Analysis of heterogeneous Markov media for particle transport problems

Markov media provide a prototype class of stochastic geometries that are widely used in order to model several complex and disordered systems encompassing, e.g., turbulent fluids and plasma, atmospheric layers, or biological tissues, especially in relation to particle transport problems. In several key applications, the statistical properties of random media may display spatial gradients due to material stratification, which means that the typical spatial scale and the probability of finding a given material phase at a spatial location become nonhomogeneous. In this paper we investigate the main features of spatially heterogeneous Markov media, using Poisson hyperplane tessellations and Arak polygonal fields. We show that both models can generate geometry realizations sharing Markov-like properties, and discuss their distinct advantages and drawbacks in terms of flexibility and ease of use. The impact of these models on the observables related to particle transport will be assessed using Monte Carlo simulations.