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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

Dynamical thermalization in time-dependent billiards

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Hansen, Matheus [1] ; Ciro, David [2] ; Caldas, Ibere L. [1] ; Leonel, Edson D. [3]
Total Authors: 4
[1] Univ Sao Paulo, Inst Fis, BR-05508090 Sao Paulo, SP - Brazil
[2] Univ Sao Paulo, Inst Astron Geofis & Ciencias Atmosfer, BR-05508090 Sao Paulo, SP - Brazil
[3] UNESP, Dept Fis, BR-13506900 Rio Claro, SP - Brazil
Total Affiliations: 3
Document type: Journal article
Source: Chaos; v. 29, n. 10 OCT 2019.
Web of Science Citations: 0

Numerical experiments of the statistical evolution of an ensemble of noninteracting particles in a time-dependent billiard with inelastic collisions reveals the existence of three statistical regimes for the evolution of the speed ensemble, namely, diffusion plateau, normal growth/exponential decay, and stagnation. These regimes are linked numerically to the transition from Gauss-like to Boltzmann-like speed distributions. Furthermore, the different evolution regimes are obtained analytically through velocity-space diffusion analysis. From these calculations, the asymptotic root mean square of speed, initial plateau, and the growth/decay rates for an intermediate number of collisions are determined in terms of the system parameters. The analytical calculations match the numerical experiments and point to a dynamical mechanism for ``thermalization,{''} where inelastic collisions and a high-dimensional phase space lead to a bounded diffusion in the velocity space toward a stationary distribution function with a kind of ``reservoir temperature{''} determined by the boundary oscillation amplitude and the restitution coefficient. Published under license by AIP Publishing. (AU)

FAPESP's process: 18/03211-6 - Non linear dynamics
Grantee:Iberê Luiz Caldas
Support type: Research Projects - Thematic Grants
FAPESP's process: 17/14414-2 - Scaling investigation in dynamical systems
Grantee:Edson Denis Leonel
Support type: Regular Research Grants