Excess number of percolation clusters on the surface of a sphere

Monte Carlo simulations were performed in order to determine the excess num ber of clusters b and the average density of clusters n(c) for the two-dime nsional;'Swiss cheese' continuum percolation model on a planar L x L system and on the surface of a sphere. The excess number of clusters for the L x L system was confirmed to be a universal quantity with a value b=0.8841 as previously predicted and verified only for lattice percolation. The excess number of clusters on the surface of a sphere was found to have the value b = 1.215(1) for discs with the same coverage as the flat critical system. F inally, the average critical density of clusters was calculated for continu um systems as n(c) = 0.04075(5). (C) 2001 Elsevier Science B.V. All rights reserved.