Inverse velocity space spectra and kinetic equations.
Inverse velocity space spectra as alternate to velocity distribution functions for statistical description of particle collections
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Inverse velocity space spectra as alternate to velocity distribution functions for statistical description of particle collections
Optimum methods of optical communication accounting for the effects of the turbulent atmosphere and quantum mechanics, both by the semi-classical method and the full-fledged quantum theoretical model are described. A concerted effort to apply the techniques of communication theory to the novel problems of optical communication by a careful study of realistic models and their statistical descriptions, the finding of appropriate optimum structures and the calculation of their performance and, insofar as possible, comparing them to conventional and other suboptimal systems are discussed. In this unified way the bounds on performance and the structure of optimum communication systems for transmission of information, imaging, tracking, and estimation can be determined for optical channels.
A global rain rate statistic model is used to link microwave propagation statistics to measurable rain statistics in order to develop international telecommunication site criteria for radio relay and communication satellite services that minimize interference between receivers and transmitters. This rain coordination procedure utilizes a rain storm cell size, a statistical description of the rainfall rate within the cell valid for most of the earth's surface, approximations between Raleigh scatter and constancy of precipitation with altitude, and an analytic relation between radar reflectivity and rain rate.
Earth viewing space missions offer exciting new possibilities in several earth resources disciplines - geography, hydrology, agriculture, geology, and oceanography, to name a few. A most useful tool in planning experiments and applying space technology to earth observation is a statistical description of atmospheric parameters. Four dimensional atmospheric models and a world wide cloud model are used to produce atmospheric attenuation models to predict degradation effects for all classes of sensors for application to earth sensing experiments from spaceborne platforms. To insure maximum utility and application of these products, the development of an interaction model of microwave energy and atmospheric variables provides a complete description of the effects of atmospheric moisture upon microwaves.
Relationships between LANDSAT-1 multispectral scanner (MSS) data and the trophic status of a group of lakes in the north-northeastern part of the United States were studied by predicting the magnitudes of two trophic state indicators, estimating lake position on a multivariate trophic scale, and automatically classifying lakes according to their trophic state. Initially, the principal component ordination was employed with 100 lakes. MSS data for some 20 lakes was then extracted from computer-compatible tapes (CCT) using a binary marking technique. The output was in the form of descriptive statistics and photographic concatenations. Color ratios were incorporated into regression models for the prediction of Secchi disc transparency, chlorophyll a, and lake position on the tropic scale. Results indicate that the LANDSAT-1 system, although handicapped by low spectral and spatial resolutions as well as excessive cloud cover, can be used as a supplemental data source in lake survey programs.
The author has identified the following significant results. The geological interpretation on data exhibiting the Italian peninsula led to the recognition of tectonic features which are explained by a clockwise rotation of various blocks along left-handed transform faults. These faults can be interpreted as resulting from shear due to main stress directed north-eastwards. A land use map of the mountainous regions of Italy was produced on a scale of 1:250,000. For the digital treatment of MSS-CCTs an image processing software was written in FORTRAN 4. The software package includes descriptive statistics and also classification algorithms.
Measurements of the response of a large frame-stringer panel excited by supersonic turbulent boundary layer are reported. The statistical description of the wall pressure fluctuations in terms of the mean flow parameters governing the turbulent boundary layer is given. These results can be used in the development of design criteria on the response of sidewall structure of a large airplane in supersonic flight, since both forcing field and structure are realistic. Results indicate the significant importance of the modal coupling and the acoustic damping. The acoustic damping plays a major role in the response of the structure.
A rigorous real-variables treatment of general data compression and encoding problems, centered on formulation and proof of relevant existence theorems and a unified formulation of source coding (both noiseless and with a fidelity criterion) in inaccurately or incompletely specified statistical environments. Difficulties in modeling of sources with unknown or imperfectly known statistical descriptions are analyzed and source codes (SC) are classified (variable-rate noiseless SC, fixed-rate noiseless SC) and analyzed, along with types of code sequences (weighted-universal, maximin-universal, strongly or weakly minimax-universal). Universal coding on video data, variable-rate coding with distortion, and distortion-rate functions are discussed. Design strategies for universal coding algorithms are suggested, but the article is not oriented to specific methods of synthesizing data compression systems.
A series of microwave measurements was conducted to determine the radar cross section of the Space Shuttle Orbiter vehicle at a frequency and at aspect angles applicable to re-entry radar acquisition and tracking. The measurements were performed in a microwave anechoic chamber using a 1/15th scale model and a frequency applicable to C-band tracking radars. The data were digitally recorded and processed to yield statistical descriptions useful for prediction of orbiter re-entry detection and tracking ranges.
The author has identified the following significant results. Each state model was separately evaluated to determine if a projected performance to the country level would satisfy a 90/90 criterion. All state models, except the North Dakota and Kansas models, satisfied that criterion both for district estimates aggregated to the state level and for state estimates directly from the models. In addition to the tests of the 90/90 criterion, the models were examined for their ability to adequately respond to fluctuations in weather. This portion of the analysis was based on a subjective interpretation of values of certain description statistics. As a result, 10 of the 12 models were judged to respond inadequately to variation in weather-related variables.
A statistical description of variations in the torque acting on a rotating neutron star is developed in terms of stationary random processes and is used to calculate the torque power spectrum, stellar response power spectrum, and the total mean square variation in the crustal angular velocity of the star. The response of a star with a finite frequency internal mode is calculated with the aid of phenomenological equations which correspond to a generalized two-component model of the star. The form of the stellar response functions is examined in a number of limiting cases of physical interest, and the dependence of the response power on both the period of observation and the time over which fluctuating torques have been acting is discussed.
A statistical description of turbulence in an incompressible fluid obeying the Navier-Stokes equations is proposed, where pressure is regarded as a potential for the interaction between fluid elements. A scaling procedure divides a fluctuation into three ranks representing the three transport processes of macroscopic evolution, transport property, and relaxation. Closure is obtained by relaxation, and a kinetic equation is obtained for the fluctuation of the macroscopic rank of the distribution function. The solution gives the transfer function and eddy viscosity. When applied to the inertia subrange of the energy spectrum the analysis recovers the Kolmogorov law and its numerical coefficient.
LANDSAT MSS data from four different dates were extracted from computer tapes using a semiautomated digital data handling and analysis system. Reservoirs were extracted from the surrounding land matrix by using a Band 7 density level slice of 3; and descriptive statistics to include mean, variance, and ratio between bands for each of the four bands were calculated. Significant correlations ( 0.80) were identified between the MSS statistics and many trophic indicators from ground truth water quality data collected at 35 reservoirs in the greater Tennessee Valley region. Regression models were developed which gave significant estimates of each reservoir's trophic state as defined by its trophic state index and explained in all four LANDSAT frames at least 85 percent of the variability in the data. To illustrate the spatial variations within reservoirs as well as the relative variations between reservoirs, a table look up elliptical classification was used in conjunction with each reservoir's trophic state index to classify each reservoir on a pixel by pixel basis and produce color coded thematic representations.
A study of the optical characteristics of cloud-to-ground dischargers and how they compare with intracloud flashes was completed. Time resolved optical (7774A) and electric field-change waveforms were measured above clouds from a U2 airplane coincident with ground-based measurements of lightning. The optical pulse trains are studied for within and between flash variability. Specifically, for each flash researchers examine the 10, 50 (full width half maximum), and 90 percent pulse widths; the 10-10, 10-50, 10-90, and 10-peak percent amplitude rise times; the radiances (optical power densities); radiant energy densities; and pulse intervals. The optical pulse characteristics of first strokes, subsequent strokes, the intracloud components of cloud-to-ground flashes and intracloud flashes as viewed from above cloud are shown to exhibit very similar waveshapes, radiances and radiant energy densities. Descriptive statistics on these pulse categories were tabulated for 25 visually confirmed cloud-to-ground flashes (229 optical pulses) and 232 intracloud flashes (3126 optical pulses). A companion study of lightning observations above and below cloud in storms, storm complexes, and mesoscale convective systems has also been completed. Researchers compared the mapping of total lightning activity from above clouds with ground-based measurements and storm evolution. Although the total (IC + CG) lightning activity is the more representative indication of thunderstorm growth and decay, the ground strike data can be used to locate, diagnose, and track storm evolution in a number of instances.
The procedures and results of a study of a conceptual system for measuring the debris environment on the space station is discussed. The study was conducted in two phases: the first consisted of experiments aimed at evaluating location of impact through panel response data collected from acoustic emission sensors; the second analyzed the available statistical description of the environment to determine the probability of the measurement system producing useful data, and analyzed the results of the previous tests to evaluate the accuracy of location and the feasibility of extracting impactor characteristics from the panel response. The conclusions were that for one panel the system would not be exposed to any event, but that the entire Logistics Module would provide a modest amount of data. The use of sensors with higher sensitivity than those used in the tests could be advantageous. The impact location could be found with sufficient accuracy from panel response data. The waveforms of the response were shown to contain information on the impact characteristics, but the data set did not span a sufficient range of the variables necessary to evaluate the feasibility of extracting the information.
Probabilistic structural analysis has been developed to analyze the effects of fluctuating loads, variable material properties, and uncertain analytical models especially for high performance structures such as SSME turbopump blades. The computer code NESSUS (Numerical Evaluation of Stochastic Structure Under Stress) was developed to serve as a primary computation tool for the characterization of the probabilistic structural response due to the stochastic environments by statistical description. The code consists of three major modules NESSUS/PRE, NESSUS/FEM, and NESSUS/FPI. NESSUS/PRE is a preprocessor which decomposes the spatially correlated random variables into a set of uncorrelated random variables using a modal analysis method. NESSUS/FEM is a finite element module which provides structural sensitivities to all the random variables considered. NESSUS/FPI is Fast Probability Integration method by which a cumulative distribution function or a probability density function is calculated.
This paper describes the analysis and results of an investigation of the Mars Rover/Sample Return mission's landing strategy, together with the trade-offs of different landing strategies. The percentile points and the descriptive statistics of the probability distribution of traverse distances are calculated using a simple model formulated on the basis of landing error characteristics. The results show that variations in the landing stratgegy can significantly affect the traverse distance requirements, which range from 20 to 200 km.
The statistical description of ground clutter at an airport and in the surrounding area is addressed. These data are being utilized in a program to detect microbursts. Synthetic Aperture Radar (SAR) data were collected at the Philadelphia Airport. These data and the results of the clutter study are described. This 13 km x 10 km scene was imaged at 9.38 GHz and HH-polarization and contained airport grounds and facilities (6 percent), industrial (14 percent), residential (14 percent), fields (10 percent), forest (8 percent), and water (33 percent). Incidence angles ranged from 40 to 84 deg. Even at the smallest incidence angles, the distributed targets such as forest, fields, water, and residential rarely had mean scattering coefficients greater than -10 dB. Eighty-seven percent of the image had scattering coefficients less than -17.5 dB. About 1 percent of the scattering coefficients exceeded 0 dB, with about 0.1 percent above 10 dB. Sources which produced the largest cross sections were largely confined to the airport grounds and areas highly industrialized. The largest cross sections were produced by observing broadside large buildings surrounded by smooth surfaces.