Sandpiles and Dunes: Mathematical Models for Granular Matter

Granular materials are everywhere, in the environment but also in our pantry. Their properties are different from those of any solid material, due to the possibility of sudden phenomena (such as avalanches or landslides). Here we present a brief survey on their characteristics and on what can be found (over the past thirty years) in the recent mathematic literature in order to reproduce their behavior. We discuss in particular differential models proposed for the growth of a sandpile on a table, and, when even wind comes into play, for the formation and dynamics of sand dunes. This field of research is still of great interest, since there is no consolidated general model for the dynamics of granular matter, but rather singular models adapted to specific situations.