Deterministic diffusion in flower-shaped billiards

Takahisa Harayama, Rainer Klages, Pierre Gaspard

Research output: Contribution to journalArticlepeer-review

17 Citations (Scopus)


We propose a flower-shaped billiard in order to study the irregular parameter dependence of chaotic normal diffusion. Our model is an open system consisting of periodically distributed obstacles in the shape of a flower, and it is strongly chaotic for almost all parameter values. We compute the parameter dependent diffusion coefficient of this model from computer simulations and analyze its functional form using different schemes, all generalizing the simple random walk approximation of Machta and Zwanzig. The improved methods we use are based either on heuristic higher-order corrections to the simple random walk model, on lattice gas simulation methods, or they start from a suitable Green-Kubo formula for diffusion. We show that dynamical correlations, or memory effects, are of crucial importance in reproducing the precise parameter dependence of the diffusion coefficent.

Original languageEnglish
JournalPhysical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Issue number2
Publication statusPublished - 2002 Aug 23
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics


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