Particles of size 1 merge pairwise under constant kernel K=1. Clusters grow and merge, producing a broadening size distribution. Smoluchowski's mean-field solution: n_k(t) = (t/2)^(k-1) · (2/(t+2))^(k+1).
Particles (colored by size)
Size Distribution
Constant kernel: exact solution gives exponential size distribution. Mean size grows as ⟨k⟩ ~ 1+t.