Finite-size effects and percolation properties of Poisson geometries

TL;DR

This paper studies the statistical properties and percolation behavior of Poisson geometries in various dimensions, focusing on finite-size effects and binary mixtures through Monte Carlo simulations.

Contribution

It provides a detailed numerical analysis of Poisson geometries' properties and percolation thresholds, especially in three dimensions, expanding understanding of heterogeneous media models.

Findings

Percolation threshold identified for Poisson geometries

Finite-size effects characterized in different dimensions

Percolation properties of binary mixtures analyzed

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.