SYMBOLIC MONTE CARLO METHOD BASED ON ORTHOGONAL POLYNOMIALS SERIES: APPLICATION TO PHASE FUNCTION

A combined two-step computational method incorporating (1) transport approximation of the scattering phase function, (2) P1 approximation and the finite element method for computing the radiation source function at the first step, and (3) the Monte Carlo method for computing radiative intensity at the second step, is developed. The accuracy of the combined method is examined for model problems involving two multi-dimensional configurations of an anisotropically scattering medium. A detailed analysis is performed for a medium with scattering phase function described by a family of the Henyey–Greenstein functions. The accuracy of the two-step method is assessed by comparing the distribution of the radiative flux leaving the medium to that obtained by a reference complete Monte Carlo method. This study confirms the main results of previous papers on the errors of the two-step solution method. The combined method leads to a significant reduction in computational time as compared to the reference method, by at least 1 order of magnitude. Finally, possible applications of the combined method are briefly discussed.

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Modeling the propagation of light in realistic tissue structures with MMC-fpf: a meshed Monte Carlo method with free phase function

Optics Express ◽

10.1364/oe.23.017467 ◽

2015 ◽

Vol 23 (13) ◽

pp. 17467 ◽

Cited By ~ 26

Author(s):

Rodrigo Watté ◽

Ben Aernouts ◽

Robbe Van Beers ◽

Els Herremans ◽

Quang Tri Ho ◽

...

Keyword(s):

Monte Carlo ◽

Monte Carlo Method ◽

Phase Function ◽

Propagation Of Light ◽

Tissue Structures

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Outbursts of comet Schwassmann-Wachmann 1, and the cloud of interplanetary boulders

International Astronomical Union Colloquium ◽

10.1017/s0252921100034035 ◽

1974 ◽

Vol 22 ◽

pp. 307 ◽

Cited By ~ 3

Author(s):

Zdenek Sekanina

Keyword(s):

Monte Carlo ◽

Monte Carlo Method ◽

Interplanetary Space ◽

Porous Matrix ◽

Maximum Diameter ◽

Expansion Velocity ◽

Solid Constituent ◽

Meteoric Material ◽

Periodic Comet

AbstractIt is suggested that the outbursts of Periodic Comet Schwassmann-Wachmann 1 are triggered by impacts of interplanetary boulders on the surface of the comet’s nucleus. The existence of a cloud of such boulders in interplanetary space was predicted by Harwit (1967). We have used the hypothesis to calculate the characteristics of the outbursts – such as their mean rate, optically important dimensions of ejected debris, expansion velocity of the ejecta, maximum diameter of the expanding cloud before it fades out, and the magnitude of the accompanying orbital impulse – and found them reasonably consistent with observations, if the solid constituent of the comet is assumed in the form of a porous matrix of lowstrength meteoric material. A Monte Carlo method was applied to simulate the distributions of impacts, their directions and impact velocities.

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Structures and crystallization of vacuum-deposited amorphous Se and Sb films

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100173832 ◽

1990 ◽

Vol 48 (4) ◽

pp. 140-141

Author(s):

Makoto Shiojiri ◽

Toshiyuki Isshiki ◽

Tetsuya Fudaba ◽

Yoshihiro Hirota

Keyword(s):

Monte Carlo ◽

Electron Microscope ◽

Monte Carlo Method ◽

Computer Program ◽

Radial Distribution ◽

Film Formation ◽

Amorphous State ◽

Two Dimensional ◽

Amorphous Films ◽

Binding Condition

In hexagonal Se crystal each atom is covalently bound to two others to form an endless spiral chain, and in Sb crystal each atom to three others to form an extended puckered sheet. Such chains and sheets may be regarded as one- and two- dimensional molecules, respectively. In this paper we investigate the structures in amorphous state of these elements and the crystallization.HRTEM and ED images of vacuum-deposited amorphous Se and Sb films were taken with a JEM-200CX electron microscope (Cs=1.2 mm). The structure models of amorphous films were constructed on a computer by Monte Carlo method. Generated atoms were subsequently deposited on a space of 2 nm×2 nm as they fulfiled the binding condition, to form a film 5 nm thick (Fig. 1a-1c). An improvement on a previous computer program has been made as to realize the actual film formation. Radial distribution fuction (RDF) curves, ED intensities and HRTEM images for the constructed structure models were calculated, and compared with the observed ones.

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