Glass transition in driven granular fluids: a mode-coupling approach

Abstract

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, ε, at a critical packing fraction φ(c)(ε) 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 nonuniversal with exponents depending on space dimension and degree of dissipation.