Europhys. Lett.
Volume 60, Number 2, October 2002
Page(s) 220 - 226
Section Electromagnetism, optics, acoustics, heat transfert, classical mechanics and fluid dynamics
Published online 01 October 2002
DOI: 10.1209/epl/i2002-00355-6

Europhys. Lett., 60 (2) , pp. 220-226 (2002)

Dynamics of particles in a vertical rough channel

R. L. Costa1, J. J. P. Veerman2 and G. L. Vasconcelos1

1  Laboratório de Física Teórica e Computacional, Departamento de Física Universidade Federal de Pernambuco - 50670-901, Recife, Brazil
2  Mathematical Sciences, Portland State University - Portland, OR 97207, USA

(Received 22 April 2002; accepted in final form 26 July 2002)

A simple model is presented for the gravity-driven motion of a particle in a two-dimensional vertical channel with rough walls, where the dynamics is described by a 2D nonlinear mapping. It is shown that if the collisions with the channel walls are inelastic then the particle reaches a steady state where it falls with a constant average velocity. If the collisions are elastic, then the dynamics is governed by a 2D area-preserving mapping that exhibits a complex behavior in phase space. The model is then extended to include the case of several vertical plates falling under gravity inside a channel, where a steady state is reached with a parabolic velocity profile across the channel.

45.70.-n - Granular systems.
83.80.Fg - Granular solids.
05.45.-a - Nonlinear dynamics and nonlinear dynamical systems.

© EDP Sciences 2002