Pre-asymptotic corrections to fractional diffusion equations

Details Pre-asymptotic corrections to fractional diffusion equations Pre-asymptotic corrections to fractional diffusion equations

2007-11-13

arxiv.org/abs/0711.1947v2

Physica A 387 (12), 2668-2674 (2008)

Physics

Condensed Matter

Statistical Mechanics

6 pages, 3 figures

Scientific paper

10.1016/j.physa.2008.01.087

The motion of contaminant particles through complex environments such as fractured rocks or porous sediments is often characterized by anomalous diffusion: the spread of the transported quantity is found to grow sublinearly in time due to the presence of obstacles which hinder particle migration. The asymptotic behavior of these systems is usually well described by fractional diffusion, which provides an elegant and unified framework for modeling anomalous transport. We show that pre-asymptotic corrections to fractional diffusion might become relevant, depending on the microscopic dynamics of the particles. To incorporate these effects, we derive a modified transport equation and validate its effectiveness by a Monte Carlo simulation.

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