Generating ensembles and measuring mixing in a model granular system

A major open question in the field of granular materials is the identification of relevant state variables which can predict macroscopic behavior. We experimentally investigate the mixing properties of an idealized granular liquid in the vicinity of its jamming transition, through the generation of ensembles of configurations under various boundary conditions. Our apparatus consists of a two-dimensional aggregate of particles which rearrange under agitation from the outer boundaries. As expected, the system acts like a slow liquid at low pressure or low packing fraction, and jams at higher pressure or high packing fraction. We characterize mixing in the system by computing the topological entropy of the braids formed by the trajectories of the grains. This entropy is shown to be well-defined and very sensitive to the approach to jamming, reflecting the dynamical arrest of the assembly.