Multiple Invaded Consolidating Materials

TL;DR

This paper investigates a multiple invasion model simulating corrosion or intrusion, revealing how critical exponents, fractal dimensions, and avalanche distributions evolve with the number of invasion cycles, indicating a transition between universality classes.

Contribution

It introduces a novel multiple invasion model and analyzes how critical properties change with the number of invasions, showing a transition between different universality classes.

Findings

Critical exponents vary with the number of invasions G.

The mass of invaded regions decreases as a power-law with G, with exponent ~0.6.

Fractal dimension transitions from approximately 1.887 to 1.217 as G increases.

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 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 $G$, $M\sim G^{\beta}$, where the exponent $\beta\approx 0.6$. We also find that the fractal dimension of the invaded cluster changes from $d_{1}=1.887\pm0.002$ to $d_{s}=1.217\pm0.005$. This result confirms that the multiple invasion process follows a continuous transition from one universality class (NTIP) 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 $P(S,L)\sim S^{-\tau}$ 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 $G$.