Fractal Dimensions of the Hydrodynamic Modes of Diffusion
Chaotic Dynamics
2013-07-15 v1
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
Cite
@article{arxiv.nlin/0007008,
title = {Fractal Dimensions of the Hydrodynamic Modes of Diffusion},
author = {T. Gilbert and J. R. Dorfman and P. Gaspard},
journal= {arXiv preprint arXiv:nlin/0007008},
year = {2013}
}
Comments
20 pages, 6 figures, submitted to Nonlinearity