Slow and long-ranged dynamical heterogeneities in dissipative fluids. Issue 24 (27th May 2016) - Avila, Karina E.; Castillo, Horacio E.; Vollmayr-Lee, Katharina; Zippelius, Annette
Abstract : A two-dimensional bidisperse granular fluid is shown to exhibit pronounced long-ranged dynamical heterogeneities as dynamical arrest is approached. Abstract : A two-dimensional bidisperse granular fluid is shown to exhibit pronounced long-ranged dynamical heterogeneities as dynamical arrest is approached. Here we focus on the most direct approach to study these heterogeneities: we identify clusters of slow particles and determine their size, N c, and their radius of gyration, R G . We show that, providing direct evidence that the most immobile particles arrange in fractal objects with a fractal dimension, d f, that is observed to increase with packing fraction ϕ . The cluster size distribution obeys scaling, approaching an algebraic decay in the limit of structural arrest, i.e., ϕ → ϕ c . Alternatively, dynamical heterogeneities are analyzed via the four-point structure factor S 4 ( q, t ) and the dynamical susceptibility χ 4 ( t ). S 4 ( q, t ) is shown to obey scaling in the full range of packing fractions, 0.6 ≤ ϕ ≤ 0.805, and to become increasingly long-ranged as ϕ → ϕ c . Finite size scaling of χ 4 ( t ) provides a consistency check for the previously analyzed divergences of χ 4 ( t ) ∝ ( ϕ − ϕ c ) − γ χ and the correlation length ξ ∝ ( ϕ − ϕ c ) − γ ξ . We check the robustness of our results with respect to our definition of mobility. The divergences and the scaling for ϕ → ϕ c suggest a non-equilibrium glass transition which seems qualitatively independent of the coefficient of restitution.