Jamming Transition — Soft Sphere Packing

At packing fraction φ_J ≈ 0.64 (random close packing in 3D, ≈0.84 in 2D), soft spheres jam. Below φ_J: particles rearrange freely. Above: system rigidifies, pressure diverges.

Packing Control

Packing fraction φ: 0.60 N spheres: 80 Softness exponent α: 2

φ_J ≈ 0.84 (2D)
Z_J ≈ 2d=4 (isostatic)
P ~ (φ−φ_J)^(α−1)
Contacts: —