Search

The homogeneous cooling state (HCS) of a granular gas described by the inelastic Boltzmann equation is reconsidered. As usual, particles are taken as inelastic hard disks or spheres, but now the coefficient of normal restitution $\alpha$ is allowed to take negative values $\alpha\in[-1,1]$, a simple way of modeling more complicated inelastic interactions. The distribution function of the HCS is studied at the long-time limit, as well as for intermediate times. At the long-time limit, the relevant information of the HCS is given by a scaling distribution function $\phi_s(c)$, where the time dependence occurs through a dimensionless velocity $c$. For $\alpha\gtrsim -0.75$, $\phi_s$ remains close to the gaussian distribution in the thermal region, its cumulants and exponential tails being well described by the first Sonine approximation. On the contrary, for $\alpha\lesssim -0.75$, the distribution function becomes multimodal, its maxima located at $c\ne 0$, and its observable tails algebraic. The latter is a consequence of an unbalanced relaxation-dissipation competition, and is analytically demonstrated for $\alpha\simeq -1$ thanks to a reduction of the Boltzmann equation to a Fokker-Planck-like equation. Finally, a generalized scaling solution to the Boltzmann equation is also found $\phi(c,\beta)$. Apart from the time dependence occurring through the dimensionless velocity, $\phi(c,\beta)$ depends on time through a new parameter $\beta$ measuring the departure of the HCS from its long-time limit. It is shown that $\phi(c,\beta)$ describes the time evolution of the HCS for almost all times. The relevance of the new scaling is also discussed., Comment: 19 pages, 7 figures

The hydrodynamic Burnett equations and the associated transport coefficients are exactly evaluated for generalized inelastic Maxwell models. In those models, the one-particle distribution function obeys the inelastic Boltzmann equation, with a velocity-independent collision rate proportional to the $\gamma$ power of the temperature. The pressure tensor and the heat flux are obtained to second order in the spatial gradients of the hydrodynamic fields with explicit expressions for all the Burnett transport coefficients as functions of $\gamma$, the coefficient of normal restitution, and the dimensionality of the system. Some transport coefficients that are related in a simple way in the elastic limit become decoupled in the inelastic case. As a byproduct, existing results in the literature for three-dimensional elastic systems are recovered, and a generalization to any dimension of the system is given. The structure of the present results is used to estimate the Burnett coefficients for inelastic hard spheres., Comment: 16 pages, 5 figures; v2: new Appendix (D) and new references added

Segregation induced by a thermal gradient of an impurity in a driven low-density granular gas is studied. The system is enclosed between two parallel walls from which we input thermal energy to the gas. We study here steady states occurring when the inelastic cooling is exactly balanced by some external energy input (stochastic force or viscous heating), resulting in a uniform heat flux. A segregation criterion based on Navier-Stokes granular hydrodynamics is written in terms of the tracer diffusion transport coefficients, whose dependence on the parameters of the system (masses, sizes and coefficients of restitution) is explicitly determined from a solution of the inelastic Boltzmann equation. The theoretical predictions are validated by means of Monte Carlo and molecular dynamics simulations, showing that Navier-Stokes hydrodynamics produces accurate segregation criteria even under strong shearing and/or inelasticity., Comment: 10 pages, 5 figures, to be published in Phys. Rev. E

The steady states of two vibrated granular gases separated by an adiabatic piston are investigated. The system exhibits a non-equilibrium phase transition with an spontaneous symmetry breaking. Even if the gases at both sides of the piston have the same number of particles and are mechanically identical, their steady volumes and temperatures can be rather different. The transition can be explained by a simple kinetic theory model expressing mechanical equilibrium and the energy balance occurring in the system. The model predictions are in good agreement with molecular dynamics simulation results. The macroscopic description of the steady states is discussed, as well as some physical implications of the symmetry breaking., Comment: 5 figures

A dilute suspension of impurities in a low density gas is described by the Boltzmann and Boltzman-Lorentz kinetic theory. Scaling forms for the species distribution functions allow an exact determination of the hydrodynamic fields, without restriction to small thermal gradients or Navier-Stokes hydrodynamics. The thermal diffusion factor characterizing sedimentation is identified in terms of collision integrals as functions of the mechanical properties of the particles and the temperature gradient. An evaluation of the collision integrals using Sonine polynomial approximations is discussed. Conditions for segregation both along and opposite the temperature gradient are found, in contrast to the Navier-Stokes description for which no segregation occurs., Comment: 9 figures

Two granular gases separated by an adiabatic piston and initially in the same macroscopic state are considered. It is found that a phase transition with an spontaneous symmetry breaking occurs. When the mass of the piston is increased beyond a critical value, the piston moves to a stationary position different from the middle of the system. The transition is accurately described by a simple kinetic model that takes into account the velocity fluctuations of the piston. Interestingly, the final state is not characterized by the equality of the temperatures of the subsystems but by the cooling rates being the same. Some relevant consequences of this feature are discussed., Comment: 6 figures