Models of anomalous diffusion in crowded environments

Abstract

A particle's motion in crowded environments often exhibits anomalous diffusion, whose nature depends on the situation at hand and is formalized within different physical models. Thus, such environments may contain traps, labyrinthine paths or macromolecular structures, which the particles may be attached to. Physical assumptions are translated into mathematical models which often come with nice mathematical instruments for their description, e.g. fractional diffusion equations. The beauty of the instrument sometimes seduces an investigator to use it without any connection to the physical model. The author hopes that the present discussion will reduce the danger of such inappropriate use.