Restoring site percolation on damaged square lattices.
Restoring site percolation on a damaged square lattice with the nearest neighbor (N2) is investigated using two different strategies. In the first one, a density y of new sites are created on the empty sites with longer range links, either next-nearest neighbor (N3) or next-next-nearest neighbor (N4), but without N2. In the second one, new longer range links N3 or N4 are added to N2 but only for a fraction v of the remaining non-destroyed sites. Starting at p(c)(N2), with a density x of randomly destroyed sites, the values of y(c) and v(c), which restore site percolation, are calculated for both strategies with, respectively, N3 and N4 using Monte Carlo simulations. Results are obtained for the whole range 0 < or = x < or = p(c)(N2).
Galam
Serge
S
Centre de Recherche en Epistémologie Appliquée, CNRS UMR 7656, CREA--Ecole Polytechnique, 1 rue Descartes, F-75005 Paris, France. galam@shs.polytechnique.fr
Malarz
Krzysztof
K