Related papers: The Boltzmann equation for a multi-species inelast…
We study the transport properties of an impurity in a sheared granular gas, in the framework of the Boltzmann equation for inelastic Maxwell models. We investigate here the impact of a nonequilibrium phase transition found in such systems,…
The stochastic properties of the total internal energy of a dilute granular gas in the steady uniform shear flow state are investigated. A recent theory formulated for fluctuations about the homogeneous cooling state is extended by analogy…
Non-cohesive granular media exhibit complex responses to sudden impact that often differ from those of ordinary solids and liquids. We investigate how this response is mediated by the presence of interstitial gas between the grains. Using…
We prove the so-called generalized Haff's law yielding the optimal algebraic cooling rate of the temperature of a granular gas described by the homogeneous Boltzmann equation for inelastic interactions with non constant restitution…
Recent computer simulation results [Barrat {\em et al.}, Physica A 334 (2004) 513] for granular mixtures subject to stochastic driving have shown the validity of the Einstein relation $\epsilon\equiv D/(T_0\lambda)=1$ between the diffusion…
We describe in detail a recently proposed lattice-Boltzmann model for simulating flows with multiple phases and components. In particular, the focus is on the modeling of one-component fluid systems which obey non-ideal gas equations of…
The hypothesis of ``molecular chaos'' is shown to fail when applied to spatially inhomogeneous evolution of a low-density gas, because this hypothesis is incompatible with reduction of interactions of gas particles to ``collisions''. The…
Multi-species Boltzmann equations for gaseous mixtures, with analytic cross sections and under Grad's angular cutoff assumption, are considered under diffusive scaling. In the limit, we formally obtain an explicit expression for the binary…
We consider the socalled Bathnagar-Gross-Krook (BGK) model, an approximation of the Boltzmann equation, describing the time evolution of a single momoatomic rarefied gas and satisfying the same two main properties (conservation properties…
We review a few representative examples of granular experiments or models where phase separation, accompanied by domain coarsening, is a relevant phenomenon. We first elucidate the intrinsic non-equilibrium, or athermal, nature of granular…
We consider a multi component gas mixture with translational and internal energy degrees of freedom without chemical reactions assuming that the number of particles of each species remains constant. We will illustrate the derived model in…
We consider a non-interacting one-dimensional gas accelerated by a constant and uniform external field. The energy absorbed from the field is transferred via elastic collisions to a bath of scattering obstacles. At gas-obstacle encounters…
The behavior of a bidisperse inelastic gas vertically shaken in a compartmentalized container is investigated using two different approaches: the first is a mean-field dynamical model, which treats the number of particles in the two…
This paper provides the first rigorous derivation of a binary-ternary Boltzmann equation describing the kinetic properties of a dense hard-spheres gas, where particles undergo either binary or ternary instantaneous interactions, while…
We study the Boltzmann equation for a space-homogeneous gas of inelastic hard spheres, with a diffusive term representing a random background forcing. Under the assumption that the initial datum is a nonnegative $L^2$ function, with bounded…
The dynamics of a tracer particle in a stationary driven granular gas is investigated. We show how to transform the linear Boltzmann equation describing the dynamics of the tracer into a master equation for a continuous Markov process. The…
We study a dilute granular gas immersed in a thermal bath made of smaller particles with masses not much smaller than the granular ones in this work. Granular particles are assumed to have inelastic and hard interactions, losing energy in…
Tracer diffusion in a granular gas in simple shear flow is analyzed. The analysis is made from a perturbation solution of the Boltzmann kinetic equation through first order in the gradient of the mole fraction of tracer particles. The…
We propose a new kinetic BGK-type model for a mixture of four monatomic gases, undergoing a bimolecular and reversible chemical reaction. The elastic and reactive interactions are described separately by distinct relaxation terms and the…
A steady state of a granular gas with homogeneous granular temperature, no mass flow, and nonzero heat flux is studied. The state is created by applying an external position--dependent force or by enclosing the grains inside a curved…