Reaction kinetics of cluster impurities.

dimension di, while the rest of the d-dimensional space is occupied by identical mobile particles. The Smoluchowski rate theory suggests that the immobile reactants concentration, s(t), exhibits interesting behavior as a function of the codimension, d̄ ≡ d− di. This survival probability undergoes a survival-to-extinction transition at d̄c = 2. For d̄ < d̄c, a finite fraction of the immobile reactants survives, while for d̄ ≥ d̄c, s(t) decays indefinitely. The corresponding asymptotic properties of the concentration are discussed. The theoretical predictions are verified by numerical simulations in 2D