Jamming Transition in Soft Sphere Packings

From flowing liquid to rigid amorphous solid at Point J

The jamming transition at φ_J ≈ 0.64 (random close packing in 2D: ~0.84) marks the onset of rigidity in amorphous materials. Below φ_J particles flow freely; above it, a percolating contact network bears stress. The force network (shown in orange) is heterogeneous — force chains carry far more stress than average.