Thermal breakage of a discrete one-dimensional string

TL;DR

This paper analyzes the thermal breakage of a discrete one-dimensional string using Kramers escape theory, providing analytical predictions for breakage rates and locations, validated by numerical simulations.

Contribution

It introduces an analytical approach to predict breakage rates and locations in a damped string, combining theory with numerical validation.

Findings

Analytical expressions for mean breakage rate

Predicted breakage propensity along the string

Numerical simulations confirm theoretical predictions

Abstract

We study the thermal breakage of a discrete one-dimensional string, with open and fixed ends, in the heavily damped regime. Basing our analysis on the multidimensional Kramers escape theory, we are able to make analytical predictions on the mean breakage rate, and on the breakage propensity with respect to the breakage location on the string. We then support our predictions with numerical simulations.