Asymmetry in the percolation thresholds of fully penetrable disks with two different radii

Phys Rev E Stat Nonlin Soft Matter Phys. 2007 Nov;76(5 Pt 1):051115. doi: 10.1103/PhysRevE.76.051115. Epub 2007 Nov 14.

Abstract

We perform simulations of continuum gradient percolation to measure the percolation threshold of systems of fully penetrable disks of two different radii. As a function of volumetric proportion v, the percolation threshold phic(v,lambda) is approximately symmetric about v=0.5 for a fixed ratio lambda of the radii. However, the difference from symmetry is strongly statistically significant. We also improve, by an order of magnitude, the measurement of the percolation threshold for disks of equal radius: phic*=0.676 347 5(6).