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. 2014 Nov 12;5:437. doi: 10.3389/fphys.2014.00437

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Copyright © 2014 Berry and Soula.

This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

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Non-homogeneous CTRW and non-homogeneous Brownian yield identical accumulation inside the patch. The fraction of molecules inside the central patch N_in/N_T at equilibrium increases with the slowdown of diffusion inside the patch (where N_in and N_T are the number of molecules inside the central patch and the total number of molecules, respectively). NHC conditions are represented with blue plus signs whereas the NHB results are shown with brown empty circles. The full curves are the predictions from the theoretical expression for NHB, Equation (2) The dashed horizontal lines locate N_in/N_T = 0.25 and N_in/N_T = 0.01. The fraction area occupied by the central patch is ϕ = 0.25 (top curve) or 0.010 (bottom curve). In the NHC case, D_in is here the macroscopic diffusion coefficient of the transient CTRW inside the patch.