Jamming Transition — Sphere Packing

Compress bidisperse disks: watch the system jam at φ_J ≈ 0.84 as contacts become rigid

N disks 60

φ = 0.00 | Contacts = 0 | Jammed: No

Point J (Liu-Nagel 1998): random close packing in 2D occurs at φ_J ≈ 0.84 for bidisperse disks. At jamming, the contact number reaches the isostatic value z = 2d = 4, and the system suddenly acquires mechanical rigidity.