Zusammenfassung
We investigate the process of invasion percolation between two sites
(injection and extraction sites) separated by a distance r in
two-dimensional lattices of size L. Our results for the nontrapping
invasion percolation model indicate that the statistics of the mass of
invaded clusters is significantly dependent on the local occupation probability (pressure) p(e) at the extraction site. For p(e)=0, we show
that the mass distribution of invaded clusters P(M) follows a power-law
P(M)similar to M-alpha for intermediate values of the mass M, with an exponent alpha=1.39 +/- 0.03. When the local pressure is set to p(e)=p(c), where p(c) corresponds to the site percolation threshold of
the lattice topology, the distribution P(M) still displays a scaling region, but with an exponent alpha=1.02 +/- 0.03. This last behavior is
consistent with previous results for the cluster statistics in standard
percolation. In spite of these differences, the results of our
simulations indicate that the fractal dimension of the invaded cluster
does not depend significantly on the local pressure p(e) and it is
consistent with the fractal dimension values reported for standard
invasion percolation. Finally, we perform extensive numerical
simulations to determine the effect of the lattice borders on the
statistics of the invaded clusters and also to characterize the
self-organized critical behavior of the invasion percolation process.
Nutzer