Hydrodynamic correlation functions of a driven granular fluid in steady state

We study a homogeneously driven granular fluid of hard spheres at intermediate volume fractions and focus on time-delayed correlation functions in the stationary state. Inelastic collisions are modeled by incomplete normal restitution, allowing for efficient simulations with an event-driven algorithm. The incoherent scattering function Fincoh(q,t ) is seen to follow time-density superposition with a relaxation time that increases significantly as the volume fraction increases. The statistics of particle displacements is approximately Gaussian. For the coherent scattering function S(q,ω), we compare our results to the predictions of generalized fluctuating hydrodynamics, which takes into account that temperature fluctuations decay either diffusively or with a finite relaxation rate, depending on wave number and inelasticity. For sufficiently small wave number q we observe sound waves in the coherent scattering function S(q,ω) and the longitudinal current correlation function Cl(q,ω). We determine the speed of sound and the transport coefficients and compare them to the results of kinetic theory.

Mass Transport Perspective on an Accelerated Exclusion Process: Analysis of Augmented Current and Unit-Velocity Phases

In an accelerated exclusion process (AEP), each particle can "hop" to its adjacent site if empty as well as "kick" the frontmost particle when joining a cluster of size ℓ⩽ℓ_{max}. With various choices of the interaction range, ℓ_{max}, we find that the steady state of AEP can be found in a homogeneous phase with augmented currents (AC) or a segregated phase with holes moving at unit velocity (UV). Here we present a detailed study on the emergence of the novel phases, from two perspectives: the AEP and a mass transport process (MTP). In the latter picture, the system in the UV phase is composed of a condensate in coexistence with a fluid, while the transition from AC to UV can be regarded as condensation. Using Monte Carlo simulations, exact results for special cases, and analytic methods in a mean field approach (within the MTP), we focus on steady state currents and cluster sizes. Excellent agreement between data and theory is found, providing an insightful picture for understanding this model system.