Self-diffusion in granular gases: Green-Kubo versus Chapman-Enskog

Universal cover-time distributions of random motion in bounded granular gases

The exhaustive random exploration of a complex domain is a fundamental issue in many natural, social, and engineering systems. The key characterizing quantity is the cover time, which is the time to visit every site in the system. One prototypical experimental platform is the confined granular gas, where the random motion of granular particles mimics the wandering of random walkers in a confined region. Here, we investigate the cover-time distribution of the random motion of tracer particles in granular gases confined in four containers to account for different boundary and angle effects and examine whether the cover time of the heterogeneous random motion of the granular gases can be rescaled into the universal Gumbel distribution according to a recent theory [Dong et al., arXiv:2210.05122 (2022)]. It is found that for long cover times, the experimental results are in full accord, while for short cover times, the agreement is reasonable, with noticeable deviations that can be attributed to spatial correlations of the sites in the covering process. Our results, thus, call for further theoretical investigations in order to take into full account these nonideal issues.

Velocity Distribution of a Homogeneously Driven Two-Dimensional Granular Gas

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 velocity distribution whose exponent agrees well with the theoretic prediction.

Stochastic behavior of the coefficient of normal restitution

We consider the collision of a rough sphere with a plane by detailed analysis of the collision geometry. Using stochastic methods, the effective coefficient of restitution may be described as a fluctuating quantity whose probability density follows an asymmetric Laplace distribution. This result agrees with recent experiments by Montaine et al. [Phys. Rev. E 84, 041306 (2011)].

Intermediate regimes in granular Brownian motion: superdiffusion and subdiffusion

Brownian motion in a granular gas in a homogeneous cooling state is studied theoretically and by means of molecular dynamics. We use the simplest first-principles model for the impact-velocity dependent restitution coefficient, as it follows for the model of viscoelastic spheres. We reveal that for a wide range of initial conditions the ratio of granular temperatures of Brownian and bath particles demonstrates complicated nonmonotonic behavior, which results in a transition between different regimes of Brownian dynamics: It starts from the ballistic motion, switches later to a superballistic one, and turns at still later times into subdiffusion; eventually normal diffusion is achieved. Our theory agrees very well with the molecular dynamics results, although extreme computational costs prevented us from detecting the final diffusion regime. Qualitatively, the reported intermediate diffusion regimes are generic for granular gases with any realistic dependence of the restitution coefficient on the impact velocity.

Long-time tails and cage effect in driven granular fluids

We study the velocity autocorrelation function of a driven granular fluid in the stationary state in three dimensions. As the critical volume fraction of the glass transition in the corresponding elastic system is approached, we observe pronounced cage effects in the velocity autocorrelation function as well as a strong decrease of the diffusion constant, depending on the inelasticity. At moderate densities the velocity autocorrelation function is shown to decay algebraically in time, like t(-3/2), if momentum is conserved locally, and like t(-1), if momentum is not conserved by the driving. A simple scaling argument supports the observed long-time tails.

Long-time tails in freely cooling granular gases

The long-time behavior of the current autocorrelation functions for the velocity, the shear stress, and the heat flux is investigated in freely cooling granular gases. It is found that the correlation functions for the velocity and the shear stress have the long-time tails obeying tau(-d/2), while the correlation function for heat flux decays as tau(-(d+2)/2) exp(-zeta*tau) with the dimensionless cooling rate zeta*, the spatial dimension d, and the scaled time tau in terms of the collision frequency. The result of our numerical simulation of the freely cooling granular gases is consistent with the theoretical prediction.