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Lattice models for granular-like velocity fields: finite-size effects ; Manacorda, Alessandro ; et al in Journal of Statistical Mechanics: Theory and Experiment (2016) Long-range spatial correlations in the velocity and energy fields of a granular fluid are discussed in the framework of a 1d lattice model. The dynamics of the velocity field occurs through nearest ... [more ▼] Long-range spatial correlations in the velocity and energy fields of a granular fluid are discussed in the framework of a 1d lattice model. The dynamics of the velocity field occurs through nearest-neighbour inelastic collisions that conserve momentum but dissipate energy. A set of equations for the fluctuating hydrodynamics of the velocity and energy mesoscopic fields give a first approximation for (i) the velocity structure factor and (ii) the finite-size correction to the Haff law, both in the homogeneous cooling regime. At a more refined level, we have derived the equations for the two-site velocity correlations and the total energy fluctuations. First, we seek a perturbative solution thereof, in powers of the inverse of system size. On the one hand, when scaled with the granular temperature, the velocity correlations tend to a stationary value in the long time limit. On the other hand, the scaled standard deviation of the total energy diverges, that is, the system shows multiscaling. Second, we find an exact solution for the velocity correlations in terms of the spectrum of eigenvalues of a certain matrix. The results of numerical simulations of the microscopic model confirm our theoretical results, including the above described multiscaling phenomenon. [less ▲] Detailed reference viewed: 23 (0 UL)Lattice models for granular-like velocity fields: hydrodynamic description Manacorda, Alessandro ; ; et al in Journal of Statistical Physics (2016) A recently introduced model describing—on a 1d lattice—the velocity field of a granular fluid is discussed in detail. The dynamics of the velocity field occurs through next-neighbours inelastic collisions ... [more ▼] A recently introduced model describing—on a 1d lattice—the velocity field of a granular fluid is discussed in detail. The dynamics of the velocity field occurs through next-neighbours inelastic collisions which conserve momentum but dissipate energy. The dynamics is described through the corresponding Master Equation for the time evolution of the probability distribution. In the continuum limit, equations for the average velocity and temperature fields with fluctuating currents are derived, which are analogous to hydrodynamic equations of granular fluids when restricted to the shear modes. Therefore, the homogeneous cooling state, with its linear instability, and other relevant regimes such as the uniform shear flow and the Couette flow states are described. The evolution in time and space of the single particle probability distribution, in all those regimes, is also discussed, showing that the local equilibrium is not valid in general. The noise for the momentum and energy currents, which are correlated, are white and Gaussian. The same is true for the noise of the energy sink, which is usually negligible [less ▲] Detailed reference viewed: 25 (0 UL)Fluctuating hydrodynamics and mesoscopic effects of spatial correlations in dissipative systems with conserved momentum ; Manacorda, Alessandro ; et al in New Journal of Physics (2015) We introduce a model described in terms of a scalar velocity field on a 1D lattice, evolving through collisions that conserve momentum but do not conserve energy. Such a system possesses some of the main ... [more ▼] We introduce a model described in terms of a scalar velocity field on a 1D lattice, evolving through collisions that conserve momentum but do not conserve energy. Such a system possesses some of the main ingredients of fluidized granular media and naturally models them. We deduce non-linear fluctuating hydrodynamics equations for the macroscopic velocity and temperature fields, which replicate the hydrodynamics of shear modes in a granular fluid. Moreover, this Landau-like fluctuating hydrodynamics predicts an essential part of the peculiar behaviour of granular fluids, like the instability of homogeneous cooling state at large size or inelasticity. We also compute the exact shape of long range spatial correlations which, even far from the instability, have the physical consequence of noticeably modifying the cooling rate. This effect, which stems from momentum conservation, has not been previously reported in the realm of granular fluids. [less ▲] Detailed reference viewed: 33 (0 UL) |
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