Effective two-dimensional model for granular matter with phase separation.

Granular systems confined in vertically vibrated shallow horizontal boxes (quasi-two-dimensional geometry) present a liquid-to-solid phase transition when the frequency of the periodic forcing is increased. An effective model, where grains move and collide in two-dimensions is presented, which reproduces the aforementioned phase transition. The key element is that besides the two-dimensional degrees of freedom, each grain has an additional variable ɛ that accounts for the kinetic energy stored in the vertical motion in the real quasi-two-dimensional motion.

Effect of the vibration profile on shallow granular systems.

We describe the collective behaviour of a system of many inelastic spherical particles inside a box which is being periodically vibrated. The box is shallow, with large horizontal dimensions, while the height is less than two particle diameters. The vibrations are not symmetric: the time the box is moving up is, in general, different from the time it is moving down.

Shear viscosity of a model for confined granular media.

The shear viscosity in the dilute regime of a model for confined granular matter is studied by simulations and kinetic theory. The model consists on projecting into two dimensions the motion of vibrofluidized granular matter in shallow boxes by modifying the collision rule: besides the restitution coefficient that accounts for the energy dissipation, there is a separation velocity that is added in each collision in the normal direction. The two mechanisms balance on average, producing stationary homogeneous states.

Hydrodynamic modes in a confined granular fluid.

Confined granular fluids, placed in a shallow box that is vibrated vertically, can achieve homogeneous stationary states due to energy injection mechanisms that take place throughout the system. These states can be stable even at high densities and inelasticities allowing for a detailed analysis of the hydrodynamic modes that govern the dynamics of granular fluids. By analyzing the decay of the time correlation functions it is shown that there is a crossover from a quasielastic regime in which energy evolves as a slow mode to an inelastic regime with energy slaved to the other conserved fields.

Sudden chain energy transfer events in vibrated granular media.

In a mixture of two species of grains of equal size but different mass, placed in a vertically vibrated shallow box, there is spontaneous segregation. Once the system is at least partly segregated and clusters of the heavy particles have formed, there are sudden peaks of the horizontal kinetic energy of the heavy particles, that is otherwise small. Together with the energy peaks the clusters rapidly expand and the segregation is partially lost.

Rise of a Brazil nut: a transition line.

Using molecular dynamics we study the behavior of a large particle immersed in a bed of smaller ones. The system is bidimensional, consisting of many rough inelastic hard disks of equal size plus a larger one: the intruder. All possible parameters of the system are kept fixed except for two dimensionless parameters determining the frequency and amplitude of the vibrating base.

Friction and convection in a vertically vibrated granular system.

The effect of friction in the thermal convection instability of granular fluids is studied by means of molecular dynamics simulations. It is found that the transitions between different convective states (zero, one, and two rolls) are primarily governed by the average energy loss per collisions and not by the friction and restitution coefficients separately, and can be roughly described in terms of a single effective restitution coefficient. The average energy loss per collisions, for a fixed value of the restitution coefficient, shows a maximum for a friction coefficient kappa approximately 0.

Dynamics of rarefied granular gases.

This paper presents quite general bidimensional gas-dynamic equations--derived from kinetic theory-which include the fourth cumulant kappa(r,t) as a dynamic field. The dynamics describes a low-density system of inelastic hard spheres (disks) with normal restitution coefficient r. Two illustrative examples are given and the role of kappa in them is discussed.