  We investigate via Monte Carlo numerical simulations and theoretical
considerations the outflux of random walkers moving in an interval bounded by
an interface exhibiting channels (pores, doors) which undergo an open/close
cycle according to a periodic schedule. We examine the onset of a limiting
boundary behavior characterized by a constant ratio between the outflux and the
local density, in the thermodynamic limit. We compare such a limit with the
predictions of a theoretical model already obtained in the literature as the
homogenization limit of a suitable diffusion problem.
