Scaling theory for ballistic aggregation

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Abstract
The authors develop a Smoluchowski-type mean-field treatment for a recently introduced model of ballistic agglomeration. The predictions of this mean-field theory for the exponent characterizing typical cluster size are in agreement with earlier results for all dimensions. Nevertheless, the predicted monomer decay and particle size distribution are totally at variance with the numerical observations in one dimension. The reason for this discrepancy is found to be the fact that high velocity particles coalesce rapidly independently of their mass, which introduces correlations not taken into account by the mean-field treatment. This is likely to persist in all dimensions, so that the model has no upper critical dimension. The case where the initial velocity distribution function of the particles has a power-law tail is also examined. It is found that, at least in one dimension, the typical cluster size behaves in a way that depends on the specific velocity distribution function, whereas the monomer decay does not.

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