Brownian walkers within subdiffusing territorial boundaries

Inspired by the collective phenomenon of territorial emergence, whereby animals move and interact through the scent marks they deposit, we study the dynamics of a 1D Brownian walker in a random environment consisting of confining boundaries that are themselves diffusing anomalously. We show how to r...

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Bibliographic Details
Published in:Physical review. E, Statistical, nonlinear, and soft matter physics Statistical, nonlinear, and soft matter physics, 2011-06, Vol.83 (6 Pt 1), p.061138-061138, Article 061138
Main Authors: Giuggioli, L, Potts, J R, Harris, S
Format: Article
Language:English
Subjects:
Diffusion
Models, Theoretical
Motion
Probability
Stochastic Processes
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Summary:Inspired by the collective phenomenon of territorial emergence, whereby animals move and interact through the scent marks they deposit, we study the dynamics of a 1D Brownian walker in a random environment consisting of confining boundaries that are themselves diffusing anomalously. We show how to reduce, in certain parameter regimes, the non-Markovian, many-body problem of territoriality to the analytically tractable one-body problem studied here. The mean square displacement (MSD) of the 1D Brownian walker within subdiffusing boundaries is calculated exactly and generalizes well known results when the boundaries are immobile. Furthermore, under certain conditions, if the boundary dynamics are strongly subdiffusive, we show the appearance of an interesting nonmonotonicity in the time dependence of the MSD, giving rise to transient negative diffusion.
ISSN:1539-3755
1550-2376
DOI:10.1103/PhysRevE.83.061138