Stationary states and energy cascades in inelastic gases

In contrast to molecular gases, granular gases are characterized by inelastic collisions and require therefore permanent driving to maintain a constant kinetic energy. The kinetic theory of granular gases describes how the average velocity of the particles decreases after the driving is shut off. Moreover it predicts that the rescaled particle velocity distribution will approach a stationary state with overpopulated high-velocity tails as compared to the Maxwell-Boltzmann dis...

Collisional thermalization of a particle ensemble under the energy dissipation can be seen in variety of systems, such as heated granular gasses and particles in plasmas. Despite its universal existence, analytical descriptions of the steady-state distribution have been missing. Here, we show that the steady-state energy distribution of the wide class of collisional energy cascades can be well approximated by the generalized Mittag-Leffler distribution, which is one of stable...

We consider a one-dimensional "gas" of inelastically colliding particles where kinetic energy is dissipated by the excitation of vibrational degrees of freedom. In our model the coefficient of restitution is a stochastic quantity whose distribution can be calculated from an exact stochastic equation of motion. We investigate the equipartition properties of the system and propose a new algorithm for computer simulations, that is a combination of event-driven and Monte-Carlo me...

We study steady-state properties of inelastic gases in two-dimensions in the presence of an energy source. We generalize previous hydrodynamic treatments to situations where high and low density regions coexist. The theoretical predictions compare well with numerical simulations in the nearly elastic limit. It is also seen that the system can achieve a nonequilibrium steady-state with asymmetric velocity distributions, and we discuss the conditions under which such situations...

Hamiltonian systems with long-range interactions give rise to long lived out of equilibrium macroscopic states, so-called quasi-stationary states. We show here that, in a suitably generalized form, this result remains valid for many such systems in the presence of dissipation. Using an appropriate mean-field kinetic description, we show that models with dissipation due to a viscous damping or due to inelastic collisions admit "scaling quasi-stationary states", i.e., states wh...

We investigate in this article the long-time behaviour of the solutions to the energy-dependant, spatially-homogeneous, inelastic Boltzmann equation for hard spheres. This model describes a diluted gas composed of hard spheres under statistical description, that dissipates energy during collisions. We assume that the gas is "anomalous", in the sense that energy dissipation increases when temperature decreases. This allows the gas to cool down in finite time. We study existenc...

This paper deals with solutions of the nonlinear Boltzmann equation for spatially uniform freely cooling inelastic Maxwell models for large times and for large velocities, and the nonuniform convergence to these limits. We demonstrate how the velocity distribution approaches in the scaling limit to a similarity solution with a power law tail for general classes of initial conditions and derive a transcendental equation from which the exponents in the tails can be calculated. ...

The properties of a dilute granular gas in the homogeneous cooling state are mapped to those of a stationary state by means of a change in the time scale that does not involve any internal property of the system. The new representation is closely related with a general property of the granular temperature in the long time limit. The physical and practical implications of the mapping are discussed. In particular, simulation results obtained by the direct simulation Monte Carlo...

We explore the velocity distributions in a vibrated binary granular gas system, focusing on how these distributions are influenced by the coefficient of restitution (CoR) and the inelasticity of particle collisions. Through molecular dynamics simulations, we examine the system's behavior for a range of CoR values below unity: specifically, 0.80, 0.85, 0.90, and 0.95. We track the evolution of velocity distributions as the system approaches a non-equilibrium steady state. Our ...

We employ granular hydrodynamics to investigate a paradigmatic problem of clustering of particles in a freely cooling dilute granular gas. We consider large-scale hydrodynamic motions where the viscosity and heat conduction can be neglected, and one arrives at the equations of ideal gas dynamics with an additional term describing bulk energy losses due to inelastic collisions. We employ Lagrangian coordinates and derive a broad family of exact non-stationary analytical soluti...