Artigo
A theoretical characterization of scaling properties in a bouncing ball system
Registro en:
Physica A-statistical Mechanics And Its Applications. Amsterdam: Elsevier Science Bv, v. 404, p. 279-284, 2014.
0378-4371
10.1016/j.physa.2014.02.053
WOS:000335638300026
6130644232718610
Autor
Leonel, Edson D. [UNESP]
Livorati, Ande L. P.
Cespedes, Andre M. [UNESP]
Resumen
Analytical arguments are used to describe the behavior of the average velocity in the problem of an ensemble of particles bouncing a heavy and periodically moving platform. The dynamics of the system is described by using a two-dimensional mapping for the variables' velocity and discrete time n. In the absence of dissipation and depending on the control parameter and initial conditions, diffusion in energy is observed. Considering the introduction of dissipation via inelastic collisions, we prove that the diffusion is interrupted and a transition from unlimited to limited energy growth is characterized. Our result is general and can be used when the initial condition is a very low velocity leading to a growth of average velocity with root n or for large initial velocity where an exponential decay of the average velocity is observed. The results obtained generalize the scaling observed in the bouncer model as well as the stochastic and dissipative Fermi Ulam-model. The formalism can be extended to many other different types of models, including a class of time-dependent billiards. (c) 2014 Elsevier B.V. All rights reserved. Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) Fundação para o Desenvolvimento da UNESP (FUNDUNESP) Center for Scientific Computing (NCC/GridUNESP) of the Sao Paulo State University (UNESP) Univ Estadual Paulista, UNESP, Dept Fis, BR-13506900 Rio Claro, SP, Brazil Abdus Salem ICTP, I-34151 Trieste, Italy Univ Sao Paulo, Inst Fis, IFUSP, BR-05314970 Sao Paulo, Brazil Univ Estadual Paulista, UNESP, Dept Fis, BR-13506900 Rio Claro, SP, Brazil FAPESP: 12/23688-5