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 $\zeta \propto \exp(\beta \dot\gamma L_y)$, where $\zeta$, $\beta$, $\dot\gamma$, $L_y$ are the dissipation rate, an unimportant constant, the shear rate and the system size of the velocity gradient direction, respectively.