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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.↗

NASA NTRS1982

Heats of formation and thermodynamic functions for C2H, C3H, and C4H from 300 K to 6000 K

A review of the energy level and heat of formation data for the species C2H, C3H, and C4H is given. The procedure for computing thermochemical data from partition function is also reviewed. Working expressions for approximate partition functions, free-energy function, enthalpy function, and heat capacity for a linear polyatomic species are presented.

Saturno, A. F.↗

NASA NTRS1983

The fundamental structure function of oscillator noise models

Continuous-time models of oscillator phase noise x(t) usually have stationary nth differences, for some n. The covariance structure of such a model can be characterized in the time domain by the structure function: D sub n (t;gamma sub 1, gamma sub 2) = E delta (n) sub gamma sub 1 x(s+t) delta(n) sub gamma sub 2 x (s). Although formulas for the special case D sub 2 (0;gamma,gamma) (the Allan variance times 2 gamma(2)) exist for power-law spectral models, certain estimation problems require a more complete knowledge of (0). Exhibited is a much simpler function of one time variable, D(t), from which (0) can easily be obtained from the spectral density by uncomplicated integrations. Believing that D(t) is the simplest function of time that holds the same information as (0), D(t) is called the fundamental structure function. D(t) is computed for several power-law spectral models. Two examples are D(t) = K/t/(3) for random walk FM, D(t) = Kt(2) 1n/t/ for flicker FM. Then, to demonstrate its use, a BASIC program is given that computes means and variances of two Allan variance estimators, one of which incorporates a method of frequency drift estimation and removal.

Greenhall, C. A.↗

NASA NTRS1983

The spatial correlation function of rich clusters of galaxies

A series of objective statistical estimators is applied to directly study the three-dimensional distribution of rich clusters, using a recently completed redshift sample of 104 Abell clusters out to distance class four and galactic latitude of 30 deg or more. The sample and the relevant positional and redshift selection effects are discussed, and the two-point angular correlation function and nearest-neighbor distribution of clusters in the sample are determined, as well as in the larger D = 5+6 sample and in several subsamples of different richness classes and latitude zones. The redshift correlation function of clusters for various angular separations on the sky is examined as a test for the reality of the observed angular correlations. The two-point spatial correlation function of clusters in the sample is determined, and the consistency among the three observed correlation functions is tested. A model that describes all the observed correlations is presented.

Bahcall, N. A.↗

NASA NTRS1983

Point spread functions in imaging a Lambert surface from zenith through a thin scattering layer

Analytical techniques for good spatial resolution in remotely sensed images of renewable resources, such as crops, are discussed for satellite multispectral radiometry. A model is developed for an optically and geometrically thin scattering layer to account for atmospheric scattering above the object pixel of fluxes reflected from adjacent areas. The cross radiance is explored as a spread function of a point source and as a spurious component of measured radiance, and an integration over large source areas is formulated. The Henyey-Greenstein (HG) phase function is defined for an integral over a sphere and point-spread functions are presented for HG scattering. Cross radiance limited spatial resolution is also determined for the HG phase function and boundaries between reflecting and black half-planes are considered in terms of the cross radiance.

Otterman, J.↗

NASA NTRS1983

Luminosity enhancement in relativistic jets and altered luminosity functions for beamed objects

Due to relativistic effects, the observed emission from relativistic jets is quite different from the rest frame emission. Systematic differences between the observed and intrinsic intensities of sources in which jet phenomena are occurring are discussed. Assuming that jets have a power law luminosity function of a slope B, the observed luminosity distribution as a function of the velocity of the jet, the spectral index of the rest frame emission, and the range of angles of the jets relative to our line of sight are calculated. The results is well-approximated by two power laws, the higher luminosity end having the original power law index X and the lower luminosity end having a flattened exponent independent of B and only slightly greater than 1. A model consisting of beamed emission from a jet and unbeamed emission from a stationary central component is investigated. The luminosity functions for these two-component sources are calculated for two ranges of angles. For sources in which beaming is important, the luminosity function is much flatter. Because of this, the relative numbers of ""beamed'' and ""unbeamed'' sources detected on the sky depend strongly on the luminosity at which the comparison is made.

Urry, C. M.↗

NASA NTRS1984

Generalization of the subsonic kernel function in the s-plane, with applications to flutter analysis

A generalized subsonic unsteady aerodynamic kernel function, valid for both growing and decaying oscillatory motions, is developed and applied in a modified flutter analysis computer program to solve the boundaries of constant damping ratio as well as the flutter boundary. Rates of change of damping ratios with respect to dynamic pressure near flutter are substantially lower from the generalized-kernel-function calculations than from the conventional velocity-damping (V-g) calculation. A rational function approximation for aerodynamic forces used in control theory for s-plane analysis gave rather good agreement with kernel-function results, except for strongly damped motion at combinations of high (subsonic) Mach number and reduced frequency.

Cunningham, H. J.↗

NASA NTRS1983

On obtaining the forward phase functions of Saturn ring features from radio occultation observations

It is noted that the near-forward scattering functions of particles in Saturn ring features are related to 3.6 cm radio occultation power spectra by a Fredholm integral equation of the first kind. The equation reduces to an algebraic system of equation whose solution by usual inversion techniques (that is, least mean squares) is ruled out by the near singularity of the forward transformation matrix. A combination of constrained linear inversion and a filtering algorithm based on eigenvector decomposition of the matrix reduces the instabilities; this yields derived phase functions valid over the range of zero to about 12 mrad. It is noted that these functions represent the collective forward diffraction lobe of particles greater than about 1 m in radius. Since multiple scattering of the signal is a significant effect, the measured phase functions must be adjusted to obtain the singly scattered component. This single-scattering correction is examined for two physical models, namely the monolayer and the classical discrete random slab; in addition, the fraction of opacity in submeter particles for each model for particular ring features is estimated.

Zebker, H. A.↗

NASA NTRS1983

Spline approximation of quantile functions

The study reported here explored the development and utility of a spline representation of the sample quantile function of a continuous probability distribution in providing a functional description of a random sample and a method of generating random variables. With a spline representation, the random samples are generated by transforming a sample of uniform random variables to the interval of interest. This is useful, for example, in simulation studies in which a random sample represents the only known information about the distribution. The spline formulation considered here consists of a linear combination of cubic basis splines (B-splines) fit in a least squares sense to the sample quantile function using equally spaced knots. The following discussion is presented in five parts. The first section highlights major results realized from the study. The second section further details the results obtained. The methodology used is described in the third section, followed by a brief discussion of previous research on quantile functions. Finally, the results of the study are evaluated.

Schiess, J. R.↗

NASA NTRS1984

Luminosity enhancement in relativistic jets and altered luminosity functions for beamed objects

Due to relativistic effects, the observed emission from relativistic jets is quite different from the rest frame emission. Systematic differences between the observed and intrinsic intensities of sources in which jet phenomena are occurring are discussed. Assuming that jets have a power law luminosity function of a slope B, the observed luminosity distribution as a function of the velocity of the jet, the spectral index of the rest frame emission, and the range of angles of the jets relative to our line of sight are calculated. The results is well-approximated by two power laws, the higher luminosity end having the original power law index X and the lower luminosity end having a flattened exponent independent of B and only slightly greater than 1. A model consisting of beamed emission from a jet and unbeamed emission from a stationary central component is investigated. The luminosity functions for these two-component sources are calculated for two ranges of angles. For sources in which beaming is important, the luminosity function is much flatter. Because of this, the relative numbers of 'beamed' and 'unbeamed' sources detected on the sky depend strongly on the luminosity at which the comparison is made. Previously announced in STAR as N84-12889

Urry, C. M.↗

NASA NTRS1984

Functional evaluation of the Galileo attitude and articulation control subsystem using FUNSIM

The functional performance of the Galileo spacecraft's attitude and articulation control subsystem is evaluated. The tests are performed utilizing the simulation program developed on an IBM 370 system known as the Functional Simulation (FUNSIM). FUNSIM is an entirely software-based simulation which uses the actual flight software in HAL/S and simulated spacecraft dynamics in FORTRAN language. A description of how the test cases were selected to verify that the algorithms perform functionally correctly, and a summary of the problems encountered are included in the paper. The benefits of having an alternative test bed such as FUNSIM to the real-time simulation test beds which utilize the spacecraft hardware components in discovering the problems are described. A sample test case which shows that the desired tasks were performed functionally correctly is included in the paper. The commands in this test are selected to start the dual-spin spacecraft initially in launch mode and lead it all the way to inertial mode. Major attitude control algorithms such as rotor and platform attitude estimators, clock and core platform attitude estimators, clock and core platform controllers, and the command turn and burn are examined.

Namiri, M. K.↗

NASA NTRS1985

Rotorcraft digital advanced avionics system (RODAAS) functional description

A functional design of a rotorcraft digital advanced avionics system (RODAAS) to transfer the technology developed for general aviation in the Demonstration Advanced Avionics System (DAAS) program to rotorcraft operation was undertaken. The objective was to develop an integrated avionics system design that enhances rotorcraft single pilot IFR operations without increasing the required pilot training/experience by exploiting advanced technology in computers, busing, displays and integrated systems design. A key element of the avionics system is the functionally distributed architecture that has the potential for high reliability with low weight, power and cost. A functional description of the RODAAS hardware and software functions is presented.

Peterson, E. M.↗

NASA NTRS1985

The local characteristic function of interplanetary particle propagation

An easily measurable intensity function which characterizes the interplanetary propagation of charged solar flare particles is presented. This function is nearly time invariant during a solar event despite the large variations of intensity and anisotropy, but varies from event to event. It characterizes the systematic and stochastic forces of the interplanetary magnetic field which focus and scatter the particles in pitch angle. The model of focused transport shows that this function is essentially determined by the local shape and amplitude of the pitch angle diffusion coefficient kappa (mu) and by the local value of the focusing length. The time profile of the solar particle injection is typically of negligible influence. The local characteristic function may be used as a powerful new tool for a systematic analysis of flare particle angular distributions, Examples are given.

Green, G.↗

NASA NTRS1984

Distribution functions of intergalactic clouds

Width spectrum data derived from high-redshift QSO Ly-alpha absorption lines are used to study the statistical properties of intergalactic clouds. Several theoretical distribution functions for size and density are derived and tested against observational data for two types of line broadening: thermal and cosmological. Good agreement was found between the theoretical distribution functions and the observational data when the clouds were thermally broadened, and when distribution functions for both cloud size and width have a nonzero width. Attempts to fit the data with a single radius or density distribution function were unsuccessful.

Sherman, R. D.↗

NASA NTRS1984

An analysis of the AVE-SESAME I period using statistical structure and correlation functions

Structure and correlation functions are used to describe atmospheric variability during the 10-11 April day of AVE-SESAME 1979 that coincided with the Red River Valley tornado outbreak. The special mesoscale rawinsonde data are employed in calculations involving temperature, geopotential height, horizontal wind speed and mixing ratio. Functional analyses are performed in both the lower and upper troposphere for the composite 24 h experiment period and at individual 3 h observation times. Results show that mesoscale features are prominent during the composite period. Fields of mixing ratio and horizontal wind speed exhibit the greatest amounts of small-scale variance, whereas temperature and geopotential height contain the least. Results for the nine individual times show that small-scale variance is greatest during the convective outbreak. The functions also are used to estimate random errors in the rawinsonde data. Finally, sensitivity analyses are presented to quantify confidence limits of the structure functions.

Fuelberg, H. E.↗