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.

The abstract of this article will be published in the September 2012 issue of "Intellectual Archive Bulletin", ISSN 1929-1329.

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