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

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.

23 pages, 19 figures

References in corpus (6)

• Benchmark solutions for transport in $d$-dimensional Markov binary mixtures
• Holey Random Walks: Optics of Heterogeneous Turbid Composites
• Finite-size effects and percolation properties of Poisson geometries
• Properties of branching exponential flights in bounded domains
• Cauchy's formulas for random walks in bounded domains
• Universal properties of branching random walks in confined geometries

Cited by in corpus (4)

• Monte Carlo Chord Length Sampling for $d$-dimensional Markov binary mixtures
• Poisson-Box Sampling algorithms for three-dimensional Markov binary mixtures
• Probability density function for random photon steps in a binary (isotropic-Poisson) statistical mixture
• A Reciprocal Formulation of Nonexponential Radiative Transfer. 3: Binary Mixtures