Effect of discontinuity in threshold distribution on the critical behaviour of a random fiber bundle

TL;DR

This paper investigates how a discontinuity in the threshold distribution of fibers affects the critical behavior and avalanche dynamics in a random fiber bundle model with global load sharing, revealing non-universal behaviors and new critical phenomena.

Contribution

It introduces the impact of threshold distribution discontinuity on critical stress and avalanche behavior, providing analytical insights into non-universal avalanche size distributions.

Findings

Discontinuity modifies critical stress and parameter restrictions.

Non-universal avalanche size distribution for small avalanches.

New behavior observed near critical threshold distribution.

Abstract

The critical behaviour of a Random Fiber Bundle Model with mixed uniform distribution of threshold strengths and global load sharing rule is studied with a special emphasis on the nature of distribution of avalanches for different parameters of the distribution. The discontinuity in the threshold strength distribution of fibers non-trivially modifies the critical stress as well as puts a restriction on the allowed values of parameters for which the recursive dynamics approach holds good. The discontinuity leads to a non-universal behaviour in the avalanche size distribution for smaller values of avalanche size. We observe that apart from the mean field behaviour for larger avalanches, a new behaviour for smaller avalanche size is observed as a critical threshold distribution is approached. The phenomenological understanding of the above result is provided using the exact analytical result for the avalanche size distribution. Most interestingly,the prominence of non-universal behaviour in avalanche size distribution depends on the system parameters.