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We investigate via Monte Carlo numerical simulations and theoreticalconsiderations the outflux of random walkers moving in an interval bounded byan interface exhibiting channels (pores, doors) which undergo an open/closecycle according to a periodic schedule. We examine the onset of a limitingboundary behavior characterized by a constant ratio between the outflux and thelocal density, in the thermodynamic limit. We compare such a limit with thepredictions of a theoretical model already obtained in the literature as thehomogenization limit of a suitable diffusion problem.

Flux through a time-periodic gate: Monte Carlo test of a homogenization result