Granular matter can behave ‒ depending on the circumstances ‒ like a solid, a fluid or a gas, yet often with an unexpected twist owing to the special nature of this complex, multi-particle medium. Here we present two case studies:
1.Vibrated sand: a counter-intuitive gas. If granular matter is shaken vigorously, the particles fly about, forming a kind of gas. Unexpectedly, however, they do not spread out uniformly over the available space as a standard gas would do, but they tend to cluster together. This spontaneous breakdown of equipartition shows up in a particularly clear-cut fashion when the space is divided in two compartments, as in the so-called “Maxwell’s Demon” experiment. We describe this experiment in terms of Dynamical Systems theory and show how the clustering transition manifests itself as a pitchfork bifurcation.
2. Flowing sand: roll waves as stick-slip oscillations. Our second case study focuses on granular matter flowing down a chute, and more specifically, on the roll wave patterns frequently encountered in this type of flow. These nonlinear waves consist of long rising flanks followed by abrupt falls and can adequately be described by the generalized Saint-Venant equations for shallow granular flows. More surprisingly, as we will demonstrate, they can also be seen as the Fluid Dynamical analogue of the famous stick-slip phenomenon found in many mechanical systems.