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

TL;DR

This paper uses Monte Carlo simulations and theoretical analysis to study how particles exit a domain with a periodically opening and closing boundary, comparing results with existing homogenization theory.

Contribution

It provides a numerical validation of the homogenization limit for a time-periodic boundary condition in a diffusion process.

Findings

Identification of a limiting boundary behavior with a constant flux-density ratio

Agreement between Monte Carlo results and homogenization predictions

Insights into the effects of periodic boundary gating on particle flux

Abstract

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.