Institute of Computational Mathematics and Mathematical Geophysics

International Conference on Mathematical Methods in Geophysics «MMG-2003»

Akademgorodok, Novosibirsk, Russia, October 8-12, 2003

Abstracts

Stochastic modeling in geophysics and atmospheric physics

Monte Carlo methods for estimating critical parameters of the transport equation in stochastic media

Lotova G.Z.

Institute of Computational Mathematics and Mathematical Geophysics (Novosibirsk)

We consider a nonstationary particle transfer process with multiplication.The medium is divided into several parts; in each part the microscopic cross-sections are independent random variables. We consider two critical parameters of the transfer equation: the effective coefficient and time constant of particle multiplication. These parameters can be found by the special iteration method [1] or by the method obtained with Green function [2]. Earlier these methods were applied to computation of the parameters in homogeneous or two-layer media. In this paper, we consider multilayer media. The methods can be also used for calculating the exponential time asymptotic in problems of laser sensing.

[1] Mikhailov G.A. New Monte Carlo methods for computing critical values of parameters of the particle transport equation. // Russian Acad. Sci. Dokl. Math., V.48, N 2, p. 244-247, 1994.
[2] Lotova G.Z., Mikhailov G.A. New Monte Carlo methods for the solution of nonstationary problems in the radiation transfer theory // Russ. J. Num. Anal. Math. Model., Vol.15, № 3-4, pp.285-295 (2000).

Support of Grant "Leading scientific school" (HIII-1271.2003.1) and Grant of Russian Ministry of Education (PD02-1.1-257) is gratefully acknowledged.

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