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We introduce a new and extremely simple model for coagulation in which the reaction kernel Kᵢⱼ in the Smoluchowski equation corresponding to the model can be adjusted exactly. For the special case of a constant Kᵢⱼ, we deduce that for spatial dimension d>dc=2, the exact solution of the Smoluchowski equation is valid (mean-field theory). For d<dc, fluctuations give rise to dimension-dependent kinetic exponents and a novel nonmonotonic cluster size distribution.
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Kang et al. (1984) studied this question.
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