Size distribution and waiting times for the avalanches of the Cell Network Model of Fracture

TL;DR

This study analyzes the avalanche size distribution and waiting times in the Cell Network Model of Fracture, revealing power-law behavior and exponential waiting times, and compares it to the Random Fuse Model.

Contribution

It demonstrates that the avalanche size distribution exponent remains consistent across various threshold distributions and explores the effects of partial breakings and damage.

Findings

Avalanche sizes follow a power-law distribution with exponent -3.0.

Waiting times between avalanches are exponentially distributed.

Partial breakings induce a crossover between power-law regimes.

Abstract

The Cell Network Model is a fracture model recently introduced that resembles the microscopical structure and drying process of the parenchymatous tissue of the Bamboo Guadua angustifolia. The model exhibits a power-law distribution of avalanche sizes, with exponent -3.0 when the breaking thresholds are randomly distributed with uniform probability density. Hereby we show that the same exponent also holds when the breaking thresholds obey a broad set of Weibull distributions, and that the humidity decrements between successive avalanches (the equivalent to waiting times for this model) follow in all cases an exponential distribution. Moreover, the fraction of remaining junctures shows an exponential decay in time. In addition, introducing partial breakings and cumulative damages induces a crossover behavior between two power-laws in the avalanche size histograms. This results support the idea that the Cell Network Model may be in the same universality class as the Random Fuse Model.