The 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, 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.

16 pages, 9 figures

References in corpus (29)

• Jamming at Zero Temperature and Zero Applied Stress: the Epitome of Disorder
• Jamming, Force Chains and Fragile Matter
• Supercooled Liquids for Pedestrians
• Fluctuation-Dissipation: Response Theory in Statistical Physics
• Theory of nonlinear rheology and yielding of dense colloidal suspensions
• Dynamical density functional theory for interacting Brownian particles: stochastic or deterministic?
• How does the relaxation of a supercooled liquid depend on its microscopic dynamics?
• Crystallization of hard-sphere glasses
• Stationary state volume fluctuations in a granular medium
• Forced motion of a probe particle near the colloidal glass transition
• Randomly Driven Granular Fluids: large scale structure
• Caging dynamics in a granular fluid
• Subdiffusion and cage effect in a sheared granular material
• A mode coupling theory for Brownian particles in homogeneous steady shear flow
• Randomly Driven Granular Fluids: collisional statistics and short scale structure
• Active and Nonlinear Microrheology in Dense Colloidal Suspensions
• Forcing and Velocity Correlations in a Vibrated Granular Monolayer
• Approach to jamming in an air-fluidized granular bed
• Creep motion of an intruder within a granular glass close to jamming
• Experimental investigation of the freely cooling granular gas
• Dynamic Glass Transition in Two Dimensions
• Velocity Distributions of Granular Gases with Drag and with Long-Range Interactions
• Glass Transition for Driven Granular Fluids
• Velocity Fluctuations in Electrostatically Driven Granular Media
• Logarithmic Relaxation in a Colloidal System
• Signatures of glass formation in a fluidized bed of hard spheres
• The partition of energy for air-fluidized grains
• Partitioning of energy in highly polydisperse granular gases
• Single-Particle Dynamics in Dense Granular Fluids under Driving

Cited by in corpus (21)

• Mode-Coupling Theory of the Glass Transition: A Primer
• Nonequilibrium glassy dynamics of self-propelled hard disks
• Coarse-Grained Modelling Out of Equilibrium
• Active glasses
• Active Microrheology of Driven Granular Particles
• Divergence of Viscosity in Jammed Granular Materials: A Theoretical Approach
• Strong Dynamical Heterogeneity and Universal Scaling in Driven Granular Fluids
• Rheology of inelastic hard spheres at finite density and shear rate
• Slow time scales in a dense vibrofluidized granular material
• Integration through transients approach to the $\mu (\mathcal{I})$ rheology
• Comments on the validity of the non-stationary Generalized Langevin Equation as a coarse-grained evolution equation for microscopic stochastic dynamics
• Integration through transients for inelastic hard sphere fluids
• Rheology of granular liquids in extensional flows: Beyond the $\mu (\mathcal{I})$-law
• Scaling equations for mode-coupling theories with multiple decay channels
• Glassy Dynamics of Brownian Particles with Velocity-Dependent Friction
• Dynamic properties of quasi-confined colloidal hard-sphere liquids near the glass transition
• A classical long-time tail in a driven granular fluid
• Slow and Long-ranged Dynamical Heterogeneities in Dissipative Fluids
• Tagged-particle motion in quasi-confined colloidal hard-sphere liquids
• Kinetic theory for strong uniform shear flow of granular media at high density
• How non-equilibrium correlations in active matter reveal the topological crossover in glasses