We study the velocity autocorrelation function (VACF) of a driven granular fluid in the stationary state in 3 dimensions (3d). As the critical volume fraction of the glass transition in the corresponding elastic system is approached, we observe pronounced cage effects in the VACF as well as a strong decrease of the diffusion constant depending on the inelasticity. At moderate densities the VACF is shown to decay algebraically in time, like t −3/2 , if momentum is conserved locally and like t −1 , if momentum is not conserved by the driving. A simple scaling argument supports the observed long time tails.PACS numbers: 45.70.-n, 51.20.+d, 47.10.-g Strongly agitated granular fluids have attracted a lot of attention in recent years [1]. Most of the theoretical work which is based on microscopic dynamics has been done for either rather dilute or weakly inelastic sytems, generalising kinetic theory to gases of inelastically colliding particles. The velocity autocorrelation function [2] as well as transport coefficients [3] have been calculated for the homogeneous cooling state, which has also been simulated for a wide range of inelasticities [4].Comparatively few studies have been performed on the stationary state of granular fluids in the moderate or high density regime. This is surprising, given the fact that the corresponding (elastic) molecular fluids have been studied in great detail [5] and revealed several interesting features already in the dynamics of a single tagged particle: backscattering as indicated by a negative velocity autocorrelation, long-time tails due to the coupling of the tagged particle's density to a shear flow and a glass transition at a volume fraction η ≈ 0.58 accompanied by a strong decrease of the diffusion constant as a precursor to structural arrest. It is our aim to understand which of these features pertain to an inelastic gas and how they are destroyed by increasingly more dissipative collisions. This applies in particular to the glass transition, which has been conjectured to be related to the jamming transition in granular matter [6].Several experimental groups have measured the VACF in dense granular flow [7][8][9][10][11][12].The VACF in the steady state of a 3d vibro-fluidized bed [8] was shown to exhibit strong backscattering effects. In 2d vibrated layers, high speed cameras have been used to measure the VACF. Even though long-time tails seem to be beyond the experimental resolution, these experiments give evidence for a nonexponential decay [11]. Caging effects have clearly been seen in air-fluidized beds [13] as well as in sheared granular materials [14]. In recent experiments [12] the development of a plateau in the mean square displacement has been observed, but may be related to crystallization as seen in monodisperse vibrated layers [11,12].Model-We investigate a system of monodisperse hard spheres of diameter a and mass m. The time evolution is governed by instantaneous inelastic two-particle collisions. Given the relative velocity g := v 1 −v 2 , the change of g in ...

We investigate the dynamics of an intruder pulled by a constant force in a dense two-dimensional granular fluid by means of event-driven molecular dynamics simulations. In a first step, we show how a propagating momentum front develops and compactifies the system when reflected by the boundaries. To be closer to recent experiments (Candelier and Dauchot in Phys Rev 81(1):011304, 2010; Phys Rev 103(12):128001, 2009), we then add a frictional force acting on each particle, proportional to the particle's velocity. We show how to implement frictional motion in an event-driven simulation. This allows us to carry out extensive numerical simulations aiming at the dependence of the intruder's velocity on packing fraction and pulling force. We identify a linear relation for small and a nonlinear regime for high pulling forces and investigate the dependence of these regimes on granular temperature.

We use event driven simulations to analyze glassy dynamics as a function of density and energy dissipation in a two-dimensional bidisperse granular fluid under stationary conditions. Clear signatures of a glass transition are identified, such as an increase of relaxation times over several orders of magnitude. As the inelasticity is increased, the glass transition is shifted to higher densities, and the precursors of the transition become less and less pronounced, in agreement with a recent mode-coupling theory. We analyze the long-time tails of the velocity autocorrelation and discuss its consequences for the nonexistence of the diffusion constant in two dimensions.

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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Large-scale simulations and analytical theory have been combined to obtain the nonequilibrium velocity distribution, f(v), of randomly accelerated particles in suspension. The simulations are based on an event-driven algorithm, generalized to include friction. They reveal strongly anomalous but largely universal distributions, which are independent of volume fraction and collision processes, which suggests a one-particle model should capture all the essential features. We have formulated this one-particle model and solved it analytically in the limit of strong damping, where we find that f(v) decays as 1/v for multiple decades, eventually crossing over to a Gaussian decay for the largest velocities. Many particle simulations and numerical solution of the one-particle model agree for all values of the damping.

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We suggest a simple model for the dynamics of granular particles in suspension which is suitable for an event driven algorithm, allowing to simulate N = O(10 6 ) particles or more. As a first application we consider a dense granular packing which is fluidized by an upward stream of liquid, i.e. a fluidized bed. In the stationary state, when all forces balance, we always observe a well defined interface whose width is approximately independent of packing fraction. We also study the dynamics of expansion and sedimentation after a sudden change in flow rate giving rise to a change in stationary packing fraction and determine the timescale to reach a stationary state.