Simplest piston problem. II. Inelastic collisions.
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 a effective restitution coefficient picture. Many dynamical features of the three-particle system closely resemble those of the many-body inelastic piston problem.
Institute Carlos I for Theoretical and Computational Physics, Universidad de Granada, 18071 Granada, Spain. phurtado@onsager.ugr.es
Pablo I
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Hurtado
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Redner