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The standard coagulation process is generalized to include the effects of fragmentation and a scaling description for the cluster size distribution is developed. The Smoluchowski rate equation is used to calculate the critical exponents describing the steady-state size distribution. Predictions of the scaling and the rate equation are tested by numerical simulations. The mean-field rate-equation results are found to be valid in $d>~1$ implying that the upper critical dimension dc is less than 1.
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Family et al. (1986) studied this question.
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