Chains of Viscoelastic Spheres

Given a chain of viscoelastic spheres with fixed masses of the first and last particles. We raise the question: How to chose the masses of the other particles of the chain to assure maximal energy transfer? The results are compared with a chain of particles for which a constant coefficient of restitution is assumed. Our simple example shows that the assumption of viscoelastic particle properties has not only important consequences for very large systems (see [1]) but leads also to qualitative changes in small systems as compared with particles interacting via a constant restitution coefficient.Comment: 11 pages, 6 figure

Impact of high-energy tails on granular gas properties

The velocity distribution function of granular gases in the homogeneous cooling state as well as some heated granular gases decays for large velocities as $f\propto\exp(- {\rm const.} v)$. That is, its high-energy tail is overpopulated as compared with the Maxwell distribution. At the present time, there is no theory to describe the influence of the tail on the kinetic characteristics of granular gases. We develop an approach to quantify the overpopulated tail and analyze its impact on granular gas properties, in particular on the cooling coefficient. We observe and explain anomalously slow relaxation of the velocity distribution function to its steady state.Comment: 5 pages, 5 figure

Collision of Viscoelastic Spheres: Compact Expressions for the Coefficient of Normal Restitution

The coefficient of restitution of colliding viscoelastic spheres is analytically known as a complete series expansion in terms of the impact velocity where all (infinitely many) coefficients are known. While beeing analytically exact, this result is not suitable for applications in efficient event-driven Molecular Dynamics (eMD) or Monte Carlo (MC) simulations. Based on the analytic result, here we derive expressions for the coefficient of restitution which allow for an application in efficient eMD and MC simulations of granular Systems.Comment: 4 pages, 4 figure

Third and fourth degree collisional moments for inelastic Maxwell models

The third and fourth degree collisional moments for $d$-dimensional inelastic Maxwell models are exactly evaluated in terms of the velocity moments, with explicit expressions for the associated eigenvalues and cross coefficients as functions of the coefficient of normal restitution. The results are applied to the analysis of the time evolution of the moments (scaled with the thermal speed) in the free cooling problem. It is observed that the characteristic relaxation time toward the homogeneous cooling state decreases as the anisotropy of the corresponding moment increases. In particular, in contrast to what happens in the one-dimensional case, all the anisotropic moments of degree equal to or less than four vanish in the homogeneous cooling state for $d\geq 2$.Comment: 15 pages, 3 figures; v2: addition of two new reference

Granular mixtures modeled as elastic hard spheres subject to a drag force

Granular gaseous mixtures under rapid flow conditions are usually modeled by a multicomponent system of smooth inelastic hard spheres with constant coefficients of normal restitution. In the low density regime an adequate framework is provided by the set of coupled inelastic Boltzmann equations. Due to the intricacy of the inelastic Boltzmann collision operator, in this paper we propose a simpler model of elastic hard spheres subject to the action of an effective drag force, which mimics the effect of dissipation present in the original granular gas. The Navier--Stokes transport coefficients for a binary mixture are obtained from the model by application of the Chapman--Enskog method. The three coefficients associated with the mass flux are the same as those obtained from the inelastic Boltzmann equation, while the remaining four transport coefficients show a general good agreement, especially in the case of the thermal conductivity. Finally, the approximate decomposition of the inelastic Boltzmann collision operator is exploited to construct a model kinetic equation for granular mixtures as a direct extension of a known kinetic model for elastic collisions.Comment: The title has been changed, 4 figures, and to be published in Phys. Rev.

Rolling friction of a hard cylinder on a viscous plane

The resistance against rolling of a rigid cylinder on a flat viscous surface is investigated. We found that the rolling-friction coefficient reveals strongly non-linear dependence on the cylinder's velocity. For low velocity the rolling-friction coefficient rises with velocity due to increasing deformation rate of the surface. For larger velocity, however, it decreases with velocity according to decreasing contact area and deformation of the surface.Comment: 7 pages, 3 figure

Peculiarity of the Coulombic criticality ?

International audienceWe study the Coulombic criticality of ionic fluids within the restricted primitive model (RPM). We indicate that for the RPM, analysed in terms of the field of charge density, the corresponding Landau-Ginzburg-Wilson effective Hamiltonian has a negative $\varphi ^{4}$-coefficient. In that case, solving the ``exact'' renormalization group equation in the local potential approximation, we show that close initial Hamiltonians may lead either to a first order transition or to an Ising-like critical behavior, the partition being formed by the tri-critical surface. This situation apparently illustrates the theoretical wavering encountered in the literature concerning the nature of the Coulombic criticality. Nevertheless, it is most probable that, in terms of the field considered, the model does not display any criticality

Phase separation of a driven granular gas in annular geometry

This work investigates phase separation of a monodisperse gas of inelastically colliding hard disks confined in a two-dimensional annulus, the inner circle of which represents a "thermal wall". When described by granular hydrodynamic equations, the basic steady state of this system is an azimuthally symmetric state of increased particle density at the exterior circle of the annulus. When the inelastic energy loss is sufficiently large, hydrodynamics predicts spontaneous symmetry breaking of the annular state, analogous to the van der Waals-like phase separation phenomenon previously found in a driven granular gas in rectangular geometry. At a fixed aspect ratio of the annulus, the phase separation involves a "spinodal interval" of particle area fractions, where the gas has negative compressibility in the azimuthal direction. The heat conduction in the azimuthal direction tends to suppress the instability, as corroborated by a marginal stability analysis of the basic steady state with respect to small perturbations. To test and complement our theoretical predictions we performed event-driven molecular dynamics (MD) simulations of this system. We clearly identify the transition to phase separated states in the MD simulations, despite large fluctuations present, by measuring the probability distribution of the amplitude of the fundamental Fourier mode of the azimuthal spectrum of the particle density. We find that the instability region, predicted from hydrodynamics, is always located within the phase separation region observed in the MD simulations. This implies the presence of a binodal (coexistence) region, where the annular state is metastable. The phase separation persists when the driving and elastic walls are interchanged, and also when the elastic wall is replaced by weakly inelastic one.Comment: 9 pages, 10 figures, to be published in PR