Numerical-Statistical Investigation of Superexponential Growth of Mean Particle Flow with Multiplication in a Homogeneous Random Medium

Abstract

A new correlative-grid approximation of a homogeneous random field is introduced for an effective numerical-analytical investigation of the superexponential growth of the mean particle flow with multiplication in a random medium. The complexity of particle trajectory realization is independent of the correlation scale. Test computations for a critical ball with isotropic scattering showed high accuracy of the corresponding mean flow estimates. For the correlative-grid approximation of a random density field, the possibility of Gaussian asymptotics of the mean particle multiplication rate as the correlation scale decreases is justified.