FROM LATTICE TO CONTINUUM PERCOLATION VIA CLUSTERING

Considers the growth of Eden clusters on a square lattice about randomly distributed seeds, or through continuous nucleation. The author analyses the dependence of the percolation threshold, pc, on the seed density, or ratio of nucleation to growth rates, i.e. on parameters controlling the average size of individual clusters or islands before coalescence. It is found that pc approaches a large island size continuum limit from below at a rate depending on the active zone width scaling exponent. This result applies to a variety of island-forming models.