Transport and dynamical properties for a bouncing ball model with regular and stochastic perturbations

Autor(es)

da Costa, Diogo Ricardo ^{[1, 2, 3]} ; Dettmann, Carl P. ^[1] ; Leonel, Edson D. ^[3]

Afiliação do(s) autor(es)

^[1] Univ Bristol, Sch Math, Bristol, Avon - England

^[2] Univ Sao Paulo, Inst Fis, BR-05508090 Sao Paulo - Brazil

^[3] UNESP Univ Estadual Paulista, Dept Fis, BR-13506900 Rio Claro, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION; v. 20, n. 3, p. 871-881, MAR 2015.
• Citações Web of Science: 10

Resumo

Some statistical properties related to the diffusion in energy for an ensemble of classical particles in a bouncing ball model are studied. The particles are confined to bounce between two rigid walls. One of them is fixed while the other oscillates. The dynamics is described by a two dimensional nonlinear map for the velocity of the particle and time at the instant of the collision. Two different types of change of momentum are considered: (i) periodic due to a sine function and; (ii) stochastic. For elastic collisions case (i) leads to finite diffusion in energy while (ii) produces unlimited diffusion. On the other hand, inelastic collisions yield either (i) and (ii) to have limited diffusion. Scaling arguments are used to investigate some properties of the transport coefficient in the chaotic low energy region. Scaling exponents are also obtained for both conservative and dissipative case for cases (i) and (ii). We show that the parameter space has complicated structures either in Lyapunov as well as period coordinates. When stochasticity is introduced in the dynamics, we observed the destruction of the parameter space structures. (C) 2014 Elsevier B.V. All rights reserved. (AU)

• Processo FAPESP: 12/18962-0 - Transporte, escape de partículas e propriedades dinâmicas de alguns mapeamentos não lineares
• Beneficiário: Diogo Ricardo da Costa
• Modalidade de apoio: Bolsas no Exterior - Estágio de Pesquisa - Doutorado
• Processo FAPESP: 10/52709-5 - Transporte, escape de particulas e propriedades dinamicas de mapeamentos nao lineares
• Beneficiário: Diogo Ricardo da Costa
• Modalidade de apoio: Bolsas no Brasil - Doutorado
• Processo FAPESP: 13/22764-2 - Propriedades dinâmicas e de transporte em sistemas dinâmicos conservativos e dissipativos
• Beneficiário: Diogo Ricardo da Costa
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado