Anomalous diffusion models in the presence of a moving interface

Abstract

Many systems exhibit subdiffusive transport in which a diffusing particle’s mean-squared displacement has a time dependence that is slower than linear. Here, we study a model of subdiffusion, scaled Brownian motion (SBM), in the context of two-phase moving-boundary problems. In certain cases, the problems admit similarity solutions, though, in general, numerical approaches are required. Turn-around of the moving interface is observed when one domain exhibits subdiffusive transport and the other classical diffusive transport. In each case, the SBM dynamics is compared with another model of subdiffusion, fractional anomalous diffusion (FAD). In the limit that the subdiffusive region is nearly-classical in nature we explore the notion of using SBM as an approximation to FAD. One advantage of this approach is that computations involving SBM are less intensive than those for the corresponding FAD models.