2D disk packing approaching the jamming transition — force chains visualized
The jamming transition (Liu-Nagel 1998) occurs near packing fraction φ_J ≈ 0.84 (2D random close packing). Below φ_J grains flow; above, the system rigidifies and transmits stress through heterogeneous force chains — the bright lines here. Force chains carry ~100× the mean stress and extend ~10 grain diameters. The contact force distribution P(f) ∝ exp(−f/⟨f⟩) for f > ⟨f⟩, an empirical observation explained by the q-model.