Equilibrium of a confined, randomly-accelerated, inelastic particle: Is there inelastic collapse?

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.

Cited by in corpus (5)

• On the Inelastic Collapse of a Ball Bouncing on a Randomly Vibrating Platform
• Statistics of the first passage area functional for an Ornstein-Uhlenbeck process
• Randomly accelerated particle in a box: mean absorption time for partially absorbing and inelastic boundaries
• Equilibrium statistics of an inelastically bouncing ball, subject to gravity and a random force
• Inelastic collapse and near-wall localization of randomly accelerated particles