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At least 271 records · Page 15
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NASA NTRS1972

Degree and plane of polarization of multiple scattered light. 1: Homogeneous cloud layers

The degree of polarization and the direction of the plane of polarization are calculated by a Monte Carlo method for homogeneous layers. Two solar zenith angles and a range of optical thicknesses up to 10 are considered. The results are compared with calculations for single scattered photons. For a given pair of incident and scattered directions, there are only two possible values for the direction of the plane of polarization differing by 90 deg for single scattering from spherical aerosols. The choice between these two values depends only on the sign of the element M(-) in the first row and second column of the scattering matrix in the I, Q, U, V representation. In most cases there is little change in the direction of the plane of polarization when multiple scattering is taken into account, so that this quantity can usually be predicted from a very simple trigonometric relationship to good accuracy. Measurements of the direction of the plane of polarization at appropriately chosen angles provides information about the size distribution of the scattering centers.

Kattawar, G. W.↗
NASA NTRS1972

Degree and plane of polarization of multiple scattered light. 2: Earth's atmosphere with aerosols

The degree of polarization, as well as the direction of the plane of polarization, were calculated by a Monte Carlo method for the reflected and transmitted photons from the earth's atmosphere. The solar photons were observed during multiple collisions with aerosols and the Rayleigh scattering centers in the atmosphere. The aerosol number density, as well as the ratio of aerosol to Rayleigh scattering, varies with height. The proportion of aerosol to Rayleigh scattering was appropriately chosen at each wavelength 0.4 microns and 0.7 microns; ozone absorption was included where appropriate. Three different aerosol number densities were used to study the effects of aerosol variations. Results are given for a solar zenith angle of 81.37 deg and a surface albedo of zero. The polarization of the reflected and transmitted photons was found to be sensitive to the amount of aerosols in the atmosphere at certain angles of observation.

Plass, G. N.↗
NASA NTRS1972

Variance reduction in Monte Carlo analysis of rarefied gas diffusion

The present analysis uses the Monte Carlo method to solve the problem of rarefied diffusion between parallel walls. The diffusing molecules are evaporated or emitted from one of two parallel walls and diffused through another molecular species. The analysis treats the diffusing molecule as undergoing a Markov random walk and the local macroscopic properties are found as the expected value of the random variable, the random walk payoff. By biasing the transition probabilities and changing the collision payoffs the expected Markov walk payoff is retained but its variance is reduced so that the M. C. result has a much smaller error.

Perlmutter, M.↗
NASA NTRS1972

Adaptive control of stochastic linear systems with unknown parameters

The problem of optimal control of linear discrete-time stochastic dynamical system with unknown and, possibly, stochastically varying parameters is considered on the basis of noisy measurements. It is desired to minimize the expected value of a quadratic cost functional. Since the simultaneous estimation of the state and plant parameters is a nonlinear filtering problem, the extended Kalman filter algorithm is used. Several qualitative and asymptotic properties of the open loop feedback optimal control and the enforced separation scheme are discussed. Simulation results via Monte Carlo method show that, in terms of the performance measure, for stable systems the open loop feedback optimal control system is slightly better than the enforced separation scheme, while for unstable systems the latter scheme is far better.

Ku, R. T.↗
NASA NTRS1971

The earth and the moon /Harold Jeffreys Lecture/.

The internal structures of the earth and the moon are compared in the light of the latest extensive data on the earth structure, mobility of the earth outer layers, and the properties of lunar crust. The Monte Carlo method is applied to develop an earth model by a stepwise process beginning with a random distribution of two elastic velocities and the density as a function of de pth. Lunar seismic, magnetic, and rock analysis data are used to infer the properties of the moon. The marked planetological contrast between the earth and the moon is shown to consist in that the earth is highly differentiated and still undergoes a large-scale differentiation, while the moon has lost its volatiles in its early history and has a cold dynamically inactive shell which has been without basic changes for three billion years.

Press, F.↗
NASA NTRS1971

Geometrical factor and directional response of single and multi-element particle telescopes.

After a general treatment of the gathering power of particle telescopes, exact formulae are presented for the geometrical factor and directional response of multielement cylindrically symmetric telescopes with circular or rectangular cross sections. Some useful approximations to these formulae are given. For the gathering power in arbitrary geometries, there is a discussion of applicable digital computer techniques focusing particularly on a Monte Carlo method.

Sullivan, J. D.↗
NASA NTRS1972

Calculation of the lunar photon albedo from galactic and solar proton bombardment.

The lunar photon albedo due to cosmogenic and primordial photon sources has been calculated. The individual photon leakage spectra from prompt photons produced by galactic cosmic ray (GCR) and solar cosmic ray (SCR) induced nuclear interactions, from the decay of GCR- and SCR-induced radionuclides, and from the decay of naturally occurring radionuclides are given. An approximate estimate of the leakage from the photon-electron cascade initiated by the decay of neutral pions is also given. Monte Carlo methods have been used to determine the nucleon-meson cascade, and discrete-ordinates methods were used for the photon and low-energy neutron transport.

Armstrong, T. W.↗
NASA NTRS1972

Transfer of resonance-line radiation in differentially expanding atmospheres. I - General considerations and Monte Carlo calculations.

A Monte Carlo method is given for analyzing the transfer of resonance radiation in a rapidly and differentially expanding nebula. Coherence in the frame of the atom is shown to lead to interesting modifications of the emergent radiation field, as compared with the other more usual assumptions of coherence or redistribution in the fluid frame. Results are presented in tabular form suitable for further use. Sample line profiles produced by pure scattering out of the continuum are generated, and it is shown that an arbitrarily high peak can be obtained. This conclusion is independent of the coherence assumption used. The distribution of the number of scatterings is found in all cases. An analytic solution is presented for the case of coherence in the fluid frame.

Caroff, L. J.↗
NASA NTRS1972

Degree and direction of polarization of multiple scattered light. I - Homogeneous cloud layers.

It is shown that the Monte Carlo method can provide useful information on the polarization and its direction for homogeneous layers corresponding to the haze C, nimbostratus, and ice crystals models. Results for various optical thicknesses and two solar zenith angles show the variation with these parameters. In most cases the direction of polarization with respect to the meridian plane (which contains the outgoing photon) does not change appreciably with the optical thickness of the scattering layer, so that the conclusion that the direction of polarization is determined mainly by the direction of the incident and scattered photons, obtained for single scattering, should apply approximately when multiple scattering is taken into account.

Kattawar, G. W.↗
NASA NTRS1972

Degree and direction of polarization of multiple scattered light. II - Earth's atmosphere with aerosols.

The radiance, polarization, and direction of polarization of the radiation reflected and transmitted through the atmosphere are calculated by a Monte Carlo method on the basis of a realistic model of the atmosphere. The calculated polarization is shown to depend on the aerosol amount and to have normally a value intermediate between that for pure Rayleigh and pure aerosol scattering. The polarization for multiple scattered photons is usually less than the value calculated for single scattering, but may be larger in low-polarization regions near other regions of high polarization. The direction of polarization shows little variation with either the aerosol amount or the value of the surface albedo.

Plass, G. N.↗
NASA NTRS1973

Experimental study of shock-wave reflection from a thermally accommodating wall.

Shock-tube experiments have been conducted to study the nonequilibrium gas-surface interaction which occurs when a thick shock wave in argon reflects from a coplanar, heat-conducting wall. Fast-response instrumentation was used to monitor variations in temperature and normal stress on the surface of the shock-tube end wall during and immediately following reflection of the incident shock wave. The laboratory observations are compared with computer predictions obtained by Deiwert using the direct-simulation Monte Carlo method, and excellent agreement is obtained when a suitable average thermal accommodation coefficient is chosen for the wall surface.

Hanson, R. K.↗
NASA NTRS1972

Some new results on electron transport in the atmosphere

The penetration, diffusion and slowing down of electrons in a semi-infinite air medium has been studied by the Monte Carlo method. The results are applicable to the atmosphere at altitudes up to 300 km. Most of the results pertain to monoenergetic electron beams injected into the atmosphere at a height of 300 km, either vertically downwards or with a pitch-angle distribution isotropic over the downward hemisphere. Some results were also obtained for various initial pitch angles between 0 deg and 90 deg. Information has been generated concerning the following topics: (1) the backscattering of electrons from the atmosphere, expressed in terms of backscattering coefficients, angular distributions and energy spectra of reflected electrons, for incident energies T(o) between 2 keV and 2 MeV; (2) energy deposition by electrons as a function of the altitude, down to 80 km, for T(o) between 2 keV and 2 MeV; (3) the corresponding energy depostion by electron-produced bremsstrahlung, down to 30 km; (4) the evolution of the electron flux spectrum as function of the atmospheric depth, for T(o) between 2 keV and 20 keV. Energy deposition results are given for incident electron beams with exponential and power-exponential spectra.

Berger, M. J.↗
NASA NTRS1974

Neutron propagation and 2.2 MeV gamma-ray line production in the solar atmosphere

The 2.2 MeV gamma ray line intensity from the sun was calculated using a Monte Carlo method for neutron propagation in the solar atmosphere. Detailed results are provided on the total gamma ray yield per neutron and on the time profile of the 2.2 MeV line from an instantaneous and monoenergetic neutron source. The parameters which have the most significant effects on the line intensity are the energies of the neutrons, the position of the neutron source on the sun, and the abundance of He-3 in the photosphere. For an isotropic neutron source which is not too close to the limb of the sun, the gamma ray yield is between about 0.02 to 0.2 photons per neutron, provided that the neutron energies are in the range 1 to 100 MeV and the ratio He-3/H is less than about .00005.

Wang, H. T.↗
NASA NTRS1974

A Monte Carlo investigation of experimental data requirements for fitting polynomial functions

This report examines the extent to which sample size affects the accuracy of a low order polynomial approximation of an experimentally observed quantity and establishes a trend toward improvement in the accuracy of the approximation as a function of sample size. The task is made possible through a simulated analysis carried out by the Monte Carlo method, in which data are generated by using several transcendental or algebraic functions as models. Contaminated data of varying amounts are fitted to linear quadratic or cubic polynomials, and the behavior of the mean-squared error of the residual variance is determined as a function of sample size. Results indicate that the effect of the size of the sample is significant only for relatively small sample sizes and diminishes drastically for moderate and large amounts of experimental data.

Canavos, G. C.↗
NASA NTRS1973

A numerical study of rays in random media

Statistics of electromagnetic rays in a random medium are studied numerically by the Monte Carlo method. Two dimensional random surfaces with prescribed correlation functions are used to simulate the random media. Rays are then traced in these sample media. Statistics of the ray properties such as the ray positions and directions are computed. Histograms showing the distributions of the ray positions and directions at different points along the ray path as well as at given points in space are given. The numerical experiment is repeated for different cases corresponding to weakly and strongly random media with isotropic and anisotropic irregularities. Results are compared with those derived from theoretical investigations whenever possible.

Youakim, M. Y.↗
NASA NTRS1973

Ground state properties of spin-alined atomic hydrogen

Theoretical calculation of the ground state properties of spin-alined atomic hydrogen by the Monte Carlo method. The interatomic interaction, as described by the results of Kolos and Wolniewicz (1965), is made fit to a Morse potential form. An appropriate trail wavefunction is formed from the short-range part of the WKB solution for a pair of atoms interacting through a Morse potential.

Dugan, J. V., Jr.↗
NASA NTRS1974

On the robustness of a Bayes estimate

This paper examines the robustness of a Bayes estimator with respect to the assigned prior distribution. A Bayesian analysis for a stochastic scale parameter of a Weibull failure model is summarized in which the natural conjugate is assigned as the prior distribution of the random parameter. The sensitivity analysis is carried out by the Monte Carlo method in which, although an inverted gamma is the assigned prior, realizations are generated using distribution functions of varying shape. For several distributional forms and even for some fixed values of the parameter, simulated mean squared errors of Bayes and minimum variance unbiased estimators are determined and compared. Results indicate that the Bayes estimator remains squared-error superior and appears to be largely robust to the form of the assigned prior distribution.

Canavos, G. C.↗
NASA NTRS1974

Some new results on electron transport in the atmosphere

The penetration, diffusion and slowing down of electrons in a semiinfinite air medium has been studied by the Monte Carlo method. The results are applicable in the atmosphere at altitudes up to 300 km. Most of the results pertain to monoenergetic electron beams, with energies between 2 keV and 2 MeV, injected into the atmosphere at a height of 300 km, either vertically downwards or with a pitch-angle distribution isotropic over the downward hemisphere. Some results were also obtained for various initial pitch angles between 0 and 90 deg. Information has been generated concerning the backscattering of electrons from the atmosphere, the altitude dependence of energy deposition by electrons and by secondary bremsstrahlung, and the evolution of electron flux spectra as function of the atmospheric depth.

Berger, M. J.↗