Monte Carlo Investigation of Anomalous Transport in presence of a Discontinuity and of an Advection Field

TL;DR

This study uses Monte Carlo simulations within the CTRW framework to analyze how a discontinuity and advection influence anomalous particle transport, revealing flux continuity and concentration discontinuities at interfaces.

Contribution

It introduces a Monte Carlo approach to CTRW for transport across regions with different properties under advection, highlighting interface effects.

Findings

Flux remains continuous at the interface due to mass conservation.

Concentration exhibits a discontinuity at the interface.

Advection influences the transport behavior across the discontinuity.

Abstract

Anomalous diffusion has recently turned out to be almost ubiquitous in transport problems. When the physical properties of the medium where the transport process takes place are stationary and constant at each spatial location, anomalous transport has been successfully analyzed within the Continuous Time Random Walk (CTRW) model. In this paper, within a Monte Carlo approach to CTRW, we focus on the particle transport through two regions characterized by different physical properties, in presence of an external driving action constituted by an additional advective field, modeled within both the Galilei invariant and Galilei variant schemes. Particular attention is paid to the interplay between the distributions of space and time across the discontinuity. The resident concentration and the flux of the particles are finally evaluated and it is shown that at the interface between the two regions the flux is continuous as required by mass conservation, while the concentration may reveal a neat discontinuity. This result could open the route to the Monte Carlo investigation of the effectiveness of a physical discontinuity acting as a filter on particle concentration.