Fractal fractal dimensions of deterministic transport coefficients
arXiv:nlin/0301038 · doi:10.1088/0305-4470/36/21/305
Abstract
If a point particle moves chaotically through a periodic array of scatterers the associated transport coefficients are typically irregular functions under variation of control parameters. For a piecewise linear two-parameter map we analyze the structure of the associated irregular diffusion coefficient and current by numerically computing dimensions from box-counting and from the autocorrelation function of these graphs. We find that both dimensions are fractal for large parameter intervals and that both quantities are themselves fractal functions if computed locally on a uniform grid of small but finite subintervals. We furthermore show that there is a simple functional relationship between the structure of fractal fractal dimensions and the difference quotient defined on these subintervals.
16 pages (revtex) with 6 figures (postscript)
References in corpus (11)
- Chaotic Scattering Theory, Thermodynamic Formalism, and Transport Coefficients
- Simple Maps with Fractal Diffusion Coefficients
- Simple deterministic dynamical systems with fractal diffusion coefficients
- The Fractality of the Hydrodynamic Modes of Diffusion
- Chaotic and fractal properties of deterministic diffusion-reaction processes
- Understanding deterministic diffusion by correlated random walks
- Fractal structures of normal and anomalous diffusion in nonlinear nonhyperbolic dynamical systems
- Negative and Nonlinear Response in an Exactly Solved Dynamical Model of Particle Transport
- Fractal Dimensions of the Hydrodynamic Modes of Diffusion
- Deterministic diffusion in flower shape billiards
- The fractality of the relaxation modes in deterministic reaction-diffusion systems