Slow and long-ranged dynamical heterogeneities in dissipative fluids

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 N c ∝ R d f G , 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.

Shear-Transformation Zone Activation during Loading and Unloading in Nanoindentation of Metallic Glasses

“…The pop-ins are seen as serrated activity in the load-depth curve and have been studied in the perspective of a stick-slip mechanism or avalanche dynamics [19,20]. Also for other materials, avalanche statistics have been important for understanding how local regions communicate with each other under different stimuli [21,22,23]. Most recently, the transition from STZs to shear bands has been studied in the context of directed percolation [12,24].…”