Nonlinear Sciences > Chaotic Dynamics
[Submitted on 7 Mar 2016 (v1), last revised 13 Mar 2016 (this version, v2)]
Title:Inelastic collapse and near-wall localization of randomly accelerated particles
View PDFAbstract:The inelastic collapse of stochastic trajectories of a randomly accelerated particle moving in half-space $z > 0$ has been discovered by McKean and then independently re-discovered by Cornell et. al. The essence of this phenomenon is that particle arrives to a wall at $z = 0$ with zero velocity after an infinite number of inelastic collisions if the restitution coefficient $\beta$ of particle velocity is smaller than the critical value $\beta_c=\exp(-\pi/\sqrt{3})$. We demonstrate that inelastic collapse takes place also in a wide class of models with spatially inhomogeneous random force and, what is more, that the critical value $\beta_c$ is universal. That class includes an important case of inertial particles in wall-bounded random flows. To establish how the inelastic collapse influence the particle distribution, we construct an exact equilibrium probability density function $\rho(z,v)$ for particle position and velocity. The equilibrium distribution exists only at $\beta<\beta_c$ and indicates that inelastic collapse does not necessarily mean the near-wall localization.
Submission history
From: Sergey Belan [view email][v1] Mon, 7 Mar 2016 18:48:23 UTC (27 KB)
[v2] Sun, 13 Mar 2016 17:21:07 UTC (45 KB)
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