Scaling investigation of Fermi acceleration on a dissipative bouncer model

• Autor(a) principal: Livorati, André Luis Prando [UNESP]
• Data de Publicação: 2008
• Outros Autores: Ladeira, Denis Gouvêa [UNESP], Leonel, Edson D. [UNESP]
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Institucional da UNESP
• Texto Completo: http://dx.doi.org/10.1103/PhysRevE.78.056205; http://hdl.handle.net/11449/225343

The phenomenon of Fermi acceleration is addressed for the problem of a classical and dissipative bouncer model, using a scaling description. The dynamics of the model, in both the complete and simplified versions, is obtained by use of a two-dimensional nonlinear mapping. The dissipation is introduced using a restitution coefficient on the periodically moving wall. Using scaling arguments, we describe the behavior of the average chaotic velocities on the model both as a function of the number of collisions with the moving wall and as a function of the time. We consider variations of the two control parameters; therefore critical exponents are obtained. We show that the formalism can be used to describe the occurrence of a transition from limited to unlimited energy growth as the restitution coefficient approaches unity. The formalism can be used to characterize the same transition in two-dimensional time-varying billiard problems. © 2008 The American Physical Society.