Jamming Transition in Soft Sphere Packings

At the jamming point φ_J ≈ 0.64 (random close packing), soft repulsive spheres transition from a flowing liquid to a rigid amorphous solid. Pressure P scales as (φ−φ_J)^α and contact number Z−Z_c ∝ √(φ−φ_J), hallmarks of the Point J transition studied by Liu, Nagel, and O'Hern.

Circles: soft disks. Red contacts = force-bearing. Blue = rattlers.