| Abstract: |
| We study the diffusion of particles through a thin heterogenous membrane under a one--directional nonlinear drift. Using mean-field equations derived from a Monte Carlo lattice dynamics for the problem at hand, we study the possibility to upscale the system and to compute the effective transport coefficients accounting for the presence of the membrane. For a special scaling regime, we perform a simultaneous homogenization asymptotics and dimension reduction, allowing us to replace completely the heterogenous membrane by an homogeneous obstacle line provided with effective transmission conditions. The heterogeneities we account for in this context are assumed to be arranged periodically, but the same working techniques can cover also the locally periodic case. |
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