Finite-size effects and percolation properties of Poisson geometries

Abstract

Random tessellations of the space represent a class of prototype models of heterogeneous media, which are central in several applications in physics, engineering and life sciences. In this work, we investigate the statistical properties of $d$-dimensional isotropic Poisson geometries by resorting to Monte Carlo simulation, with special emphasis on the case $d=3$. We first analyse the behaviour of the key features of these stochastic geometries as a function of the dimension $d$ and the linear size $L$ of the domain. Then, we consider the case of Poisson binary mixtures, where the polyhedra are assigned two `labels' with complementary probabilities. For this latter class of random geometries, we numerically characterize the percolation threshold, the strength of the percolating cluster and the average cluster size.

15 pages, 14 figures

References in corpus (3)

• Percolation thresholds on 2D Voronoi networks and Delaunay triangulations
• Topological estimation of percolation thresholds
• Holey Random Walks: Optics of Heterogeneous Turbid Composites

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• Probability density functions for photon propagation in a binary (isotropic-Poisson) statistical mixture with unmatched positives/negatives refractive indexes
• A Reciprocal Formulation of Nonexponential Radiative Transfer. 3: Binary Mixtures