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Results for “Monte Carlo Methods”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 397 records · Page 22
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NASA NTRS1974

Reflection of a thick planar shock wave from a coplanar surface

The reflection of a thick shock wave from an adsorbing surface has been studied for argon and neon test gases using the direct simulation Monte Carlo method and laboratory shock-tube experiments. In the simulation, collisions between gas atoms were calculated with a point-center repulsive intermolecular potential, and collisions between gas atoms and the surface were described by a simple two-parameter model which includes the effects of adsorption and thermal accommodation. Experimental data included normal stress and temperature time histories on the surface of a shock-tube and wall. These data and published data of density variations near the end wall were compared with simulation results to assess the influence of adsorption and accommodation on the flowfield and the surface and also to infer optimum values for the surface-interaction model parameters. Good quantitative agreement between simulation and laboratory data was found with this simple surface-interaction model.

Deiwert, G. S.↗
NASA NTRS1974

Pre-mare cratering and early solar system history

An evaluation of the application of the high extra-lunar flux in pre-mare times to more general problems of early solar system history is attempted by combining the results of dynamic studies with lunar chronological data. Dynamical studies permit separate evaluation of the possible sources for both the normal flux during the first 600 m.y. years of lunar history as well as the peak which apparently occurred 4.0 b.y. ago. Dynamical studies have been carried out in order to determine the extent to which a heliocentric flux could be confined to the Moon (and Earth). A Monte Carlo method has been used to calculate the relative impact rates of planet-crossing bodies with the moon and the terrestrial planets. It is concluded that the time-variation of the flux on these planets is closely related to that on the moon.

Wetherill, G. W.↗
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

Selected Theoretical Studies Group contributions to the 14th International Cosmic Ray conference

The galactic distribution of H2 was studied through gamma radiation and through X-ray, optical, and infrared absorption measurements from SAS-2 and other sources. A comparison of the latitude distribution of gamma-ray intensity with reddening data shows reddening data to give the best estimate of interstellar gas in the solar vicinity. The distribution of galactic cosmic ray nucleons was determined and appears to be identical to the supernova remnant distribution. Interactions between ultrahigh energy cosmic-ray nuclei and intergalactic photon radiation fields were calculated, using the Monte Carlo method.

Source record↗
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 NTRS1974

Kinetic approach to the evaporation and condensation problem

In the paper, the Boltzmann equation governing the evaporation and condensation phenomena is solved by the Monte Carlo method. Based on the kinetic theory of gas the role of the non-equilibrium Knudsen layer and the growth of the hydrodynamic region outside the layer as time proceeds are simulated. Results show two possible types of transient developments in the vapor phase. The effects of the molecular absorption coefficient of the phase surface are examined. Except in the case of very strong evaporation the kinematic effects of binary collisions among vapor molecules on the mass flux rate are not serious. The limiting case of the quasi-steady evaporation and the maximal value of the evaporation rate are obtained.

Murakami, M.↗
NASA NTRS1975

Simultaneous investigation of parent electrons and bremsstrahlung X rays by rocket-borne detectors

Simultaneous measurements of the energy spectrum of precipitating electrons and the resulting bremsstrahlung X-ray spectrum were carried out during an auroral event on March 3, 1971, at the Churchill Research Range, Manitoba, Canada. The electron data were obtained with detectors on a Black Brant VB sounding rocket (275-km apogee), while the X-ray flux was measured by an instrument package that was boosted to 60 km on an Arcas rocket. The X-ray package was deployed on a parachute at apogee to provide a slow descent through the atmosphere. Thick-target bremsstrahlung theory is used to calculate the X-ray flux produced by the incident electrons, and a Monte Carlo method is used to predict the X-ray spectrum at various altitudes appropriate for comparison with the measured X-ray data. Satisfactory agreement between theory and experiment is obtained, and the value of the constant in the thick target theory has been estimated to be about 0.00002.

Vij, K. K.↗
NASA NTRS1975

Analysis of a semiclassical model for rotational transition probabilities

A semiclassical model proposed by Pearson and Hansen (1974) for computing collision-induced transition probabilities in diatomic molecules is tested by the direct-simulation Monte Carlo method. Specifically, this model is described by point centers of repulsion for collision dynamics, and the resulting classical trajectories are used in conjunction with the Schroedinger equation for a rigid-rotator harmonic oscillator to compute the rotational energy transition probabilities necessary to evaluate the rotation-translation exchange phenomena. It is assumed that a single, average energy spacing exists between the initial state and possible final states for a given collision.

Deiwert, G. S.↗
NASA NTRS1977

Thermal-radiation model

Central Cartesian coordinate system calculates thermal environment around rocket plume. Radiative heat exchange between surfaces is calculated by Monte Carlo method.

Claunch, W. C.↗
NASA NTRS1976

Monte Carlo calculations of diatomic molecule gas flows including rotational mode excitation

The direct simulation Monte Carlo method was used to solve the Boltzmann equation for flows of an internally excited nonequilibrium gas, namely, of rotationally excited homonuclear diatomic nitrogen. The semi-classical transition probability model of Itikawa was investigated for its ability to simulate flow fields far from equilibrium. The behavior of diatomic nitrogen was examined for several different nonequilibrium initial states that are subjected to uniform mean flow without boundary interactions. A sample of 1000 model molecules was observed as the gas relaxed to a steady state starting from three specified initial states. The initial states considered are: (1) complete equilibrium, (2) nonequilibrium, equipartition (all rotational energy states are assigned the mean energy level obtained at equilibrium with a Boltzmann distribution at the translational temperature), and (3) nonequipartition (the mean rotational energy is different from the equilibrium mean value with respect to the translational energy states). In all cases investigated the present model satisfactorily simulated the principal features of the relaxation effects in nonequilibrium flow of diatomic molecules.

Yoshikawa, K. K.↗
NASA NTRS1976

Monte Carlo investigation of thrust imbalance of solid rocket motor pairs

The Monte Carlo method of statistical analysis is used to investigate the theoretical thrust imbalance of pairs of solid rocket motors (SRMs) firing in parallel. Sets of the significant variables are selected using a random sampling technique and the imbalance calculated for a large number of motor pairs using a simplified, but comprehensive, model of the internal ballistics. The treatment of burning surface geometry allows for the variations in the ovality and alignment of the motor case and mandrel as well as those arising from differences in the basic size dimensions and propellant properties. The analysis is used to predict the thrust-time characteristics of 130 randomly selected pairs of Titan IIIC SRMs. A statistical comparison of the results with test data for 20 pairs shows the theory underpredicts the standard deviation in maximum thrust imbalance by 20% with variability in burning times matched within 2%. The range in thrust imbalance of Space Shuttle type SRM pairs is also estimated using applicable tolerances and variabilities and a correction factor based on the Titan IIIC analysis.

Sforzini, R. H.↗
NASA NTRS1976

Impulsive solar X-ray bursts. 4: Polarization, directivity and spectrum of the reflected and total bremsstrahlung radiation from a beam of electrons directed toward the photosphere

A Monte Carlo method is described for evaluation of the spectrum, directivity and polarization of X-rays diffusely reflected from stellar photospheres. the accuracy of the technique is evaluated through comparison with analytic results. Using the characteristics of the incident X-rays of the model for solar X-ray flares, the spectrum, directivity and polarization of the reflected and the total X-ray fluxes are evaluated. The results are compared with observations.

Langer, S. H.↗
NASA NTRS1976

Remote sensing of chlorophyll concentration: State-of-the-art, 1975

Remote measurement of chlorophyll concentration of the world's oceans from satellite observations could potentially be extremely useful for assessments of productivity in large areas for which measurements by other means would be impractical. The basis of these measurements rests with the physics of the interaction of light with material dissolved and suspended in the water. It is theoretically possible to predict the nature of light upwelled from the ocean surface from a solution to the radiative transfer equation. Practically, however, this is difficult. Monte-Carlo methods presently are thought to be the most viable method to treat the general theoretical problem. With restrictive assumptions of the nature of scattering, it is possible to construct simpler models. Algorithms developed to relate chlorophyll concentration (or some other parameter, i.e., seechi depth) to the upwelled light spectrum are discussed.

Atwell, B. H.↗
NASA NTRS1976

Solid-propellant rocket motor internal ballistic performance variation analysis, phase 2

The Monte Carlo method was used to investigate thrust imbalance and its first time derivative throughtout the burning time of pairs of solid rocket motors firing in parallel. Results obtained compare favorably with Titan 3 C flight performance data. Statistical correlations of the thrust imbalance at various times with corresponding nominal trace slopes suggest several alternative methods of predicting thrust imbalance. The effect of circular-perforated grain deformation on internal ballistics is discussed, and a modified design analysis computer program which permits such an evaluation is presented. Comparisons with SRM firings indicate that grain deformation may account for a portion of the so-called scale factor on burning rate between large motors and strand burners or small ballistic test motors. Thermoelastic effects on burning rate are also investigated. Burning surface temperature is calculated by coupling the solid phase energy equation containing a strain rate term with a model of gas phase combustion zone using the Zeldovich-Novozhilov technique. Comparisons of solutions with and without the strain rate term indicate a small but possibly significant effect of the thermoelastic coupling.

Sforzini, R. H.↗
NASA NTRS1977

The reality of comet groups and pairs

Although the common genetic origin of the Kreutz family of sun-grazing comets has generally been accepted, there remains uncertainty with regard to genetic identity among other groups of comets whose orbital elements are nearly alike. Porter (1952) has listed a number of such groups, and Opik (1971) has made a statistical study of the orbits of 472 comets with aphelion distances beyond Saturn. Opik lists 97 groups that show similarities among their three angular elements, calculates an overall probability of some 10 to the -39th power that these similarities could have occurred by chance, and thus concludes that 60% or more of such comets fall into genetic groups containing from two to seven members. This paper explores the statistical reality of Opik's groups utilizing the Monte Carlo method of statistics as well as ordinary probability theory. The conclusion is reached that except for a few pairs, the similarity among orbital elements within the groups is no greater than random expectation.

Whipple, F. L.↗
NASA NTRS1977

Impulsive solar X-ray bursts. III - Polarization, directivity, and spectrum of the reflected and total bremsstrahlung radiation from a beam of electrons directed toward the photosphere

The paper presents the spectrum, directivity, and state of polarization of the bremsstrahlung radiation expected from a beam of high-energy electrons spiraling along radial magnetic field lines toward the photosphere. A Monte Carlo method is then described for evaluation of the spectrum, directivity, and polarization of X-rays diffusely reflected from stellar photospheres. The accuracy of the technique is evaluated through comparison with analytic results. The calculated characteristics of the incident X-rays are used to evaluate the spectrum, directivity, and polarization of the reflected and total X-ray fluxes. The results are compared with observations.

Langer, S. H.↗
NASA NTRS1977

Albedo of the ocean-atmosphere system - Influence of sea foam

The influence of the ocean's optical properties and wind induced sea surface foam (white caps) on the short-wave albedo of the ocean-atmosphere system is studied by solving the radiative transfer equation using a Monte Carlo method. It is found that for a foam free ocean, the planetary albedo of a very clear ocean is at most 10 percent greater than that for a totally absorbing ocean. However, the introduction of a relatively small amount of sea foam on the surface can produce a considerable increase in the albedo, especially if the foam is highly reflecting. For example, it is shown that for foam which is totally reflecting (the foam albedo is 1), an increase in the wind speed from 6 to 14 m/sec would double the planetary albedo for small solar zenith angles.

Gordon, H. R.↗