Transit-Length Distribution for Particle Transport in Binary Markovian Mixed Media

TL;DR

This paper establishes a link between the telegraph process and particle transport in binary Markovian mixtures, deriving a distribution for transit lengths and validating it through simulations, with applications to light and charged particle transmission.

Contribution

It introduces a new distribution function for transit lengths in binary mixtures, including an asymptotic form for highly mixed materials, validated by Monte Carlo simulations.

Findings

Asymptotic distribution accurately models highly mixed materials

Distribution converges to the atomic-mix limit in less mixed cases

Analytical transmission probabilities are derived for slab geometries

Abstract

The correspondence between the telegraph random process and transport within a binary stochastic Markovian mixture is established. This equivalence is used to derive the distribution function for the transit length, defined as the distance a particle moving along a straight-line trajectory travels through a specific material zone within the random mixture. A numerically robust asymptotic form of this distribution is obtained for highly mixed materials and the convergence to the atomic-mix limit is shown. The validity of the distribution is verified using a Monte Carlo simulation of the transport process. The distribution is applied to particle transport in slab geometry containing porous media for two cases: the transmission of light and the stopping of charged particles. For both of these applications, analytical forms using the approximate asymptotic model for the transmission probability of beam sources are obtained and illustrative numerical results are provided. These results show that in cases of highly mixed materials, the asymptotic forms are more accurate than the atomic-mix limit.