We introduce a new and extremely simple model for coagulation in which the reaction kernel $K_{\mathrm{ij}}$ in the Smoluchowski equation corresponding to the model can be adjusted exactly. For the special case of a constant $K_{\mathrm{ij}}$, we deduce that for spatial dimension $d>\mathrm{}{d}_c=2\mathrm{}$, the exact solution of the Smoluchowski equation is valid (mean-field theory). For $d<\mathrm{}{d}_c$, fluctuations give rise to dimension-dependent kinetic exponents and a novel nonmonotonic cluster size distribution.

• Received 17 August 1984

DOI:https://doi.org/10.1103/PhysRevA.30.2833