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}.