Long-range Correlation in Sheared Granular Fluids
نویسندگان
چکیده
The time and the spatial correlations play important roles in non-equilibrium statistical physics [1-16]. The behaviors of the correlation functions in ordinary fluids are well understood. It is known that there exist long-time tails in the time correlation functions in fluids at equilibrium [1, 2, 3, 4]. In addition, long-range correlations exist in the spatial correlation functions in non-equilibrium ordinary fluids [5, 6, 7, 8]. On the other hand, interest in the correlations of granular fluids is rapidly growing. In the case of the freely cooling state, it is confirmed that long-time tails for the time-correlation of the velocity and the shear stress exist but the time-correlation function for the heat flux decays exponentially [10]. In addition, the spatial correlation functions are analytically calculated by using fluctuating hydrodynamics and the theoretical results are verified by numerical simulations [11]. See also the studies on the long-time tails in granular flows [12, 13]. In sheared granular fluids, there are some studies on time correlations, but the situation is still confusing [14, 15, 16]. Indeed, Kumaran predicted that the correlation function satisfies t−3d/2 with the spatial dimension d [14], while we obtained crossover from t−d/2 to t−(d+2)/2 for the velocity auto-correlation function of nearly elastic granular gases [15]. However, there is no corresponding theoretical or numerical argument on the spatial correlation functions in sheared granular fluids. In this paper, thus, we investigate the spatial correlation functions in sheared granular fluids. In section 2.1, we will explain the set up. In section 2.2, we will present the analytic results for the spatial correlation of the momentum density. In section 2.3, the validity of the analytic results will be tested by our numerical simulation. Finally, we will discuss and conclude our results in section 3.
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