Effect of fractal disorder on static friction in the Tomlinson model

TL;DR

This paper investigates how fractal disorder, modeled by a generalized random Cantor set, influences static friction in a modified Tomlinson model, revealing scale-invariant distribution properties.

Contribution

It introduces a novel fractal disorder model into the Tomlinson framework and analyzes its impact on static friction force distribution.

Findings

Static friction force distribution becomes scale-invariant with fractal disorder.

Disorder modeled by a generalized random Cantor set affects static friction.

Distribution of static friction force is independent of the generation of the fractal set.

Abstract

We propose a modified version of the Tomlinson model for static friction between two chains of beads. We introduce disorder in terms of vacancies in the chain, and distribute the remaining beads in a scale invariant way. For this we utilize a generalized random Cantor set. We relate the static friction force, to the overlap distribution of the chains, and discuss how the distribution of the static friction force depends on the distribution of the remaining beads. For the random Cantor set we find a scaled distribution which is independent on the generation of the set.