Global ballistic acceleration in a bouncing-ball model.
The ballistic increase for the velocity of a particle in a bouncing-ball model was investigated. The phenomenon is caused by accelerating structures in phase space known as accelerator modes. They lead to a regular and monotonic increase of the velocity. Here, both regular and ballistic Fermi acceleration coexist in the dynamics, leading the dynamics to two different growth regimes. We characterized deaccelerator modes in the dynamics, corresponding to unstable points in the antisymmetric position of the accelerator modes. In control parameter space, parameter sets for which these accelerations and deaccelerations constitute structures were obtained analytically. Since the mapping is not symplectic, we found fractal basins of influence for acceleration and deacceleration bounded by the stable and unstable manifolds, where the basins affect globally the average velocity of the system.
Universidade Tecnológica Federal do Paraná, Pato Branco, Paraná, Brazil.
Tiago
T
Kroetz
Instituto de Física, Universidade de São Paulo, São Paulo, São Paulo, Brazil.|Departamento de Física, Universidade Estadual Paulista, Rio Claro, São Paulo, Brazil.
André L P
AL
Livorati
Departamento de Física, Universidade Estadual Paulista, Rio Claro, São Paulo, Brazil.|Abdus Salam International Center for Theoretical Physics, Strada Costiera 11, 34151 Trieste, Italy.
Edson D
ED
Leonel
Instituto de Física, Universidade de São Paulo, São Paulo, São Paulo, Brazil.
Iberê L
IL
Caldas