Asymmetry in the percolation thresholds of fully penetrable disks with two different radii.
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).
Quintanilla
John A
JA
Department of Mathematics, P.O. Box 311430, University of North Texas, Denton, Texas 76203, USA. jquintanilla@unt.edu
Ziff
Robert M
RM