Statistical models for granular materials

Granular materials, like sand or powders, have many peculiar properties, most of them not yet fully understood. These are due to the special physical properties of granular media like dissipation, friction, dilatancy and the possibilities of having grains of many different sizes and shapes. In the last 10 years much progress has been achieved in the basic understanding of granular media due to the use of tools from Statistical Physics, including disordered systems, critical phenomena, instabilities and chaos. We will present in this talk two examples: Models for compaction which very much resemble those of structural glasses and predict the logarithmic time dependence experimentally measured in Chicago. Models that describe the evolution of free surfaces giving the angle of repose, invariant shapes with logarithmic tails and stratification patterns in agreement with observations.