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Simulation of pattern dynamics of cohesive granular particles under a plane shear

We have performed three-dimensional molecular dynamics simulation of cohesive granular particles under a plane shear. From the simulation, we found the existence of three distinct phases in steady states: (I) a uniform shear phase, (II) a coexistent phase of a shear band and a gas region and (III) a crystal phase. We also found that the critical line between (II) and (III) is approximately represented by $ζ\propto \exp(β\dotγL_y)$, where $ζ$, $β$, $\dotγ$, $L_y$ are the dissipation rate, an unimportant constant, the shear rate and the system size of the velocity gradient direction, respectively.