Master equation approach to friction at the mesoscale

TL;DR

This paper introduces a master equation approach to mesoscale friction, offering analytical solutions and insights into contact dynamics, temperature effects, and stick-slip behavior, advancing understanding beyond traditional numerical models.

Contribution

It presents a novel master equation framework for mesoscale friction, enabling analytical and efficient numerical analysis of contact dynamics and their statistical properties.

Findings

Analytical solutions for contact dynamics under certain conditions.

Temperature and aging significantly influence frictional behavior.

Insights into the conditions leading to stick-slip phenomena.

Abstract

At the mesoscale friction occurs through the breaking and formation of local contacts. This is often described by the earthquake-like model which requires numerical studies. We show that this phenomenon can also be described by a master equation, which can be solved analytically in some cases and provides an efficient numerical solution for more general cases. We examine the effect of temperature and aging of the contacts and discuss the statistical properties of the contacts for different situations of friction and their implications, particularly regarding the existence of stick-slip.