Jamming Transition

2D disk packing approaches φ_c ≈ 0.84 — pressure diverges, contact number Z → 4, force chains emerge

φ_c ≈ 0.84 (jamming)
Contacts Z:
Pressure P:
Overlaps:
Jamming: Below φ_c disks rattle freely. At φ_c, a rigid contact network spans the system. Pressure P ~ (φ−φ_c)^α, contact number Z−Z_c ~ (φ−φ_c)^0.5. Force chains (bright lines) carry stress.