  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.
