Smoluchowski Coagulation Equation

Clusters of size i and j merge at rate K(i,j) to form clusters of size i+j. The cluster mass distribution n_k(t) evolves via the coagulation equation. With constant kernel K=1, the exact solution is known: n_k ~ k⁻³/² at the gel point.

Kernel K(i,j)

Kernel type Initial max cluster size 8 Sim speed 1.0 Max display mass 60

t = 0.00
N_total = 0
M_total = 0
⟨k⟩ = 0

∂n_k/∂t = ½Σ_{i+j=k} K(i,j)n_i n_j
- n_k Σ_j K(k,j) n_j

Const kernel: n_k(t)=
4t^(k-1)/(1+2t)^(k+1)