Stationary states and energy cascades in inelastic gases

We analyze the deviations from Maxwell-Boltzmann statistics found in recent experiments studying velocity distributions in two-dimensional granular gases driven into a non-equilibrium stationary state by a strong vertical vibration. We show that in its simplest version, the ``stochastic thermostat'' model of heated inelastic hard spheres, contrary to what has been hitherto stated, is incompatible with the experimental data, although predicting a reminiscent high velocity stre...

The theory of homogeneously driven granular gases of hard particles predicts that the stationary state is characterized by a velocity distribution function with overpopulated high-energy tails as compared to the exponential decay valid for molecular gases. While this fundamental theoretical result was confirmed by numerous numerical simulations, an experimental confirmation is still missing. Using self-rotating active granular particles, we find a power-law decay of the veloc...

We address the problem of the so-called ``granular gases'', i.e. gases of massive particles in rapid movement undergoing inelastic collisions. We introduce a class of models of driven granular gases for which the stationary state is the result of the balance between the dissipation and the random forces which inject energies. These models exhibit a genuine thermodynamic limit, i.e. at fixed density the mean values of kinetic energy and dissipated energy per particle are indep...

This paper presents a molecular dynamics simulation of an inelastic gas, where collisions between molecules are characterized by a coefficient of restitution less than unity. The simulation employs an event-driven algorithm to efficiently propagate the system in time, tracking molecular positions and velocities. A thermostat mechanism is incorporated to maintain the system's temperature by applying Gaussian white noise to the molecular velocities. The system's kinetic energy ...

We study dynamics of freely cooling granular gases in two-dimensions using large-scale molecular dynamics simulations. We find that for dilute systems the typical kinetic energy decays algebraically with time, E(t) ~ t^{-1}, in the long time limit. Asymptotically, velocity statistics are characterized by a universal Gaussian distribution, in contrast with the exponential high-energy tails characterizing the early homogeneous regime. We show that in the late clustering regime ...

We determine the asymptotic behavior of the tails of the steady state velocity distribution of a homogeneously driven granular gas comprising of particles having a scalar velocity. A pair of particles undergo binary inelastic collisions at a rate that is proportional to a power of their relative velocity. At constant rate, each particle is driven by multiplying its velocity by a factor $-r_w$ and adding a stochastic noise. When $r_w <1$, we show analytically that the tails of...

The connection between granular gases and sticky gases has recently been considered, leading to the conjecture that inelastic collapse is avoided for space dimensions higher than 4. We report Molecular Dynamics simulations of hard inelastic spheres in dimensions 4, 5 and 6. The evolution of the granular medium is monitored throughout the cooling process. The behaviour is found to be very similar to that of a two-dimensional system, with a shearing-like instability of the velo...

Combining analytical and numerical methods, we study within the framework of the homogeneous non-linear Boltzmann equation, a broad class of models relevant for the dynamics of dissipative fluids, including granular gases. We use the new method presented in a previous paper [J. Stat. Phys. 124, 549 (2006)] and extend our results to a different heating mechanism, namely a deterministic non-linear friction force. We derive analytically the high energy tail of the velocity distr...

Motivated by recent experiments reporting non-Gaussian velocity distributions in driven dilute granular materials, we study by numerical simulation the properties of 2D inelastic gases. We find theoretically that the form of the observed velocity distribution is governed primarily by the coefficient of restitution $\eta$ and $q=N_H/N_C$, the ratio between the average number of heatings and the average number of collisions in the gas. The differences in distributions we find b...

We consider the single-particle velocity distribution of a one-dimensional fluid of inelastic particles. Both the freely evolving (cooling) system and the non-equilibrium stationary state obtained in the presence of random forcing are investigated, and special emphasis is paid to the small inelasticity limit. The results are obtained from analytical arguments applied to the Boltzmann equation along with three complementary numerical techniques (Molecular Dynamics, Direct Mont...