Crossover behavior in a mixed mode fiber bundle model

TL;DR

This paper investigates a fiber bundle model with mixed load sharing, revealing a crossover from mean-field to short-range behavior through numerical analysis of various properties.

Contribution

Introduces a mixed-mode load sharing fiber bundle model that interpolates between ELS and LLS, analyzing the crossover behavior in one dimension.

Findings

Identifies a crossover point between mean-field and short-range regimes.

Shows that fiber bundle models exhibit crossover behavior even in one dimension.

Analyzes avalanche statistics, susceptibility, and cluster correlations to characterize regimes.

Abstract

We introduce a mixed-mode load sharing scheme in fiber bundle model. This model reduces exactly to equal load sharing (ELS) and local load sharing (LLS) models at the two extreme conditions of the load sharing rule. We identify two distinct regimes: a) Mean-field regime where ELS mode dominates and b) short range regime dominated by LLS mode. The crossover behavior is explored through the numerical study of strength variation, the avalanche statistics, susceptibility and relaxation time variations, the correlations among the broken fibers and their cluster analysis. Analyzing the moments of the cluster size distributions we locate the crossover point of these regimes. We thus conclude that even in one dimension, fiber bundle model shows crossover behavior from mean-field to short range interactions.