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|
Dynamics of particles in a vertical rough channel
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
Corresponding author: email@example.com
Accepted: 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.
PACS: 45.70.-n – Granular systems / 83.80.Fg – Granular solids / 05.45.-a – Nonlinear dynamics and nonlinear dynamical systems
© EDP Sciences, 2002
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