Аннотация
We study a multiple invasion model to simulate corrosion or intrusion
processes. Estimated values for the fractal dimension of the invaded
region reveal that the critical exponents vary as a function of the
generation number G, i.e., with the number of times the invasion process
takes place. The averaged mass M of the invaded region decreases with a
power law as a function of G, Msimilar toG(beta), where the exponent
betaapproximate to0.6. We also find that the fractal dimension of the invaded cluster changes from d(1)=1.887+/-0.002 to d(s)=1.217+/-0.005.
This result confirms that the multiple invasion process (for the case in
which uninvaded regions are forbidden) follows a continuous transition
from one universality class (nontrapping invasion percolation) to
another (optimal path). In addition, we report extensive numerical
simulations that indicate that the mass distribution of avalanches
P(S,L) has a power-law behavior and we find that the exponent tau
governing the power-law P(S,L)similar toS(-tau) changes continuously as
a function of the parameter G. We propose a scaling law for the mass
distribution of avalanches for different number of generations G.
