Fractal dimensions of the hydrodynamic modes of diffusion
- 6 February 2001
- journal article
- Published by IOP Publishing in Nonlinearity
- Vol. 14 (2) , 339-358
- https://doi.org/10.1088/0951-7715/14/2/309
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
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