Slow dynamics and precursors of the glass transition in granular fluids

Gholami, Irash; Fiege, Andrea; Zippelius, Annette

doi:10.1103/physreve.84.031305

Cited by 14 publications

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References 34 publications

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“…The system presented here is the same as the one in Ref. [22], where additional simulation details can be found.In this work, we analyze simulations for ε = 0.90 with packing fractions 0.6 ≤ φ ≤ 0.805, and for ε = 0.70, 0.80, 1.00 with packing fractions 0.72 ≤ φ ≤ 0.79. The system contains N tot = 4, 000, 000 particles for 0.60 ≤ φ ≤ 0.78 and N tot = 360, 000 particles for 0.79 ≤ φ ≤ 0.805.…”

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Strong Dynamical Heterogeneity and Universal Scaling in Driven Granular Fluids

et al. 2014

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Large scale simulations of two-dimensional bidisperse granular fluids allow us to determine spatial correlations of slow particles via the four-point structure factor S 4 (q,t). Both cases, elastic (ε = 1) as well as 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: S 4 (q,t)/χ 4 (t) = s(qξ (t)). Both the dynamic susceptibility, χ 4 (τ α ), as well as the dynamic correlation length, ξ (τ α ), evaluated at the α relaxation time, τ α , can be fitted to a power law divergence at a critical packing fraction. The measured ξ (τ α ) widely exceeds the largest one previously observed for hard sphere 3d fluids. The number of particles in a slow cluster and the correlation length are related by a robust power law, χ 4 (τ α ) ≈ ξ d−p (τ α ), with an exponent d − p ≈ 1.6. This scaling is remarkably independent of ε, even though the strength of the dynamical heterogeneity increases dramatically as ε grows.Viscous liquids, colloidal suspensions, and granular fluids are all capable of undergoing dynamical arrest, either by reducing the temperature in the case of viscous liquids, or by increasing the density in the cases of colloidal suspensions and of granular systems [1][2][3][4]. As the dynamical arrest is approached, not only does the dynamics become dramatically slower, but it becomes increasingly heterogeneous [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21]. One of the most common ways to characterize the heterogeneity in the dynamics is to probe its fluctuations [4]. Since probing the dynamics requires observing the system at two times, probing the spatial fluctuations in the dynamics naturally leads to defining quantities that correlate the changes in the state of the system between two times, at two spatial points, i.e. four-point functions. Those quantities include the dynamic susceptibility χ 4 (t), which gives a spatially integrated measurement of the total fluctuations, and the four point structure factor S 4 (q,t), which is the Fourier transform of the spatial correlation function describing the local fluctuations in the dynamics [4,12,15]. From the small wave-vector behavior of S 4 (q,t), a correlation length ξ (t) can be extracted, and it has been found in simulations of viscous liquids and dense colloidal suspensions that this correlation length grows as dynamical arrest is approached [4,12,15,16]. For granular matter, on the other hand, the jamming transition has been analyzed extensively, but studies on dynamic heterogeneity (DH) are few. Two experimental groups have investigated driven 2d granular beds in the context of DH. These studies are restricted to small systems of order a few thousand particles [13,14,[17][18][19][20][21]. χ 4 (t) has been measured, but spatial correlations have not been investigated systematically due to small system size. Instead, compact regions of correlated particles are usually assumed, χ 4 (t) ∼ ξ d (t), thereby determining a correlation len...

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“…The system presented here is the same as the one in Ref. [22], where additional simulation details can be found. sub-boxes of equal areas L 2 .…”

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Strong Dynamical Heterogeneity and Universal Scaling in Driven Granular Fluids

et al. 2014

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“…This is the same system as the one presented in Ref. 13 , which can also be consulted for additional details of the simulation.…”

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“…The driving frequency is chosen to be equal to the Enskog collision frequency, ω coll = 2.59φ G c (1/π), where G c is the pair correlation at contact (for details see Refs. 13,18 ). All results shown in this paper are presented in reduced units, where the length unit corresponds to r 1 and the mass unit correspond to m 1 .…”

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confidence: 99%

“…Some of the simulations were performed on a system containing N tot = 4, 000, 000 particles, for the packing fractions φ = 0.60, 0.65, 0.70, 0.72, 0.74, 0.76 and 0.78, which were also used in Ref. 13 in a different analysis, and N tot = 360, 000 for the higher packing fractions φ = 0.805, 0.80, 0.795, 0.79, 0.785 and 0.77. We performed simulations for all packing fractions mentioned above for the coefficient of restitution ε = 0.90.…”

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Slow and long-ranged dynamical heterogeneities in dissipative fluids

et al. 2016

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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.

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Slow dynamics and precursors of the glass transition in granular fluids

Cited by 14 publications

References 34 publications

Strong Dynamical Heterogeneity and Universal Scaling in Driven Granular Fluids

Strong Dynamical Heterogeneity and Universal Scaling in Driven Granular Fluids

Slow and long-ranged dynamical heterogeneities in dissipative fluids

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