Percolation through Voids around Overlapping Spheres, a Dynamically based Finite Size Scaling Analysis

TL;DR

This study rigorously determines the percolation threshold for voids around overlapping spheres using large-scale Monte Carlo simulations and finite size scaling, providing precise critical parameters for the system.

Contribution

It introduces a dynamical finite size scaling method to accurately compute the percolation threshold and critical exponents in a continuum model of overlapping spheres.

Findings

Percolation threshold phi_c = 0.0317 +/- 0.0004

Correlation length exponent nu = 0.92 +/- 0.05

Finite size scaling successfully applied to continuum percolation

Abstract

The percolation threshold for flow or conduction through voids surrounding randomly placed spheres is rigorously calculated. With large scale Monte Carlo simulations, we give a rigorous continuum treatment to the geometry of the impenetrable spheres and the spaces between them. To properly exploit finite size scaling, we examine multiple systems of differing sizes, with suitable averaging over disorder, and extrapolate to the thermodynamic limit. An order parameter based on the statistical sampling of stochastically driven dynamical excursions and amenable to finite size scaling analysis is defined, calculated for various system sizes, and used to determine the critical volume fraction phi_{c} = 0.0317 +/- 0.0004 and the correlation length exponent nu = 0.92 +/- 0.05.