Monte Carlo particle transport in random media: The effects of mixing statistics
Résumé
Particle transport in random media obeying a given mixing statistics is key in several applications in nuclear reactor physics andmore generally in diusion phenomena emerging in optics and life sciences. Exact solutions for the ensemble-averaged physicalobservables are hardly available, and several approximate models have been thus developed, providing a compromise between theaccurate treatment of the disorder-induced spatial correlations and the computational time. In order to validate these models, it ismandatory to resort to reference solutions in benchmark configurations, typically obtained by explicitly generating by Monte Carlomethods several realizations of random media, simulating particle transport in each realization, and finally taking the ensembleaverages for the quantities of interest. In this context, intense research eorts have been devoted to Poisson (Markov) mixingstatistics, where benchmark solutions have been derived for transport in one-dimensional geometries. In a recent work, we havegeneralized these solutions to two and three-dimensional configurations, and shown how dimension aects the simulation results. Inthis 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 stochastictessellations. For each tessellation, we will furthermore discuss the eects of varying the fragmentation of the stochastic geometry,the material compositions, and the cross sections of the transported particles.
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