A theoretical characterization of scaling properties in a bouncing ball system

Autor(es)

Leonel, Edson D. ^{[1, 2]} ; Livorati, Ande L. P. ^[3] ; Cespedes, Andre M. ^[1]

Afiliação do(s) autor(es)

^[1] Univ Estadual Paulista, UNESP, Dept Fis, BR-13506900 Rio Claro, SP - Brazil

^[2] Abdus Salem ICTP, I-34151 Trieste - Italy

^[3] Univ Sao Paulo, Inst Fis, IFUSP, BR-05314970 Sao Paulo - Brazil

• Tipo de documento: Artigo Científico
• Fonte: PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS; v. 404, p. 279-284, JUN 15 2014.
• Citações Web of Science: 8

Resumo

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. (AU)

• Processo FAPESP: 12/23688-5 - Expoentes e leis de escala, transições de fase e propriedades de transporte em sistemas dependentes do tempo
• Beneficiário: Edson Denis Leonel
• Modalidade de apoio: Auxílio à Pesquisa - Regular