Scaling laws in aggregation: Fragmentation models with detailed balance

Abstract
Coagulation processes may be balanced by very slow breakup reactions that lead to a self-similar stationary cluster size distribution, as recently described by Family, Meakin, and Deutch (FMD [Phys. Rev. Lett. 57, 727 (1986); 57, 2332 (1986)]. Here, a class of reversible coagulation-fragmentation models is presented that satisfies detailed balance, for which the scaling functions can be calculated explicitly. The FMD models do not have the property of detailed balance in general.

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