Fractal Dimensions of the Hydrodynamic Modes of Diffusion
Preprint
- 10 July 2000
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.Keywords
All Related Versions
- Version 1, 2000-07-10, ArXiv
- Published version: Nonlinearity, 14 (2), 339.
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