Symmetry-breaking instability of a laterally uniform granular cluster (strip
state) in a prototypical driven granular gas is investigated. The system
consists of smooth hard disks in a two-dimensional box, colliding inelastically
with each other and driven, at zero gravity, by a "thermal" wall. The limit of
nearly elastic particle collisions is considered, and granular hydrodynamics
with the Jenkins-Richman constitutive relations is employed. The hydrodynamic
problem is completely described by two scaled parameters and the aspect ratio
of the box. Marginal stability analysis predicts a spontaneous symmetry
breaking instability of the strip state, similar to that predicted recently for
a different set of constitutive relations. If the system is big enough, the
marginal stability curve becomes independent of the details of the boundary
condition at the driving wall. In this regime, the density perturbation is
exponentially localized at the elastic wall opposite to the thermal wall. The
short- and long-wavelength asymptotics of the marginal stability curves are
obtained analytically in the dilute limit. The physics of the symmetry-breaking
instability is discussed.Comment: 11 pages, 14 figure
