Velocity Profiles in Repulsive Athermal Systems under Shear

We conduct molecular dynamics simulations of athermal systems undergoing boundary-driven planar shear flow in two and three spatial dimensions. We find that these systems possess nonlinear mean velocity profiles when the velocity $u$ of the shearing wall exceeds a critical value $u_c$. Above $u_c$, we also show that the packing fraction and mean-square velocity profiles become spatially dependent with dilation and enhanced velocity fluctuations near the moving boundary. In systems with overdamped dynamics, $u_c$ is only weakly dependent on packing fraction $\varphi$. However, in systems with underdamped dynamics, $u_c$ is set by the speed of shear waves in the material and tends to zero as $\varphi$ approaches ${\varphi }_c$, which is near random close packing at small damping. For underdamped systems with $\varphi <{\varphi }_c$, $u_c$ is zero; thus they possess nonlinear velocity profiles at any nonzero $u$.