Randomly driven granular fluids: Large-scale structure (original) (raw)

Long-range interactions in randomly driven granular fluids

Physical Review E, 2013

We study the long-range spatial correlations in the nonequilibrium steady state of a randomly driven granular fluid with the emphasis on obtaining the explicit form of the static structure factors. The presence of immobile particles immersed in such a fluidized bed of fine particles leads to the confinement of the fluctuation spectrum of the hydrodynamic fields, which results in effective longrange interactions between the intruders. The analytical predictions are in agreement with the results of discrete element method simulations. By changing the shape and orientation of the intruders, we address how the effective force is affected by small changes in the boundary conditions.

Randomly driven granular fluids: Collisional statistics and short scale structure

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 2002

We present a molecular dynamics and kinetic theory study of granular material, modeled by inelastic hard disks, fluidized by a random driving force. The focus is on collisional averages and short distance correlations in the non-equilibrium steady state, in order to analyze in a quantitative manner the breakdown of molecular chaos, i.e. factorization of the two-particle distribution function, f (2) (x1, x2) ≃ χf ( 1)(x1)f (1) (x2) in a product of single particle ones, where xi = {ri, vi} with i = 1, 2 and χ represents the position correlation. We have found that molecular chaos is only violated in a small region of the two-particle phase space {x1, x2}, where there is a predominance of grazing collisions. The size of this singular region grows with increasing inelasticity. The existence of particle-and noise-induced recollisions magnifies the departure from mean field behavior. The implications of this breakdown in several physical quantities are explored. * Unité Mixte de Recherche UMR 8627 du CNRS

Fluctuating hydrodynamics and correlation lengths in a driven granular fluid

Journal of Statistical Mechanics: Theory and Experiment, 2011

Static and dynamical structure factors for shear and longitudinal modes of the velocity and density fields are computed for a granular system fluidized by a stochastic bath with friction. Analytical expressions are obtained through fluctuating hydrodynamics and are successfully compared with numerical simulations up to a volume fraction ∼ 50%. Hydrodynamic noise is the sum of external noise due to the bath and internal one due to collisions. Only the latter is assumed to satisfy the fluctuation-dissipation relation with the average granular temperature.

Mesoscopic Theory of Granular Fluids

Physical Review Letters, 1997

to be published in Physical Review Letters) Using fluctuating hydrodynamics we describe the slow build-up of long range spatial correlations in a freely evolving fluid of inelastic hard spheres. In the incompressible limit, the behavior of spatial velocity correlations (including r −d -behavior) is governed by vorticity fluctuations only and agrees well with two-dimensional simulations up to 50 to 100 collisions per particle. The incompressibility assumption breaks down beyond a distance that diverges in the elastic limit.

Strong Dynamical Heterogeneity and Universal Scaling in Driven Granular Fluids

Physical Review Letters, 2014

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.

Statistical mechanics of fluidized granular media: Short-range velocity correlations

Physical Review E, 2001

A statistical mechanical study of fluidized granular media is presented. Using a special energy injection mechanism, homogeneous fluidized stationary states are obtained. Molecular dynamics simulations and theoretical analysis of the inelastic hard-disk model show that there is a large asymmetry in the two-particle distribution function between pairs that approach and separate. Large velocity correlations appear in the postcollisional states due to the dissipative character of the collision rule. These correlations can be wellcharacterized by a state dependent pair correlation function at contact. It is also found that velocity correlations are present for pairs that are about to collide. Particles arrive at collisions with a higher probability that their velocities are parallel rather than antiparallel. These dynamical correlations lead to a decrease of the pressure and of the collision frequency as compared to their Enskog values. A phenomenological modified equation of state is presented.

Non-equilibrium length in granular fluids: From experiment to fluctuating hydrodynamics

EPL (Europhysics Letters), 2011

Velocity correlations in a quasi-2D driven granular fluid are studied in experiments and numerical simulations. The transverse velocity structure factor reveals two well defined energy scales, associated with the external "bath temperature" T b and with the internal granular one, Tg < T b , relevant at large and small wavelengths respectively. Experimental and numerical data are discussed within a fluctuating hydrodynamics model, which allows one to define and measure a non-equilibrium coherence length, growing with density, that characterizes order in the velocity field.

Dynamics of a massive intruder in a homogeneously driven granular fluid

Granular Matter, 2012

A massive intruder in a homogeneously driven granular fluid, in dilute configurations, performs a memory-less Brownian motion with drag and temperature simply related to the average density and temperature of the fluid. At volume fraction ∼ 10 − 50% the intruder's velocity correlates with the local fluid velocity field: such situation is approximately described by a system of coupled linear Langevin equations equivalent to a generalized Brownian motion with memory. Here one may verify the breakdown of the Fluctuation-Dissipation relation and the presence of a net entropy flux -from the fluid to the intruder -whose fluctuations satisfy the Fluctuation Relation.

Fluid-like behavior of a one-dimensional granular gas

The Journal of Chemical Physics, 2004

We study the properties of a one-dimensional (1D) granular gas consisting of N hard rods on a line of length L (with periodic boundary conditions). The particles collide inelastically and are fluidized by a heat bath at temperature T b and viscosity γ. The analysis is supported by molecular dynamics simulations. The average properties of the system are first discussed, focusing on the relations between granular temperature T g = m v 2 , kinetic pressure and density ρ = N/L. Thereafter, we consider the fluctuations around the average behavior obtaining a slightly non-Gaussian behavior of the velocity distributions and a spatially correlated velocity field; the density field displays clustering: this is reflected in the structure factor which has a peak in the k ∼ 0 region suggesting an analogy between inelastic hard core interactions and an effective attractive potential. Finally, we study the transport properties, showing the typical sub-diffusive behavior of 1D stochastically driven systems, i.e. |x(t) − x(0)| 2 ∼ Dt 1/2 where D for the inelastic fluid is larger than the elastic case. This is directly related to the peak of the structure factor at small wave-vectors.