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Register a new userThe Glass Transition in Driven Granular Fluids: A Mode-Coupling Approach
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We consider the stationary state of a fluid comprised of inelastic hard spheres or disks under the influence of a random, momentum-conserving external force. Starting from the microscopic description of the dynamics, we derive a nonlinear equation of motion for the coherent scattering function in two and three space dimensions. A glass transition is observed for all coefficients of restitution, epsilon, at a critical packing fraction, phi_c(epsilon), below random close packing. The divergence of timescales at the glass-transition implies a dependence on compression rate upon further increase of the density - similar to the cooling rate dependence of a thermal glass. The critical dynamics for coherent motion as well as tagged particle dynamics is analyzed and shown to be non-universal with exponents depending on space dimension and degree of dissipation.
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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.
Understanding the physics of glass formation remains one of the major unsolved challenges of condensed matter science. As a material solidifies into a glass, it exhibits a spectacular slowdown of the dynamics upon cooling or compression, but at the same time undergoes only minute structural changes. Among the numerous theories put forward to rationalize this complex behavior, Mode-Coupling Theory (MCT) stands out as the only framework that provides a fully first-principles-based description of glass phenomenology. This review outlines the key physical ingredients of MCT, its predictions, successes, and failures, as well as recent improvements of the theory. We also discuss the extension and application of MCT to the emerging field of non-equilibrium active soft matter
The terminology granular matter refers to systems with a large number of hard objects (grains) of mesoscopic size ranging from millimeters to meters. Geological examples include desert sand and the rocks of a landslide. But the scope of such systems is much broader, including powders and snow, edible products such a seeds and salt, medical products like pills, and extraterrestrial systems such as the surface regolith of Mars and the rings of Saturn. The importance of a fundamental understanding for granular matter properties can hardly be overestimated. Practical issues of current concern range from disaster mitigation of avalanches and explosions of grain silos to immense economic consequences within the pharmaceutical industry. In addition, they are of academic and conceptual importance as well as examples of systems far from equilibrium. Under many conditions of interest, granular matter flows like a normal fluid. In the latter case such flows are accurately described by the equations of hydrodynamics. Attention is focused here on the possibility for a corresponding hydrodynamic description of granular flows. The tools of nonequilibrium statistical mechanics, developed over the past fifty years for fluids composed of atoms and molecules, are applied here to a system of grains for a fundamental approach to both qualitative questions and practical quantitative predictions. The nonlinear Navier-Stokes equations and expressions for the associated transport coefficients are obtained.
We use event driven simulations to analyze glassy dynamics as a function of density and energy dissipation in a two-dimensional bidisperse granular fluid under stationary conditions. Clear signatures of a glass transition are identified, such as an increase of relaxation times over several orders of magnitude. As the inelasticity is increased, the glass transition is shifted to higher densities and the precursors of the transition become less and less pronounced -- in agreement with a recent mode-coupling theory. We analyze the long-time tails of the velocity autocorrelation and discuss its consequences for the nonexistence of the diffusion constant in two dimensions.
We study the velocity autocorrelation function (VACF) of a driven granular fluid in the stationary state in 3 dimensions. As the critical volume fraction of the glass transition in the corresponding elastic system is approached, we observe pronounced cage effects in the VACF as well as a strong decrease of the diffusion constant. At moderate densities the VACF is shown to decay algebraically in time (t^{-3/2}) like in a molecular fluid, as long as the driving conserves momentum locally.
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