A “Tetris-Like” Model for the Compaction of Dry Granular Media

We propose a two-dimensional geometrical model, based on the concept of geometrical frustration, conceived for the study of compaction in granular media. The dynamics exhibits an interesting inverse logarithmic law that is well known from real experiments. Moreover, we present a simple dynamical model of $N$ planes exchanging particles with excluded volume problems, which allows us to clarify the origin of the logarithmic relaxations and the stationary density distribution. A simple mapping allows us to cast this Tetris-like model in the form of an Ising-like spin system with vacancies.