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NASA NTRS1974

Statistical time-dependent model for the interstellar gas

We present models for temperature and ionization structure of low, uniform-density (approximately 0.3 per cu cm) interstellar gas in a galactic disk which is exposed to soft X rays from supernova outbursts occurring randomly in space and time. The structure was calculated by computing the time record of temperature and ionization at a given point by Monte Carlo simulation. The calculation yields probability distribution functions for ionized fraction, temperature, and their various observable moments. These time-dependent models predict a bimodal temperature distribution of the gas that agrees with various observations. Cold regions in the low-density gas may have the appearance of clouds in 21-cm absorption. The time-dependent model, in contrast to the steady-state model, predicts large fluctuations in ionization rate and the existence of cold (approximately 30 K), ionized (ionized fraction equal to about 0.1) regions.

Gerola, H.↗

NASA NTRS1974

On first cycle slip time of phase-locked loops in cascade

Precise measurement and spacecraft tracking are obtained by using phase-locked loops in cascade in two-way communications links. Statistics on cycle slip time are of vital importance in system planning and design. This paper presents: (1) results of a computer simulation study of the mean time to first cycle slip of cascade phase-locked loops preceded by bandpass limiters, and (2) the determination of probability distributions of cycle slip. Numerical results are obtained for a typical coherent communication system.

Yuen, J. H.↗

NASA NTRS1975

Theory of fluctuations of extended air showers

The Monte Carlo method was used to calculate the probability distribution functions of shower characteristics for primary protons at sea level. The calculation was based on the following model of the elementary event: the interaction paths are 90 g/sq cm for nucleons and 120 g/sq cm for pions. The nonelasticity coefficient for nucleons is uniformly distributed between 0.1 and 0.9, and for pions it is equal to 1. Isobaric pions are taken into account. The spectra of secondary particles were determined using Cocconi's approximation formula. The calculation for the nuclei was carried out on the assumption of a breakup of the nucleus into component nucleons. The mean number of particles and the variances of the distributions for electrons when the number of muons was fixed, and for muons when the number of electrons was fixed, were calculated.

Dedenko, L. G.↗

NASA NTRS1975

A B-B-G-K-Y framework for fluid turbulence

A kinetic theory for fluid turbulence is developed from the Liouville equation and the associated BBGKY hierarchy. Real and imaginary parts of Fourier coefficients of fluid variables play the roles of particles. Closure is achieved by the assumption of negligible five-coefficient correlation functions and probability distributions of Fourier coefficients are the basic variables of the theory. An additional approximation leads to a closed-moment description similar to the so-called eddy-damped Markovian approximation. A kinetic equation is derived for which conservation laws and an H-theorem can be rigorously established, the H-theorem implying relaxation of the absolute equilibrium of Kraichnan. The equation can be cast in the Fokker-Planck form, and relaxation times estimated from its friction and diffusion coefficients. An undetermined parameter in the theory is the free decay time for triplet correlations. Some attention is given to the inclusion of viscous damping and external driving forces.

Montgomery, D.↗

NASA NTRS1975

Use of the Wigner representation in scattering problems

The basic equations of quantum scattering were translated into the Wigner representation, putting quantum mechanics in the form of a stochastic process in phase space, with real valued probability distributions and source functions. The interpretative picture associated with this representation is developed and stressed and results used in applications published elsewhere are derived. The form of the integral equation for scattering as well as its multiple scattering expansion in this representation are derived. Quantum corrections to classical propagators are briefly discussed. The basic approximation used in the Monte-Carlo method is derived in a fashion which allows for future refinement and which includes bound state production. Finally, as a simple illustration of some of the formalism, scattering is treated by a bound two body problem. Simple expressions for single and double scattering contributions to total and differential cross-sections as well as for all necessary shadow corrections are obtained.

Bemler, E. A.↗

NASA NTRS1975

Sodium D-line emission from Io - Synoptic observations from Table Mountain Observatory

We report the first results of a program initiated at Table Mountain Observatory to study the time variation of the sodium D-line emission around Io. During 1974 July and August, 51 spectra were obtained. These data demonstrate that (1) the sodium emission is highly correlated with Io's orbital position, (2) the gross temporal and amplitude characteristics of the emission are explained if resonance scattering of sunlight is the dominant excitation mechanism, (3) the emission is not directly related to dekametric noise storms from Jupiter, (4) an upper limit of 130 kR is placed on any constant near-surface (auroral) source of emission, (5) a steady-state source of sodium operated during our 7-week observing interval, (6) the sodium cloud is probably distributed in a partial toroid, possibly with more sodium leading than trailing Io, and (7) the D-line emission does not depend strongly on the solar phase angle.

Bergstralh, J. T.↗

NASA NTRS1975

Binary galaxy orbit statistics. I - Fixed mass and major axis

Averages for the projected separation, squared radial velocity difference, and the product of these, are presented for a binary galaxy system of fixed mass and major axis, but any orbital eccentricity. The average of the product varies by a factor about 3 for eccentricities from 0 to 1.0. For circular orbits, the results agree with those of Page (1952, 1960, 1961), but for linear orbits his mass estimate is too small by a factor 6. The mutual regressions of the velocity and separation on each other are calculated, and are presented in such a way as to exhibit the relative likelihood of occupation of the different parts of the regression curves. 'Isopleths' for the probability distribution are presented for a few values of the eccentricity to illustrate the underlying cause of pileup at certain parts of the regression curves. It is concluded that previous analyses were inadequate for failing to take into account that the regression curves represent in many cases a distribution that is almost wholly depopulated through most of the range. It is evident that the data are insufficient to draw a firm conclusion about the distribution of eccentricities.

Noerdlinger, P. D.↗

NASA NTRS1975

Random coding strategies for minimum entropy

This paper proves that there exists a fixed random coding strategy for block coding a memoryless information source to achieve the absolute epsilon entropy of the source. That is, the strategy can be chosen independent of the block length. The principal new tool is an easy result on the semicontinuity of the relative entropy functional of one probability distribution with respect to another. The theorem generalizes a result from rate-distortion theory to the 'zero-infinity' case.

Posner, E. C.↗

NASA NTRS1975

Revised prediction (estimation) of Cape Kennedy, Florida, wind speed profile

The prediction of the wind profile maximum speed at Cape Kennedy, Florida, is made for any selected calendar data. The prediction is based on a normal probability distribution model with 15 years of smoothed input data and is static in the sense that no dynamic principles of persistence or synoptic features are considered. Comparison with similar predictions based on 6 years of data shows the same general pattern, but the variability decreased with the increase of sample size.

Guttman, N. B.↗

NASA NTRS1976

Support of selected X-ray studies to be performed using data from the Uhuru (SAS-A) satellite

A new measurement of the diffuse X-ray emission sets more stringent upper limits on the fluctuations of the background and on the number counts of X-ray sources with absolute value of b 20 deg than previous measurements. A random sample of background data from the Uhuru satellite gives a relative fluctuation in excess of statistics of 2.0% between 2.4 and 6.9 keV. The hypothesis that the relative fluctuation exceeds 2.9% can be rejected at the 90% confidence level. No discernable energy dependence is evident in the fluctuations in the pulse height data, when separated into three energy channels of nearly equal width from 1.8 to 10.0 keV. The probability distribution of fluctuations was convolved with the photon noise and cosmic ray background deviation (obtained from the earth-viewing data) to yield the differential source count distribution for high latitude sources. Results imply that a maximum of 160 sources could be between 1.7 and 5.1 x 10 to the -11 power ergs/sq cm/sec (1-3 Uhuru counts).

Garmire, G. P.↗

NASA NTRS1976

Stochastic sea state for SRB studies

Ocean surface characteristics at two locations were studied for a space shuttle solid rocket booster ocean impact and recovery analysis. Probability distributions of wave heights, wave slopes, wave velocities, ocean currents, and 1-kilometer altitude winds were formulated. Procedures for generating ocean wave simulations are described.

Perlmutter, M.↗

NASA NTRS1976

Aircraft motion and passenger comfort data from scheduled commercial airline flights

Data concerning the ride quality of aircraft taken on board commercial airline flights was presented. Five types of data are included: (1) root mean square (RMS) values of linear acceleration, angular acceleration or angular velocities, along with passenger subjective evaluations, (2) power spectra for the motion in each of six degrees of freedom, (3) scattergrams showing the probability density of the rms accelerations in the vertical and transverse directions, (4) probability distributions of the motion, and (5) on board noise levels during takeoff, climb, cruise, and descent.

Gruesbeck, M. G.↗

NASA NTRS1976

Nondeterministic data base for computerized visual perception

A description is given of the knowledge representation data base in the perception subsystem of the Mars robot vehicle prototype. Two types of information are stored. The first is generic information that represents general rules that are conformed to by structures in the expected environments. The second kind of information is a specific description of a structure, i.e., the properties and relations of objects in the specific case being analyzed. The generic knowledge is represented so that it can be applied to extract and infer the description of specific structures. The generic model of the rules is substantially a Bayesian representation of the statistics of the environment, which means it is geared to representation of nondeterministic rules relating properties of, and relations between, objects. The description of a specific structure is also nondeterministic in the sense that all properties and relations may take a range of values with an associated probability distribution.

Yakimovsky, Y.↗

NASA NTRS1976

The computer simulation of automobile use patterns for defining battery requirements for electric cars

A Monte Carlo simulation process was used to develop the U.S. daily range requirements for an electric vehicle from probability distributions of trip lengths and frequencies and average annual mileage data. The analysis shows that a car in the U.S. with a practical daily range of 82 miles (132 km) can meet the needs of the owner on 95% of the days of the year, or at all times other than his long vacation trips. Increasing the range of the vehicle beyond this point will not make it more useful to the owner because it will still not provide intercity transportation. A daily range of 82 miles can be provided by an intermediate battery technology level characterized by an energy density of 30 to 50 watt-hours per pound (66 to 110 W-hr/kg). Candidate batteries in this class are nickel-zinc, nickel-iron, and iron-air. The implication of these results for the research goals of far-term battery systems suggests a shift in emphasis toward lower cost and greater life and away from high energy density.

Schwartz, H. J.↗

NASA NTRS1975

SEASAT economic assessment. Volume 10: The SATIL 2 program (a program for the evaluation of the costs of an operational SEASAT system as a function of operational requirements and reliability

The SATIL 2 computer program was developed to assist with the programmatic evaluation of alternative approaches to establishing and maintaining a specified mix of operational sensors on spacecraft in an operational SEASAT system. The program computes the probability distributions of events (i.e., number of launch attempts, number of spacecraft purchased, etc.), annual recurring cost, and present value of recurring cost. This is accomplished for the specific task of placing a desired mix of sensors in orbit in an optimal fashion in order to satisfy a specified sensor demand function. Flow charts are shown, and printouts of the programs are given.

Source record↗

NASA NTRS1976

A BBGKY framework for fluid turbulence

A framework is presented for a systematic kinetic theory of turbulence originating from the Liouville equation for the Fourier coefficients of fluid variables. The real and imaginary parts of these Fourier coefficients play the role that particle coordinates (positions and momenta) play in the BBGKY theory. The basic relations of the problem are the incompressible Navier-Stokes equations in two dimensions with zero viscosity, with the probability distributions of Fourier coefficients rather than moments being the basic variables of the theory. A kinetic equation is derived and shown to possess a number of requirements that any reasonable kinetic equation must have: conservation laws, positive-definite spectral densities, and an H-theorem. The major lack in the theory is any reliable information on the relaxation predicted by the complicated linear operator H. Closure of the hierarchy is achieved by the hypothesis that the five-coefficient correlation function is negligible. Problems associated with inclusion of viscosity and external driving forces are discussed.

Montgomery, D.↗

NASA NTRS1976

A decision model for planetary missions

Many techniques developed for the solution of problems in economics and operations research are directly applicable to problems involving engineering trade-offs. This paper investigates the use of utility theory for decision making in planetary exploration space missions. A decision model is derived that accounts for the objectives of the mission - science - the cost of flying the mission and the risk of mission failure. A simulation methodology for obtaining the probability distribution of science value and costs as a function spacecraft and mission design is presented and an example application of the decision methodology is given for various potential alternatives in a comet Encke mission.

Hazelrigg, G. A., Jr.↗

NASA NTRS1978

Defining structural limit zones

Method for defining limit loads uses probability distribution of largest load occurring during given time intervals. Method is compatible with both deterministic and probabilistic structural design criteria. It also rationally accounts for fact that longer structure is exposed to random loading environment, greater is possibility that it will experience extreme load.

Merchant, D. H.↗