Linear hydrodynamics for driven granular gases

We study the dynamics of a granular gas heated by a stochastic thermostat. From a Boltzmann description, we derive the hydrodynamic equations for small perturbations around the stationary state that is reached in the long time limit. Transport coefficients are identified as Green-Kubo formulas obtaining explicit expressions as a function of the inelasticity and the spatial dimensio

Energy fluctuations in a randomly driven granular fluid

We study the behavior of the energy fluctuations in the stationary state of a uniformly heated granular gas. The equation for the one-time two-particle correlation function is derived and the hydrodynamic eigenvalues are identified. Explicit predictions are subsequently determined for energy fluctuations. The results explain Monte Carlo numerical data reported in previous studies [Eur. Phys. J. B 51, 377 (2006)].Agence Nationale de la Recherche ANR-05-JCJC-4448

Brownian motion under annihilation dynamics

The behavior of a heavy tagged intruder immersed in a bath of particles evolving under ballistic annihilation dynamics is investigated. The Fokker-Planck equation for this system is derived and the peculiarities of the corresponding diffusive behavior are worked out. In the long time limit, the intruder velocity distribution function approaches a Gaussian form, but with a different temperature from its bath counterpart. As a consequence of the continuous decay of particles in the bath, the mean-squared displacement increases exponentially in the collision per particle time scale. Analytical results are finally successfully tested against Monte Carlo numerical simulations.HPC-EUROPA project No. RII3-CT-2003-50607

Kinetic equation and nonequilibrium entropy for a quasi-two-dimensional gas

A kinetic equation for a dilute gas of hard spheres confined between two parallel plates separated a distance smaller than two particle diameters is derived. It is a Boltzmann-like equation, which incorporates the effect of the confinement on the particle collisions. A function S(t) is constructed by adding to the Boltzmann expression a confinement contribution. Then it is shown that for the solutions of the kinetic equation, S(t) increases monotonically in time, until the system reaches a stationary inhomogeneous state, when S becomes the equilibrium entropy of the confined system as derived from equilibrium statistical mechanics. From the entropy, other equilibrium properties are obtained, and molecular dynamics simulations are used to verify some of the theoretical predictions.España Mineco Grant No. FIS2014-53808-

Homogeneous dynamics in a vibrated granular monolayer

A simple model of a vibrated granular monolayer is studied. It consists of inelastic hard spheres confined between two parallel hard plates separated at a distance smaller than twice the diameter of the particles. Both walls are elastic and one of them is vibrating in a sawtooth way. For low densities, a kinetic equation is proposed, from which closed evolution equations for the horizontal and vertical temperatures are derived, assuming spatial homogeneity and that the system is very thin. An excellent agreement between the theoretical predictions and molecular dynamics simulation results is obtained, both for the stationary values and for the dynamics of the temperatures.Ministerio de Economía, Industria y Competitividad FIS2017-87117-

Understanding an instability in vibrated granular monolayers

We investigate the dynamics of an ensemble of smooth inelastic hard spheres confined between two horizontal plates separated by a distance smaller than twice the diameter of the particles, in such a way that the system is quasi-two-dimensional. The bottom wall is vibrating and, therefore, it injects energy into the system in the vertical direction and a stationary state is reached. It is found that if the size of the plates is small enough, the stationary state is homogeneous. Otherwise, a cluster of particles is developed. The instability is understood by using some effective hydrodynamic equations in the horizontal plane. Moreover, the theoretical prediction for the size of the system above which it becomes unstable agrees very well with molecular dynamics simulation results without any fitting parameter.España, Ministerio de Economía, Industria y Competitividad Grant No. FIS2017-87117-

Boltzmann kinetic equation for a strongly confined gas of hard spheres

A Boltzmann-like kinetic equation for a quasi-two-dimensional gas of hard spheres is derived. The system is confined between two parallel hard plates separated a distance between one and two particle diameters. An entropy Lyapunov function for the equation is identified. In addition to the usual Boltzmann expression, it contains a contribution associated to the confinement of the particles. The steady properties of the system agree with equilibrium statistical mechanics results. Equations describing the energy transfer between the degrees of freedom parallel and perpendicular to the confining plates are obtained for some simple initial configurations. The theoretical predictions are compared with molecular dynamics simulation data and a good agreement is foun

Self-diffusion in a quasi-two-dimensional gas of hard spheres

A quasi-two-dimensional system of hard spheres strongly confined between two parallel plates is considered. The attention is focused on the macroscopic self-diffusion process observed when the system is seen from above or from below. The transport equation, and the associated self-diffusion coefficient, are derived from a Boltzmann-Lorentz kinetic equation, valid in the dilute limit. Since the equilibrium state of the system is inhomogeneous, this requires the use of a modified Chapman-Enskog expansion that distinguishes between equilibrium and nonequilibrium gradients of the density of labeled particles. The self-diffusion coefficient is obtained as a function of the separation between the two confining plates. The theoretical predictions are compared with molecular dynamics simulation results and a good agreement is found.Ministerio de Economía, Industria y Competitividad FIS2017-87117-

Inhomogeneous cooling state of a strongly confined granular gas at low density

The inhomogeneous cooling state describing the hydrodynamic behavior of a freely evolving granular gas strongly confined between two parallel plates is studied, using a Boltzmann kinetic equation derived recently. By extending the idea of the homogeneous cooling state, we propose a scaling distribution in which all the time dependence occurs through the granular temperature of the system, while there is a dependence on the distance to the confining walls through the density. It is obtained that the velocity distribution is not isotropic, and it has two different granular temperature parameters associated to the motion perpendicular and parallel to the confining plates, respectively, although their cooling rates are the same. Moreover, when approaching the inhomogeneous cooling state, energy is sometimes transferred from degrees of freedom with lower granular temperature to those with a higher one, contrary to what happens in molecular systems. The cooling rate and the two partial granular temperatures are calculated by means of a Gaussian approximation. The theoretical predictions are compared with molecular dynamics simulation results and a good agreement is found.España Ministerio de Economía, Industria y Competitividad Grant No. FIS2017-87117-

Breakdown of the fluctuation-dissipation relations in granular gases

A numerical molecular dynamics experiment measuring the two-time correlation function of the transversal velocity field in the homogeneous cooling state of a granular gas modeled as an ensemble of inelastic hard particles is reported. By measuring the decay rate and the amplitude of the correlations, the accuracy of the Landau-Langevin equation of fluctuating hydrodynamics is checked. The results indicate that although a Langevin approach can be valid, the fluctuation-dissipation relation must be modified, since the viscosity parameter appearing in it differs from the usual hydrodynamic shear viscosity.Ministerio De Educación y Ciencia y FEDER FIS2008-01339HPC-EUROPA RII3-CT- 2003-50607