Normal and anomalous transport across an interface: Monte Carlo and analytical approach

We present a Monte Carlo scheme to simulate particles going across an interface separating two layers of a medium characterized by different physical properties, together with an analytical formulation of the same problem, for both normal diffusive and subdiffusive regimes. We relate the Monte Carlo simulation parameters to the coefficients and boundary conditions appearing in the companion analytical equations. Under suitable physical hypotheses on the constraints to be imposed on such parameters, we show that the Monte Carlo simulation results are in good agreement with the corresponding analytical solutions. In particular, we remark that – while in the normal diffusion case the conservation of particle local velocities across the interface leads to a smoothly varying concentration profile – in the subdiffusive case the same condition leads to a neat jump in resident concentration.