Fractal Dimensions of the Hydrodynamic Modes of Diffusion

Abstract

We consider the time-dependent statistical distributions of diffusive processes in relaxation to a stationary state for simple, two dimensional chaotic models based upon random walks on a line. We show that the cumulative functions of the hydrodynamic modes of diffusion form fractal curves in the complex plane, with a Hausdorff dimension larger than one. In the limit of vanishing wavenumber, we derive a simple expression of the diffusion coefficient in terms of this Hausdorff dimension and the positive Lyapunov exponent of the chaotic model.

20 pages, 6 figures, submitted to Nonlinearity

References in corpus (1)

• Entropy Production, Fractals, and Relaxation to Equilibrium

Cited by in corpus (7)

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• Fractal fractal dimensions of deterministic transport coefficients
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• Escape-rate formalism, decay to steady states, and divergences in the entropy-production rate
• Spectral Characterization of Anomalous Diffusion of a Periodic Piecewise Linear Intermittent Map