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 φ. However, in systems with underdamped dynamics, u_c is set by the speed of shear waves in the material and tends to zero as φ approaches φ_c, which is near random close packing at small damping. For underdamped systems with φ < φ_c, u_c is zero; thus they possess nonlinear velocity profiles at any nonzero u.