Fibers on a graph with local load sharing

TL;DR

This paper investigates a fiber bundle model on a graph with local load sharing, analyzing its critical behavior and avalanche size distribution, revealing mean field characteristics through numerical simulations and finite size scaling.

Contribution

It introduces a fiber bundle model on a graph with local load sharing and demonstrates its mean field critical behavior through numerical analysis.

Findings

Mean field critical behavior established

Avalanche size distribution exhibits mean field nature

Finite size scaling confirms critical properties

Abstract

We study a random fiber bundle model with tips of the fibers placed on a graph having co-ordination number 3. These fibers follow local load sharing with uniformly distributed threshold strengths of the fibers. We have studied the critical behaviour of the model numerically using a finite size scaling method and the mean field critical behaviour is established. The avalanche size distribution is also found to exhibit a mean field nature in the asymptotic limit.