Pre-asymptotic corrections to fractional diffusion equations

Marzio Marseguerra and Andrea Zoia

Physica A: Statistical Mechanics and its Applications, 2008, vol. 387, issue 12, 2668-2674

Abstract: 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.

Keywords: Anomalous diffusion; CTRW; Fractional diffusion equation; Monte Carlo (search for similar items in EconPapers)
Date: 2008
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:387:y:2008:i:12:p:2668-2674

DOI: 10.1016/j.physa.2008.01.087

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