The Simplest Piston Problem II: Inelastic Collisions

TL;DR

This paper analyzes a three-particle system with inelastic collisions, revealing a symmetry-breaking behavior where the piston oscillates near an interval end, with dynamics akin to the many-body inelastic piston problem.

Contribution

It introduces a simplified three-particle model to understand symmetry breaking and oscillatory behavior in inelastic piston systems.

Findings

Piston exhibits symmetry breaking and oscillates near an interval end.

Oscillations occur on a logarithmic time scale.

Behavior resembles the many-body inelastic piston problem.

Abstract

We study the dynamics of three particles in a finite interval, in which two light particles are separated by a heavy ``piston'', with elastic collisions between particles but inelastic collisions between the light particles and the interval ends. A symmetry breaking occurs in which the piston migrates near one end of the interval and performs small-amplitude periodic oscillations on a logarithmic time scale. The properties of this dissipative limit cycle can be understood simply in terms of an effective restitution coefficient picture. Many dynamical features of the three-particle system closely resemble those of the many-body inelastic piston problem.