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Abstract:
Large-scale simulations of two-dimensional bidisperse granular fluids allow us to determine spatial correlations of slow particles via the four-point structure factor S4(q,t). Both cases, elastic (ϵ=1) and inelastic (ϵ<1) collisions, are studied. As the fluid approaches structural arrest, i.e., for packing fractions in the range 0.6≤ϕ≤0.805, scaling is shown to hold: S4(q,t)/χ4(t)=s(qξ(t)). Both the dynamic susceptibility χ4(τα) and the dynamic correlation length ξ(τα) evaluated at the α relaxation time τα can be fitted to a power law divergence at a critical packing fraction. The measured ξ(τα) widely exceeds the largest one previously observed for three-dimensional (3d) hard sphere fluids. The number of particles in a slow cluster and the correlation length are related by a robust power law, χ4(τα)≈ξd−p(τα), with an exponent d−p≈1.6. This scaling is remarkably independent of ϵ, even though the strength of the dynamical heterogeneity at constant volume fraction depends strongly on ϵ.
