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Fractal Dimensions of the Hydrodynamic Modes of Diffusion

T. Gilbert·J. R. Dorfman·P. Gaspard
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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.

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T. Gilbert, J. R. Dorfman, P. Gaspard. 2000-07-10. Fractal Dimensions of the Hydrodynamic Modes of Diffusion. https://doi.org/10.1088/0951-7715%2F14%2F2%2F309

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