Size distribution of emitted energies in local load sharing fiber bundles

TL;DR

This paper investigates the energy burst statistics in a local load sharing fiber bundle model, revealing a universal power-law distribution of energy releases with a specific non-linear relation between avalanche size and energy.

Contribution

It demonstrates a universal power-law energy distribution and establishes a non-linear relation between avalanche size and energy in the fiber bundle model.

Findings

Energy burst distribution follows a power law with universal exponent.

Avalanche size and energy are related by a non-linear power law with exponent ~2.5.

The results are consistent across different failure threshold distributions.

Abstract

We study the local load sharing fiber bundle model and its energy burst statistics. While it is known that the avalanche size distribution of the model is exponential, we numerically show here that the avalanche size ($s$) and the corresponding energy burst ($E$) in this version of the model have a non-linear relation ($E\sim s^{\gamma}$). Numerical results indicate that $\gamma\approx 2.5$ universally for different failure threshold distributions. With this numerical observation, it is then possible to show that the energy burst distribution is a power law, with a universal exponent value of $-(\gamma+1)$.