The packing fraction ρ of a collection of hard spheres in three dimension cannot exceed a maximum of about 0.74. In that limit, the spheres are arranged in a close-packed crystalline lattice (such as the HCP lattice). If, however, a loose collection of hard spheres is compactified, starting from some random initial condition, then the maximum packing fraction ρc that can be achieved by compacti...

Due to the mathematical complexity of the Boltzmann equation for inelastic hard spheres, a kinetic model has recently been proposed whereby the collision rate (which is proportional to the relative velocity for hard spheres) is replaced by an average velocity-independent value. The resulting inelastic Maxwell model has received a large amount of recent interest, especially in connection with th...

Slow dynamics in a fluid are studied in one of the most basic systems possible: polydisperse hard spheres. Monodisperse hard spheres cannot be studied as the slow down in dynamics as the density is increased is preempted by crystallisation. As the dynamics slow they become more heterogeneous, the spread in the distances traveled by different particles in the same time increases. However, the dy...

The rich variety of densest columnar structures of identical hard spheres inside a cylinder can surprisingly be constructed from a simple and computationally fast sequential deposition of cylinder-touching spheres, if the cylinder-to-sphere diameter ratio is D is an element of [1,2.7013]. This provides a direction for theoretically deriving all these densest structures and for constructing such...