Deterministic diffusion in flower-shaped billiards

Takahisa Harayama, Rainer Klages, Pierre Gaspard

Research output: Contribution to journalArticle

13 Citations (Scopus)

Abstract

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
Article number026211
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume66
Issue number2
DOIs
Publication statusPublished - 2002 Aug
Externally publishedYes

Fingerprint

Billiards
Simple Random Walk
random walk
Green's Formula
Memory Effect
Lattice Gas
Open Systems
Simulation Methods
Diffusion Coefficient
Irregular
Computer Simulation
diffusion coefficient
computerized simulation
Model
Heuristics
Higher Order
Dependent
Approximation
approximation
gases

ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Condensed Matter Physics
  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

Deterministic diffusion in flower-shaped billiards. / Harayama, Takahisa; Klages, Rainer; Gaspard, Pierre.

In: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, Vol. 66, No. 2, 026211, 08.2002.

Research output: Contribution to journalArticle

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