Close-packed floating clusters: Granular hydrodynamics beyond the freezing point? - Meerson, Baruch; Pöschel, Thorsten; Bromberg, Yaron (Physical Review Letters, 2003)
As the kinetic equations become invalid, the constitutive relations (CRs), necessary for the closure of hydrodynamics, are not derivable from first-principles anymore. An ensemble of monodisperse, nearly elastic hard spheres in such conditions that the standard Navier-Stokes granular hydrodynamics (NSGH) breaks down becuase of large densities, not large inelasticity. This paper aims to check whether a variant of NSGH can still be used in an extreme case whether a variant of NSGH can still be used in an extreme case when the packing fraction is close to the maximum possible value, corresponding to hexagonal packing of spheres.