Thermalization of an anisotropic granular particle

Interplay between polydispersity, inelasticity, and roughness in the freely cooling regime of hard-disk granular gases

A polydisperse granular gas made of inelastic and rough hard disks is considered. Focus is laid on the kinetic-theory derivation of the partial energy production rates and the total cooling rate as functions of the partial densities and temperatures (both translational and rotational) and of the parameters of the mixture (masses, diameters, moments of inertia, and mutual coefficients of normal and tangential restitution). The results are applied to the homogeneous cooling state of the system and the associated nonequipartition of energy among the different components and degrees of freedom. It is found that disks typically present a stronger rotational-translational nonequipartition but a weaker component-component nonequipartition than spheres. A noteworthy "mimicry" effect is unveiled, according to which a polydisperse gas of disks having common values of the coefficient of restitution and of the reduced moment of inertia can be made indistinguishable from a monodisperse gas in what concerns the degree of rotational-translational energy nonequipartition. This effect requires the mass of a disk of component i to be approximately proportional to 2σ_{i}+〈σ〉, where σ_{i} is the diameter of the disk and 〈σ〉 is the mean diameter.

Energy nonequipartition in gas mixtures of inelastic rough hard spheres: The tracer limit

The dynamical properties of a tracer or impurity particle immersed in a host gas of inelastic and rough hard spheres in the homogeneous cooling state is studied. Specifically, the breakdown of energy equipartition as characterized by the tracer/host ratios of translational and rotational temperatures is analyzed by exploring a wide spectrum of values of the control parameters of the system (masses, moments of inertia, sizes, and coefficients of restitution). Three complementary approaches are considered. On the theoretical side, the Boltzmann and Boltzmann-Lorentz equations (both assuming the molecular chaos ansatz) are solved by means of a multitemperature Maxwellian approximation for the velocity distribution functions. This allows us to obtain explicit analytical expressions for the temperature ratios. On the computational side, two different techniques are used. First, the kinetic equations are numerically solved by the direct simulation Monte Carlo (DSMC) method. Second, molecular dynamics simulations for dilute gases are performed. Comparison between theory and simulations shows a general good agreement. This means that (i) the impact of the molecular chaos ansatz on the temperature ratios is not significant (except at high inelasticities and/or big impurities) and (ii) the simple Maxwellian approximation yields quite reliable predictions.

Observable-dependence of the effective temperature in off-equilibrium diatomic molecular liquids

We discuss the observable-dependence of the effective temperature Teff, defined via the fluctuation-dissipation relation, of an out-of-equilibrium system composed by homonuclear dumbbell molecules. Teff is calculated by evaluating the fluctuation and the response for two observables associated, respectively, to translational and to rotational degrees of freedom, following a sudden temperature quench. We repeat our calculations for different dumbbell elongations ζ. At high elongations (ζ > 0.4), we find the same Teff for the two observables. At low elongations (ζ ⩽ 0.4), only for very deep quenches Teff coincides. The observable-dependence of Teff for low elongations and shallow quenches stresses the importance of a strong coupling between orientational and translational variables for a consistent definition of the effective temperature in glassy systems.

Analysis of a class of granular motors in the brownian limit

We analyze the dynamics of heterogeneous granular particles immersed in a bath of thermalized particles, which are candidates for granular motors, with a mechanical approach. We first apply the method to the previously introduced asymmetric piston and show that it gives the exact drift velocity in the brownian limit. We also obtain results for the efficiency of the motor and compare with numerical simulations. Finally, we introduce a chiral rotor model and discuss opportunities for observing a real granular motor.

Angular velocity distribution of a granular planar rotator in a thermalized bath

The kinetics of a granular planar rotator with a fixed center undergoing inelastic collisions with bath particles is analyzed both numerically and analytically by means of the Boltzmann equation. The angular velocity distribution evolves from quasi-Gaussian in the Brownian limit to an algebraic decay in the limit of an infinitely light particle. In addition, we compare this model to that of a planar rotator with a free center and discuss the prospects for experimental confirmation of these results.

Boltzmann equation for a granular capped rectangle in a thermalized bath of hard disks

By using the Boltzmann approach, we study the steady-state dynamics of a granular capped rectangle placed in a two-dimensional bath of thermalized hard disks. Hard core collisions are assumed elastic between disks and inelastic between the capped rectangle and the disks, with a normal coefficient of restitution alpha < 1. Assuming a Gaussian ansatz for the probability distribution functions, we obtain analytical expressions for the granular temperatures. We show the absence of equipartition and investigate both the role of the anisotropy of the capped rectangle and of the relative ratio of the bath particles to the linear sizes of the capped rectangle. In addition, we investigate a model of a capped rectangle with two normal coefficients of restitution for collisions along the straight and curved surfaces of the capped rectangle. In this case one observes equipartition for a nontrivial ratio of the normal coefficient of restitutions.