The Simplest Piston Problem II: Inelastic Collisions

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.

8 pages, 7 figures, 2-column revtex4 format

References in corpus (4)

• Quantitative study of a freely cooling granular medium
• A Billiard-Theoretic Approach to Elementary 1d Elastic Collisions
• Dissipative collapse of the adiabatic piston
• The Simplest Piston Problem I: Elastic Collisions

Cited by in corpus (5)

• A violation of universality in anomalous Fourier's law
• Fluctuations in partitioning systems with few degrees of freedom
• Critical behavior of two freely evolving granular gases separated by an adiabatic piston
• Mesoscopic description of the adiabatic piston: kinetic equations and $\mathcal{H}$-theorem
• Non-equilibrium dynamics of the piston in the Szilard engine