Packing transition at φ_J ≈ 0.84 (2D) with force chain visualization
φ=0.75 | Contacts Z=— | Pressure P=—
Random disk packings jam at φ_J ≈ 0.84 (2D bidisperse). At jamming: contact number Z → Z_iso = 2d = 4 (isostatic).
Below φ_J: particles rearrange freely. Above φ_J: jammed — rigid force network spans the system.
Force chains carry load heterogeneously — exponential distribution of contact forces.
Line thickness encodes force magnitude. P ~ (φ − φ_J)^α with α ≈ 1.