Araújo AD, Andrade JS, Herrmann HJ. Multiple invaded consolidating materials.
PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004;
70:066150. [PMID:
15697477 DOI:
10.1103/physreve.70.066150]
[Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/01/2004] [Indexed: 05/24/2023]
Abstract
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 , M approximately Gbeta , where the exponent beta approximately 0.6 . 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) approximately S-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 .
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