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Mention of a related model appears in Z.A. Melzak, Mathematical Ideas, Modeling and Applications, Volume II of Companion to Concrete Mathematics (Wiley, New York, 1976) p. 279. We are grateful to J.L. Spouge for making us aware of this work.
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A similar two-scale structure appears in the mass distribution of additive polymerization aggregation processes with different rates for monomer-monomer and monomer-polymer reactions. See e.g., N.V. Brilliantov, P.L. Krapivsky, J. Phys. A 24, 4789 (1991).
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