Survival-Time Distribution for Inelastic Collapse

TL;DR

This paper investigates the distribution of collapse times for a particle undergoing inelastic collisions, revealing a non-universal power-law decay and framing inelastic collapse as a generalized persistence phenomenon.

Contribution

It provides an analysis of the survival probability and collapse-time distribution, highlighting their asymptotic power-law behavior and non-universality, with an approximate calculation supporting these findings.

Findings

Collapse-time distribution follows a power-law decay.

Exponent of decay is non-universal.

Collapse viewed as a generalized persistence phenomenon.

Abstract

In a recent publication [PRL {\bf 81}, 1142 (1998)] it was argued that a randomly forced particle which collides inelastically with a boundary can undergo inelastic collapse and come to rest in a finite time. Here we discuss the survival probability for the inelastic collapse transition. It is found that the collapse-time distribution behaves asymptotically as a power-law in time, and that the exponent governing this decay is non-universal. An approximate calculation of the collapse-time exponent confirms this behaviour and shows how inelastic collapse can be viewed as a generalised persistence phenomenon.