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arXiv · 0805.4054

The rule for a subdiffusive particle in an extremely diverse environment

Ophir Flomenbom
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Abstract

The dynamics of a subdiffusive continuous time random walker in an inhomogeneous environment is analyzed. In each microscopic jump, a random time is drawn from a waiting time probability density function (WT-PDF) that decays as a power law: phi(t;k)~k/(1+kt)^(1+beta), 0 beta;, mu=beta, but when 1-gamma<beta, mu=1-gamma. The transition in the scaling of psi(t) reflects the competition between two different mechanisms for subdiffusion: subdiffusion due to the heavily tailed phi(t;k) for microscopic jumps, and subdiffusion due to the collective effect of an environment made of many slow local regions. These two different mechanisms for subdiffusion are not additive, and compete each other. The reported transition is dimension independent, and disappears when the power beta is also distributed, in the range, 0<bate<1. Simulations exemplified the transition, and implications are discussed.

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Ophir Flomenbom. 2008-10-08. The rule for a subdiffusive particle in an extremely diverse environment. https://doi.org/10.1016/j.physleta.2009.02.040

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