title: Scaling investigation of Fermi acceleration on a dissipative bouncer model.
abstract: 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.
authors.affiliation: Departamento de Estatística, Matemática Aplicada e Computação, IGCE, Universidade Estadual Paulista, Avenida 24A, 1515 Bela Vista, CEP 13506-900, Rio Claro, São Paulo, Brazil.
authors.forename: André Luis Prando
authors.initials: AL
authors.lastname: Livorati
authors.forename: Denis Gouvêa
authors.initials: DG
authors.lastname: Ladeira
authors.forename: Edson D
authors.initials: ED
authors.lastname: Leonel