Glassiness, rigidity, and jamming of frictionless soft core disks

The jamming of bidisperse soft core disks is considered, using a variety of different protocols to produce the jammed state. In agreement with other works, we find that cooling and compression can lead to a broad range of jamming packing fractions ϕ{J}, depending on cooling rate and initial configuration; the larger the degree of big particle clustering in the initial configuration, the larger will be the value of ϕ{J}. In contrast, we find that shearing disrupts particle clustering, leading to a much narrower range of ϕ{J} as the shear strain rate varies. In the limit of vanishingly small shear strain rate, we find a unique nontrivial value for the jamming density that is independent of the initial system configuration. We conclude that shear driven jamming is a unique and well-defined critical point in the space of shear driven steady states. We clarify the relation between glassy behavior, rigidity, and jamming in such systems and relate our results to recent experiments.