Stochastic modeling in geophysics and atmospheric physics
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, ¹ 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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