Invariant percolation properties in random isotropic systems of conductive discorectangles on a plane: From disks to sticks

TL;DR

This study investigates how the electrical properties of 2D systems of conductive discorectangles vary with particle shape, revealing certain invariant properties across different aspect ratios from disks to sticks.

Contribution

The paper provides the first systematic analysis of invariant percolation properties in 2D systems of conductive discorectangles across a wide range of aspect ratios.

Findings

Some properties are insensitive to aspect ratio changes.

Electrical conductivity and backbone behavior show invariance.

Results support the universality of certain percolation properties.

Abstract

Recently, some eccentricity-invariant properties of random, isotropic, two-dimensional (2D) systems of conductive ellipses have been reported [Phys. Rev. B \bf{104}, 184205 (2021)]. Moreover, the authors suggested that this invariance might also be observed in systems with other particle geometries having zero-width sticks as the limiting case. To check this suggestion, we studied 2D random systems of isotropically-placed, overlapping, identical discorectangles (stadia) with aspect ratios ranging from 1 (disks) to $\infty$ (zero-width sticks). We analyzed the effect of the aspect ratio and the number density of conductive discorectangles on the behavior of the electrical conductivity, the local conductivity exponent, and the current-carrying backbone. Our own computer simulations demonstrate that some of the properties of random, isotropic 2D systems of conductive discorectangles are insensitive to the aspect ratios of the particles.