Investigation of the overexponential growth of the mean particles flux with multiplication in a random medium
G.Z. Lotova^{1,2}, G.A. Michailov^{1,2}
^{1}Institute of Computational Mathematics and Mathematical Geophysics of Siberian Branch of Russian Academy of Sciences, Novosibirsk, Russia ^{2}Novosibirsk State University, Novosibirsk, Russia
Keywords: numerical statistical simulation, particles flux, overexponential asymptotics, random medium, the Voronoi mosaic, grid approximation
Abstract
A new correlativegrid approximation of a homogeneous and isotropic random density field is introduced for the effective numericallyanalytical investigation of overexponential growth of the mean particles flux in a random medium with multiplication. In this case the complexity of the particle trajectory realization is not dependent on the correlation scale. For the correlativegrid approximation the possibility of a Gaussian asymptotics of the mean particles multiplication rate is justified for a random field of bounded density. It ensures a superexponential growth of the flux in some initial time interval. An estimate of further overexponential flux growth is constructed based on some test computations.
