The Simplest Piston Problem I: Elastic Collisions

Abstract

We study the dynamics of three elastic particles in a finite interval where two light particles are separated by a heavy ``piston''. The piston undergoes surprisingly complex motion that is oscillatory at short time scales but seemingly chaotic at longer scales. The piston also makes long-duration excursions close to the ends of the interval that stem from the breakdown of energy equipartition. Many of these dynamical features can be understood by mapping the motion of three particles on the line onto the trajectory of an elastic billiard in a highly skewed tetrahedral region. We exploit this picture to construct a qualitative random walk argument that predicts a power-law tail, with exponent -3/2, for the distribution of time intervals between successive piston crossings of the interval midpoint. These predictions are verified by numerical simulations.

8 pages, 8 figures, 2-column revtex4 format

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Cited by in corpus (8)

• A violation of universality in anomalous Fourier's law
• Critical behavior of two freely evolving granular gases separated by an adiabatic piston
• Traces of Integrability in Relaxation of One-Dimensional Two-Mass Mixtures
• The Simplest Piston Problem II: Inelastic Collisions
• Mesoscopic description of the adiabatic piston: kinetic equations and $\mathcal{H}$-theorem
• One dimensional Brownian motion in hard rods: adiabatic piston problem
• Non-equilibrium dynamics of the piston in the Szilard engine
• Non-equilibrium (thermo)dynamics of colloids under mobile piston compression