Random Hard Sphere Packing

Random Sequential Addition (RSA): place spheres one at a time at random positions, reject overlaps. Converges to jamming limit φ_J ≈ 0.547 (2D disks) — lower than the true random close packing (RCP) ≈ 0.82 because RSA gets stuck. True RCP uses compression protocols. In 3D, Bernal's 1960 experiment (ball bearings in a bag) gave φ ≈ 0.636. The J-point is a critical transition: at jamming, pressure diverges and the contact network becomes rigid.