Figure 4.

Percolation diameters d_c as a function of system size L for the indicated number densities, in units of 1000 obstacles/μm². (a) Thresholds for random overlapping disks rapidly approach their theoretical value as the system size is increased. (Points) Mean d_c from simulations. (Lines) Theoretical thresholds calculated from the known percolation threshold for overlapping disks on a continuum (Eq. 3). (b) Thresholds for 1/r¹² soft repulsive disks as a function of system size. (Points) Mean d_c from simulations. (Lines) Thresholds calculated for each number density by extrapolation to an infinite system.