Random Walk in Cellular Media

Andrey Milchev, Victor Pereyra*, Victor Fleurov

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We introduce a model for diffusion of tracer particles in cellular media in which the walls of a cell are characterized by strongly reduced permeability. Our analytical results, confirmed also by extensive Monte Carlo simulations, reveal several distinct regimes of diffusion behavior in time whereby an initially normal diffusion at very short times turns into transient one at a characteristic crossover time τs and later, after a period marked by another characteristic time, τL, returns back to normal. At fixed permeability p of the cell walls we find that these crossover times scale as τS ∝ L2 and τL ∝ L with the size of the cells L whereas for L = constant one has τL ∝ p−1. Our results for the frequency-dependent conductivity σ(ω) show that at low frequency the real and imaginary parts of σ(ω) vary as ω2 and ω, respectively, while saturating at constant values for ω → ∞ By measurement of the dc and ac conductivity of charge carriers, it appears possible to determine both the size of the cells and the permeability of their walls.

Original languageEnglish
Pages (from-to)4698-4702
Number of pages5
Issue number12
StatePublished - 1 Dec 1994


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