Tiago Botari, Edson Denis Leonel. A one-dimensional Fermi accelerator model with moving wall described by a nonlinear van der Pol oscillator
Natural Sciences / Physics / Mathematical Physics
Submitted on: Sep 13, 2012, 16:49:38
Description: A modification of the one-dimensional Fermi accelerator model is considered in this work. The dynamics of a classical particle of mass $m$, confined to bounce elastically between two rigid walls where one is described by a non-linear van der Pol type oscillator while the other one is fixed, working as a re-injection mechanism of the particle for a next collision, is carefully made by the use of a two-dimensional non-linear mapping. Two cases are considered: (i) the situation where the particle has mass negligible as compared to the mass of the moving wall and does not affect the motion of it; (ii) the case where collisions of the particle does affect the movement of the moving wall. For case (i) the phase space is of mixed type leading us to observe a scaling of the average velocity as a function of the parameter ($c{hi}$) controlling the non-linearity of the moving wall. For large $c{hi}$, a diffusion on the velocity is observed leading us to conclude that Fermi acceleration is taking place.