Simplest piston problem. I. Elastic collisions

Pablo I. Hurtado and S. Redner
Phys. Rev. E 73, 016136 – Published 27 January 2006

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 32, for the distribution of time intervals between successive piston crossings of the interval midpoint. These predictions are verified by numerical simulations.

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  • Received 28 July 2005

DOI:https://doi.org/10.1103/PhysRevE.73.016136

©2006 American Physical Society

Authors & Affiliations

Pablo I. Hurtado1,2,* and S. Redner3,†

  • 1Institute Carlos I for Theoretical and Computational Physics, Universidad de Granada, 18071 Granada, Spain
  • 2Department of Physics, Boston University, Boston, Massachusetts 02215, USA
  • 3Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA

  • *Email address: phurtado@onsager.ugr.es
  • Permanent address: Department of Physics, Boston University, Boston, Massachusetts 02215, USA. Email address: redner@bu.edu

See Also

Simplest piston problem. II. Inelastic collisions

Pablo I. Hurtado and S. Redner
Phys. Rev. E 73, 016137 (2006)

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Vol. 73, Iss. 1 — January 2006

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