Journal of Statistical Physics

, Volume 164, Issue 4, pp 810–841 | Cite as

Lattice Models for Granular-Like Velocity Fields: Hydrodynamic Description

  • Alessandro Manacorda
  • Carlos A. Plata
  • Antonio Lasanta
  • Andrea Puglisi
  • Antonio Prados
Article

Abstract

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.

Keywords

Granular fluids Hydrodynamics Momentum conservation 

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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Alessandro Manacorda
    • 1
  • Carlos A. Plata
    • 2
  • Antonio Lasanta
    • 3
  • Andrea Puglisi
    • 3
  • Antonio Prados
    • 2
  1. 1.Dipartimento di FisicaSapienza Università di RomaRomeItaly
  2. 2.Física TeóricaUniversidad de SevillaSevilleSpain
  3. 3.CNR-ISC and Dipartimento di FisicaSapienza Università di RomaRomeItaly

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