Jamming transition as probed by quasistatic shear flow.

We study the rheology of amorphous packings of soft, frictionless particles close to jamming. Implementing a quasistatic simulation method we generate a well-defined ensemble of states that directly samples the system at its yield stress. A continuous jamming transition from a freely flowing state to a yield-stress situation takes place at a well-defined packing fraction, where the scaling laws characteristic of isostatic solids are observed. We propose that long-range correlations observed below the transition are dominated by this isostatic point, while those that are observed above the transition are characteristic of dense, disordered elastic media.