# Monte Carlo particle transport in random media: the effects of mixing statistics

## TL;DR

This paper investigates how different mixing statistics affect particle transport in 3D random media, comparing Poisson, Voronoi, and Box tessellations to understand their impact on key transport properties.

## Contribution

It extends the analysis of mixing statistics effects on particle transport to three-dimensional geometries using various stochastic tessellations, providing new insights beyond previous Poisson-based models.

## Key findings

- Reflection and transmission probabilities vary with mixing statistics.
- Particle flux is influenced by the type of tessellation and fragmentation.
- Material composition and cross sections significantly affect transport outcomes.

## Abstract

Particle transport in random media obeying a given mixing statistics is key in several applications in nuclear reactor physics and more generally in diffusion phenomena emerging in optics and life sciences. Exact solutions for the ensemble-averaged physical observables are hardly available, and several approximate models have been thus developed, providing a compromise between the accurate treatment of the disorder-induced spatial correlations and the computational time. In order to validate these models, it is mandatory to resort to reference solutions in benchmark configurations, typically obtained by explicitly generating by Monte Carlo methods several realizations of random media, simulating particle transport in each realization, and finally taking the ensemble averages for the quantities of interest. In this context, intense research efforts have been devoted to Poisson (Markov) mixing statistics, where benchmark solutions have been derived for transport in one-dimensional geometries. In a recent work, we have generalized these solutions to two and three-dimensional configurations, and shown how dimension affects the simulation results. In this paper we will examine the impact of mixing statistics: to this aim, we will compare the reflection and transmission probabilities, as well as the particle flux, for three-dimensional random media obtained by resorting to Poisson, Voronoi and Box stochastic tessellations. For each tessellation, we will furthermore discuss the effects of varying the fragmentation of the stochastic geometry, the material compositions, and the cross sections of the transported particles.