Universality of Jamming Criticality in Overdamped Shear-Driven Frictionless Disks

We investigate the criticality of the jamming transition for overdamped shear-driven frictionless disks in two dimensions for two different models of energy dissipation: (i) Durian's bubble model with dissipation proportional to the velocity difference of particles in contact, and (ii) Durian's "mean-field" approximation to (i), with dissipation due to the velocity difference between the particle and the average uniform shear flow velocity. By considering the finite-size behavior of pressure, the pressure analog of viscosity, and the macroscopic friction sigma/p, we argue that these two models share the same critical behavior.