Glassiness, Rigidity and Jamming of Frictionless Soft Core Disks

The jamming of frictionless bi-disperse soft core disks is considered, using a variety of different protocols to produce the jammed state. We find, consistent with earlier works, that cooling and compression can lead to a broad range of jamming packing fractions $\phi_J$, depending on cooling or compression rate and on initial configuration. Such $\phi_J$ show no clear upper bound as the cooling or compression rate decreases. In contrast, we show that shearing leads to a jamming transition to a disordered solid, with a well-defined, non-trivial, value of $\phi_J$ as the shearing rate vanishes. We show that shearing breaks up the particle clustering (the precursor to phase separation) that can lead to increasing values of $\phi_J$ under slow cooling or compression, and argue that the process of shearing creates a well-defined ensemble that is independent of the starting configuration.