The effect of Coulombic friction on spatial displacement statistics

TL;DR

This paper investigates how Coulombic friction influences spatial displacement statistics by analyzing a Fokker-Planck model, revealing a transition from exponential to Gaussian behavior and identifying a multiscaling transient regime.

Contribution

It introduces a detailed Fokker-Planck framework incorporating Coulombic friction and uncovers a crossover in displacement statistics along with a transient multiscaling regime.

Findings

Displacement statistics transition from exponential to Gaussian.

A transient multiscaling regime is identified.

Numerical solutions illustrate the crossover behavior.

Abstract

The phenomenon of Coulombic friction enters the stochastic description of dry friction between two solids and the statistic characterization of vibrating granular media. Here we analyze the corresponding Fokker-Planck equation including both velocity and spatial components, exhibiting a formal connection to a quantum mechanical harmonic oscillator in the presence of a delta potential. Numerical solutions for the resulting spatial displacement statistics show a crossover from exponential to Gaussian displacement statistics. We identify a transient intermediate regime that exhibits multiscaling properties arising from the contribution of Coulombic friction. The possible role of these effects during observations in diffusion experiments is shortly discussed.