Burst Distribution by Asymptotic Expansion in the Equal Load Sharing Fiber Bundle Model

Abstract

We derive an asymptotic series expansion for the burst size distribution in the equal load sharing fiber bundle model, a predominant model for breakdown in disordered media. Earlier calculations give expressions with correct asymptotic behavior for large bursts, but low accuracy for small bursts, up to an order of magnitude off. The approximations from the expansion we present here give relative errors of at most several percent when compared with exact results or simulation results for large systems. We also solve the burst size distribution exactly for the Weibull threshold distributions.

Burst Distribution by Asymptotic Expansion in the Equal Load Sharing Fiber Bundle Model