Equilibrium of a confined, randomly-accelerated, inelastic particle: Is there inelastic collapse?
Statistical Mechanics
2011-07-19 v1 Soft Condensed Matter
Abstract
We consider the one-dimensional motion of a particle randomly accelerated by Gaussian white noise on the line segment 0<x<1. The reflections of the particle from the boundaries at x=0 and 1 are inelastic, with coefficient of restitution r. We have solved the Fokker-Planck equation satisfied by the equilibrium distribution function P(x,v) with a combination of exact analytical and numerical methods. Throughout the interval 0<r<1, P(x,v) remains extended, as opposed to collapsed. The particle is not localized at the boundary. However, for r<0.163 the equilibrium boundary collision rate is infinite, as predicted by Cornell et al., and all moments of the velocity just after reflection from the boundary vanish.
Keywords
Cite
@article{arxiv.cond-mat/0402628,
title = {Equilibrium of a confined, randomly-accelerated, inelastic particle: Is there inelastic collapse?},
author = {Theodore W. Burkhardt and Stanislav N. Kotsev},
journal= {arXiv preprint arXiv:cond-mat/0402628},
year = {2011}
}