Asymptotic solutions of the Becker–Döring equations with size-dependent rate constants

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Abstract
We find the large-time asymptotic behaviour for a number of physically interesting cases of the Becker–Döring equations, allowing both the forward and the backward rates to depend on cluster size in a power-law fashion. We consider in detail the constant monomer form of the equations in the special case where the powers are equal, since the structure of the large-time asymptotic behaviour is then richest. We then turn to cases in which aggregation and fragmentation have different exponents, examining both the fragmentation- and coagulation-dominated cases, again under constant monomer conditions.

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