Colloquium

Granular materials are ubiquitous both in nature and in industrial applications. Yet, our understanding of their behavior is still limited, in large part due to the presence of frictional effects. In this talk, various mathematical approaches for the study of slow granular flows will be reviewed. Specific plasticity models will be described and analyzed.
The richness of the field will be illustrated by the wide range of mathematical problems one encounters such as Hamilton-Jacobi equations, free boundary problems, and elliptic and hyperbolic systems of partial differential equations. Open problems will be identified. Several computational issues will be discussed along with computational and experimental results. We also will discuss some recent successes such as numerical computation of secondary circulation and point out shortcomings of some standard models.