Percolation thresholds for discrete-continuous models with non-uniform probabilities of bond formation

TL;DR

This paper introduces an algorithm for efficiently computing percolation thresholds and properties in models combining discrete and continuous elements with non-uniform bond probabilities, relevant for materials like activated carbon.

Contribution

It extends existing percolation algorithms to handle inhomogeneous lattices and computes critical exponents and cluster distributions in complex models.

Findings

Effective algorithm for inhomogeneous percolation models

Computed critical exponents for 2D and 3D models

Analyzed connectivity in activated carbon models

Abstract

We consider a family of percolation models in which geometry and connectivity are defined by two independent random processes. Such models merge characteristics of discrete and continuous percolation. We develop an algorithm allowing effective computation of both universal and modelspecific percolation quantities in the case when both random processes are Poisson processes. The algorithm extends percolation algorithm by Newman and Ziff (M.E.J. Newman and R.M. Ziff, Phys Rev E, 64(1):016706, 2001) to handle inhomogeneous lattices. In particular, we use the proposed method to compute critical exponents and cluster density distribution in two and three dimensions for the model of parallel random tubes connected randomly by bonds, which models the connectivity properties of activated carbon.