V, R, and I magnitudes and absolute visual magnitudes calculated from the Bahcall-Soneira Galaxy model. It is noted that eight of the fields were selected ab initio for their usefulness in determining from star counts either parameters of galactic structure, the faint end of the disk luminosity function, or the detection of a massive stellar halo. Star counts in specified fields to m sub I = 19 mag are able to reveal the faint end of the disk luminosity function down to the end of the hydrogen-burning main sequence. It is thought that star counts at high galactic latitudes to m sub I = 22 mag should reveal the stellar constituents of a massive halo if they are massive enough to be on the hydrogen-burning main sequence.

Bahcall, J. N.↗

NASA NTRS1981

Functional methods for waves in random media

Some basic ideas in functional methods for waves in random media are illustrated through a simple random differential equation. These methods are then generalized to solve certain random parabolic equations via an exponential representation given by the Feynman-Kac formula. It is shown that these functional methods are applicable to a number of problems in random wave propagation. They include the forward-scattering approximation in Gaussian white-noise media; the solution of the optical beam propagation problem by a phase-integral method; the high-frequency scattering by bounded random media, and a derivation of approximate moment equations from the functional integral representation.

Chow, P. L.↗

NASA NTRS1981

Functional methods for waves in random media

Some basic ideas in functional methods for waves in random media are illustrated through a simple random differential equation. These methods are then generalized to solve certain random parabolic equations via an exponential representation given by the Feynman-Kac formula. It is shown that these functional methods are applicable to a number of problems in random wave propagation. They include the forward-scattering approximation in Gaussian white-noise media; the solution of the optical beam propagation problem by a phase-integral method; the high-frequency scattering by bounded random media; and a derivation of approximate moment equations from the functional integral representation.

Chow, P. L.↗

NASA NTRS1983

Transient difference solutions of the inhomogeneous wave equation: Simulation of the Green's function

A time-dependent finite difference formulation to the inhomogeneous wave equation is derived for plane wave propagation with harmonic noise sources. The difference equation and boundary conditions are developed along with the techniques to simulate the Dirac delta function associated with a concentrated noise source. Example calculations are presented for the Green's function and distributed noise sources. For the example considered, the desired Fourier transformed acoustic pressures are determined from the transient pressures by use of a ramping function and an integration technique, both of which eliminates the nonharmonic pressure associated with the initial transient.

Baumeiste, K. J.↗

NASA NTRS1981

Determination of planetary photometric functions

The determination and removal of the photometric properties of the atmosphere and surfaces of pale planetary objects are of signal importance in the production of planetary mosaics and are themselves important scientific endeavors. The work done at the JPL Image Processing Laboratory in this area in support of the Voyager project is reviewed. Topics discussed include data-base generation, parameter determination, and photometric function removal. The importance of determining the photometric function for a planet in mosaicking together sets of images is stressed. It is noted that techniques have been developed and software has been written to allow scientists to easily determine the parameters to several photometric functions.

Mosher, J.↗

NASA NTRS1983

Transient difference solutions of the inhomogeneous wave equation - Simulation of the Green's function

Baumeister, K. J.↗

NASA NTRS1983

The cosmological evolution and luminosity function of X-ray selected active galactic nuclei

The cosmological evolution and the X-ray luminosity function of X-ray selected active galactic nuclei (AGNs) are derived and discussed. The sample used consists of 31 AGNs extracted from a fully identified sample of X-ray sources from the Einstein Observatory Medium Sensitivity Survey and is therefore exclusively defined by its X-ray properties. The distribution in space is found to be strongly nonuniform. The amount of cosmological evolution required by the X-ray data is derived in the framework of pure luminosity evolution and is found to be smaller than the amount determined from optically selected samples. The X-ray luminosity function is derived. It can be satisfactorily represented by a single power law only over a limited range of absolute luminosities. Evidence that the luminosity function flattens at low luminosity or steepens at high luminosity, or both, is presented and discussed.

Maccacaro, T.↗

NASA NTRS1983

Wall-function boundary conditions in the solution of the Navier-Stokes equations for complex compressible flows

To make computer codes for two-dimensional compressible flows more robust and economical, wall functions for these flows, under adiabatic conditions, have been developed and tested. These wall functions have been applied to three two-equation models of turbulence. The tests consist of comparisons of calculated and experimental results for transonic and supersonic flow over a flat plate and for two-dimensional and axisymmetrical transonic shock-wave/boundary-layer interaction flows with and without separation. The calculations are performed with an implicit algorithm that solves the Reynolds-averaged Navier-Stokes equations. It is shown that results obtained agree very well with the data for the complex compressible flows tested, provided criteria for use of the wall functions are followed. The expected savings in cost of the computations and improved robustness of the code were achieved.

Viegas, J. R.↗

NASA NTRS1983

A structure function representation theorem with applications to frequency stability estimation

Random processes with stationary nth differences serve as models for oscillator phase noise. The theorem proved here allows one to obtain the structure function (covariances of the nth differences) of such a process in terms of the differences of a single function of one time variable. In turn, this function can easily be obtained from the spectral density of the process. The theorem is used for computing the variance of two estimators of frequency stability.

Greenhall, C. A.↗

NASA NTRS1983

Explicit Hilbert-space representations of atomic and molecular photoabsorption spectra - Computational studies of Stieltjes-Tchebycheff functions

Computational methods are reported for construction of discrete and continuum Schroedinger states in atoms and molecules employing explicit Hilbert space procedures familiar from bound state studies. As theoretical development, the Schroedinger problem of interest is described, the Cauchy-Lanczos bases and orthonormal polynomials used in constructing L-squared Stieltjes-Tchebycheff (ST) approximations to the discrete and continuum states are defined, and certain properties of these functions are indicated. Advantages and limitations of the ST approach to spectral studies relative to more conventional calculations are discussed, and aspects of the approach in single-channel approximations to larger molecules are described. Procedures are indicated for construction of photoejection anisotropies and for performing coupled-channel calculations employing the ST formalism. Finally, explicit descriptive intercomparisons are made of the nature and diagnostic value of ST functions with more conventional scattering functions.

Hermann, M. R.↗

NASA NTRS1983

Error latency estimation using functional fault modeling

A complete modeling of faults at gate level for a fault tolerant computer is both infeasible and uneconomical. Functional fault modeling is an approach where units are characterized at an intermediate level and then combined to determine fault behavior. The applicability of functional fault modeling to the FTMP is studied. Using this model a forecast of error latency is made for some functional blocks. This approach is useful in representing larger sections of the hardware and aids in uncovering system level deficiencies.

Manthani, S. R.↗

NASA NTRS1984

Transfer Function Bounds for Partial-unit-memory Convolutional Codes Based on Reduced State Diagram

The performance of a coding system consisting of a convolutional encoder and a Viterbi decoder is analytically found by the well-known transfer function bounding technique. For the partial-unit-memory byte-oriented convolutional encoder with m sub 0 binary memory cells and (k sub 0 m sub 0) inputs, a state diagram of 2(K) (sub 0) was for the transfer function bound. A reduced state diagram of (2 (m sub 0) +1) is used for easy evaluation of transfer function bounds for partial-unit-memory codes.

Lee, P. J.↗

NASA NTRS1984

Facular Limb-darkening Functions for Irradiance Modeling

The limb darkening function of faculae is an important factor in estimating facular contributions to solar irradiance variations. The existing photometric data is reviewed and a synthetic limb darkening function for faculae was generated which was compared with the limb darkening functions currently in use for irradiance modeling. The excess facular flux ranges from 0.017 to 0.0349 of the solar photospheric flux for the various representations. The present limitation appears to be the lack of comprehensive photometric data. The representations are especially varied near the limb, where photometry is most difficult. Synoptic data on calcium plage areas is used as a substitute for facular areas in modeling. Based upon the existing data, the present best value for the effect of faculae on the solar constant is given by delta s/s = 3.9 x 10(-8) A (sub plage prime) for an active region near disk center, where A (sub plage) is the calcium plage area in millionths of a solar hemisphere.

Hirayama, T.↗

NASA NTRS1984

The Effect of Point-spread Function Interaction with Radiance from Heterogeneous Scenes on Multitemporal Signature Analysis

The point-spread function is an important factor in determining the nature of feature types on the basis of multispectral recorded radiance, particularly from heterogeneous scenes and particularly from scenes which are imaged repetitively, in order to provide thematic characterization by means of multitemporal signature. To demonstrate the effect of the interaction of scene heterogeneity with the point spread function (PSF)1, a template was constructed from the line spread function (LSF) data for the thematic mapper photoflight model. The template was in 0.25 (nominal) pixel increments in the scan line direction across three scenes of different heterogeneity. The sensor output was calculated by considering the calculated scene radiance from each scene element occurring between the contours of the PSF template, plotted on a movable mylar sheet while it was located at a given position.

Duggin, M. J.↗

NASA NTRS1983

Directional velocity analyzer for measuring electron distribution functions in plasmas

A directional velocity analyzer has been developed for measuring electron distribution functions in plasmas. It contains a collimating aperture which selects particles from a narrow cone in velocity space and a retarding potential analyzer. The distribution function f(v, theta, phi) is obtained from a large number of analyzer traces taken at different angles theta, phi. In addition, the small analyzer can be moved in space and the measurements are time resolved so as to obtain the complete phase space information f(v,r,t). The large data flow of this seven-variable function is processed with a high-speed digital data-acquisition system. The new electron velocity analyzer is applicable over a wide parameter range in electron energies and densities. Various cases of anisotropic distributions such as beams, shells, tails, and drifts have been successfully investigated.

Stenzel, R. L.↗

NASA NTRS1983

Estimation of a remote sensing system point-spread function from measured imagery

A general approach to identifying the point spread function (PSF) of a remotely sensed scene is demonstrated in terms of a step function for an abrupt change in the gray level along the row or column of the image data. The estimate of the PSF is made in terms of a finite sum of basis functions, employing a sequence of rectangular pulses covering the spatial extent of the PSF. The approximation, if narrow impulses are employed, provides accurate fidelity to the PSF. The method becomes practical when the geometrical structure of the scene elements producing the measured response is known. The field boundary is obtained through consideration of the differing intensities on each side of the boundary, which is a step discontinuity. The mathematical procedure for the technique is provided, together with a sample problem from Landsat-4 Thematic Mapper data. Atmospheric blurring and electronic effects on the overall PSF and the cubic convolution resampling effects are noted.

Mcgillem, C. D.↗

NASA NTRS1984

The non-Gaussian joint probability density function of slope and elevation for a nonlinear gravity wave field

On the basis of the mapping method developed by Huang et al. (1983), an analytic expression for the non-Gaussian joint probability density function of slope and elevation for nonlinear gravity waves is derived. Various conditional and marginal density functions are also obtained through the joint density function. The analytic results are compared with a series of carefully controlled laboratory observations, and good agreement is noted. Furthermore, the laboratory wind wave field observations indicate that the capillary or capillary-gravity waves may not be the dominant components in determining the total roughness of the wave field. Thus, the analytic results, though derived specifically for the gravity waves, may have more general applications.

Huang, N. E.↗

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