Conductance of Finite-Scale Systems with Multiple Percolation Channels

TL;DR

This paper studies how conductance in small, finite 2D percolation systems depends on size and percolation probability, identifying thresholds for multiple conduction channels and linking the model to real physical systems.

Contribution

It introduces a detailed analysis of conductance thresholds and dependencies in finite-scale percolation systems, connecting theoretical models with experimental observations.

Findings

Identification of successive percolation thresholds for multiple channels

Dependence of conductance on system size and percolation parameter

Finite-scale percolation models align with various physical systems

Abstract

We investigate properties of two-dimensional finite-scale percolation systems whose size along the current flow is smaller than the perpendicular size. Successive thresholds of appearing multiple percolation channels in such systems have been determined and dependencies of the conductance on their size and percolation parameter $p$ have been calculated. Various experimental examples show that the finite-scale percolation system is the natural mathematical model suitable for the qualitative and quantitative description of different physical systems.