Lattice models for granular - like velocity fields : Hydrodynamic limit

A recently introduced model describing -on a 1d latticethe 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 can be described by a stochastic equation in full phase space, or through the corresponding Master Equation for the time evolution of the probability distribution. In the hydrodynamic limit, equations for the average velocity and temperature fields with fluctuating currents are derived, which are analogous to those 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 evoA. Manacorda Dipartimento di Fisica, Sapienza Università di Roma, p.le A. Moro 2, 00185 Roma, Italy E-mail: [email protected] C. A. Plata F́ısica Teórica, Universidad de Sevilla, Apartado de Correos 1065, E-41080 Seville, Spain E-mail: [email protected] A. Lasanta CNR-ISC and Dipartimento di Fisica, Sapienza Università di Roma, p.le A. Moro 2, 00185 Roma, Italy E-mail: [email protected] A. Puglisi CNR-ISC and Dipartimento di Fisica, Sapienza Università di Roma, p.le A. Moro 2, 00185 Roma, Italy E-mail: [email protected] A. Prados F́ısica Teórica, Universidad de Sevilla, Apartado de Correos 1065, E-41080 Seville, Spain E-mail: [email protected] ar X iv :1 60 1. 01 61 7v 1 [ co nd -m at .s of t] 7 J an 2 01 6 2 Alessandro Manacorda et al. lution 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.