No Arabic abstract
I derive a mode-coupling theory for the velocity autocorrelation function, psi(t), in a fluid of randomly driven inelastic hard spheres far from equilibrium. With this, I confirm a conjecture from simulations that the velocity autocorrelation function decays algebraically, psi(t) ~ t^{-3/2}, if momentum is conserved. I show that the slow decay is due to the coupling to transverse currents.
We perform three-dimensional simulations of a granular jet impact for both frictional and frictionless grains. Small shear stress observed in the experiment[X. Cheng et al., Phys. Rev. Lett. 99, 188001 (2007) ] is reproduced through our simulation. However, the fluid state after the impact is far from a perfect fluid, and thus, similarity between granular jets and quark gluon plasma is superficial, because the observed viscosity is finite and its value is consistent with the prediction of the kinetic theory.
Modeling collective motion in non-conservative systems, such as granular materials, is difficult since a general microscopic-to-macroscopic approach is not available: there is no Hamiltonian, no known stationary densities in phase space, not a known small set of relevant variables. Phenomenological coarse-grained models are a good alternative, provided that one has identified a few slow observables and collected a sufficient amount of data for their dynamics. Here we study the case of a vibrofluidized dense granular material. The experimental study of a tracer, dispersed into the media, showed the evidence of many time scales: fast ballistic, intermediate caged, slow superdiffusive, very slow diffusive. A numerical investigation has demonstrated that tracers superdiffusion is related to slow rotating drifts of the granular medium. Here we offer a deeper insight into the slow scales of the granular medium, and propose a new phenomenological model for such a secular dynamics. Based upon the model for the granular medium, we also introduce a model for the tracer (fast and slow) dynamics, which consists in a stochastic system of equations for three coupled variables, and is therefore more refined and successful than previous models.
An experimental study of a granular surface submitted to a circular fluid motion is presented. The appearance of an instability along the sand-water interface is observed beyond a critical radius $r_c$. This creates ripples with a spiral shape on the granular surface. A phase diagram of such patterns is constructed and discussed as a function of the rotation speed $omega$ of the flow and as a function of the height of water $h$ above the surface. The study of $r_c$ as a function of $h$, $omega$ and $r$ parameters is reported. Thereafter, $r_c$ is shown to depend on the rotation speed according to a power law. The ripple wavelength is found to decrease when the rotation speed increases and is proportional to the radial distance $r$. The azimuthal angle az of the spiral arms is studied. It is found that az scales with $homega r$. This lead to the conclusion that az depends on the fluid momentum. Comparison with experiments performed with fluids allows us to state that the spiral patterns are not the signature of an instability of the boundary layer.
We investigate the dynamics of a driven system of dissipative hard spheres in the framework of mode-coupling theory. The dissipation is modeled by normal restitution, and driving is applied to individual particles in the bulk. In such a system, a glass transition is predicted for a finite transition density. For increasing inelasticity, the transition shifts to higher densities. Despite the strong driving at high dissipation, the transition persists up to the limit of totally inelastic normal restitution.
We consider a velocity field with linear viscous interactions defined on a one dimensional lattice. Brownian baths with different parameters can be coupled to the boundary sites and to the bulk sites, determining different kinds of non-equilibrium steady states or free-cooling dynamics. Analytical results for spatial and temporal correlations are provided by analytical diagonalisation of the systems equations in the infinite size limit. We demonstrate that spatial correlations are scale-free and time-scales become exceedingly long when the system is driven only at the boundaries. On the contrary, in the case a bath is coupled to the bulk sites too, an exponential correlation decay is found with a finite characteristic length. This is also true in the free cooling regime, but in this case the correlation length grows diffusively in time. We discuss the crucial role of boundary driving for long-range correlations and slow time-scales, proposing an analogy between this simplified dynamical model and dense vibro-fluidized granular materials. Several generalizations and connections with the statistical physics of active matter are also suggested.