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

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.

8 pages, 13 figures, 32 references

References in corpus (5)

• Continuum Percolation Thresholds in Two Dimensions
• Tunneling and Non-Universality in Continuum Percolation Systems
• From percolating to dense random stick networks: Conductivity model investigation
• Percolation thresholds for discorectangles: numerical estimation for a range of aspect ratios
• Electrical conductivity of random metallic nanowire networks: An analytical consideration along with computer simulation