Measurement of the percolation threshold for fully penetrable disks of different radii

We perform simulations of gradient percolation to study the percolation threshold for systems of homogeneous fully penetrable disks of variable radii. We find that, if the radii follow a uniform distribution, the percolation threshold is 0.686610±0.000007. We also investigate binary dispersions, studying the influence of constitutive parameters on the percolation threshold and suggesting an empirical formula for the threshold. We find that, with the appropriate parameters, a percolation threshold of approximately 0.76 can be achieved. The minimal threshold of 0.676339±0.000004 is achieved by disks of equal radius.