Diffusion as mixing mechanism in granular materials

We present several numerical results on granular mixtures. In particular, we examine the efficiency of diffusion as a mixing mechanism in these systems. The collisions are inelastic and to compensate the energy loss, we thermalize the grains by adding a random force. Starting with a segregated system, we show that uniform agitation (heating) leads to a uniform mixture of grains of different sizes. We define a characteristic mixing time, $\tau_{mix}$, and study theoretically and numerically its dependence on other parameters like the density. We examine a model for bidisperse systems for which we can calculate some physical quantities. We also examine the effect of a temperature gradient and demonstrate the appearance of an expected segregation.Comment: 15 eps figures, include

Glass Transition in a 2D Lattice Model

The dynamics of compaction of hard cross-shaped pentamers on the 2D square lattice is investigated. The addition of new particles is controlled by diffusive relaxation. It is shown that the filling process terminates at a glassy phase with a limiting coverage density \rho_{rcp}=0.171626(3), lower than the density of closest packing \rho_{cp}=0.2, and the long time filling rate vanishes like (\rho_{rcp}-\rho(t))^2. For the entire density regime the particles form an amorphous phase, devoid of any crystalline order. Therefore, the model supports a stable random packing state, as opposed to the hard disks system. Our results may be relevant to recent experiments studying the clustering of proteins on bilayer lipid membranes

Dense Periodic Packings of Regular Polygons

We show theoretically that it is possible to build dense periodic packings, with quasi 6- fold symmetry, from any kind of identical regular convex polygons. In all cases, each polygon is in contact with $z=6$ other ones. For an odd number of sides of the polygons, 4 contacts are side to side contacts and the 2 others are side to vertex contacts. For an even number of sides, the 6 contacts are side to side contacts. The packing fraction of the assemblies is of the order of 90%. The predicted patterns have also been obtained by numerical simulations of annealing of packings of convex polygons

Random Close Packings of Regular Polygons

We study by numerical simulation the progressive densification of assemblies of equal regular polygons (pentagons and heptagons). We follow the evolution of the packing fraction, of the coordination numbers and of the void space structure during the densification. At high packing fraction ($C\sim 0.83$), ordered zones appear. This can be compared with what occurs in equal disc assemblies in which a Random Close Packing limit exists for a packing fraction $C\sim 0.83$ above which some local order is present

Spontaneous Formation of Vortex in a System of Self Motorised Particles

We study a system of disks with inelastic collisions. Energy is given to the system via a force of constant modulus, applied on each particle in the direction of its velocity. This system shows a dynamical phase transition from a disordered system towards a system organized into a vortex when the dissipation is increased. The state equation of the disordered system is obtained by using kinetic theory arguments. We also show that the transition is similar to the kinetic-cluster transition observed in the cooling of a gas of inelastic particles