Critical Scaling and Aging in Cooling Systems Near the Jamming Transition

We conduct athermal simulations of freely cooling, viscous soft spheres around the jamming transition density phi(J) and find evidence for a growing length xi(t) that governs relaxation to mechanical equilibrium. xi(t) is manifest in both the velocity correlation function and the spatial correlations in a scalar measure of local force balance which we define. Data for different densities phi can be collapsed onto two master curves by scaling xi(t) and t by powers of |phi-phi(J)|, indicative of critical scaling. Furthermore, particle transport for phi >phi(J) exhibits aging and superdiffusion similar to a range of soft matter experiments, suggesting a common origin. Finally, we explain how xi(t) at late times maps onto known behavior away from phi(J).