Subdiffusive Transport in Heterogeneous Patchy Environments
Abstract
Transport across heterogeneous, patchy environments is a ubiquitous phenomenon spanning fields of study including ecological movement, intracellular transport and regions of specialised function in a cell. These regions or patches may be highly heterogeneous in their properties, and often exhibit anomalous behaviour (resulting from e.g. crowding or viscoelastic effects) which necessitates the inclusion of non-Markovian dynamics in their study. However, many such processes are also subject to an internal self-regulating or tempering process due to concurrent competing functions being carried out. In this work we develop a model for anomalous transport across a heterogeneous, patchy environment subject to tempering. We show that in the long-time an equilibrium may be reached with constant effective transport rates between the patches. This result is qualitatively different from untempered systems where subdiffusion results in the long-time accumulation of all particles in the patch with lowest anomalous exponent, .
Cite
@article{arxiv.1710.01982,
title = {Subdiffusive Transport in Heterogeneous Patchy Environments},
author = {Sergei Fedotov and Helena Stage},
journal= {arXiv preprint arXiv:1710.01982},
year = {2017}
}