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    Weakly nonlinear analysis of two dimensional sheared granular flow

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    Weakly nonlinear analysis of a two dimensional sheared granular flow is carried out under the Lees-Edwards boundary condition. We derive the time dependent Ginzburg-Landau (TDGL) equation of a disturbance amplitude starting from a set of granular hydrodynamic equations and discuss the bifurcation of the steady amplitude in the hydrodynamic limit.Comment: 24 pages, 6 figures. Section 3, 4 and 5 are changed. Figures 2-6 are update