KINETIC-PROPERTIES OF BALLISTIC AGGREGATION

We study a recently introduced model of ballistic aggregation by using the scaling theory of Smoluchovski's equations and numerical simulati ons. The predictions of this mean-field theory for the exponent charac terizing typical cluster size are in agreement with the earlier result s for all dimensions. Nevertheless, the predicted monomer decay and pa rticle size distribution are totally at variance with the numerical ob servations in one dimension. The reason for this discrepancy is found to be the fact that high velocity particles coalesce rapidly independe nt of their mass, which introduces correlations not taken into account by the mean-field treatment. This discrepancy is likely to persist in all dimension, so that the model has no upper critical dimension. We also generalized our study to the case where the initial velocity dist ribution function of the particles has a power-law tail. It is found t hat, at least in one dimension, the typical cluster size behaves in a way that depends on the specific velocity distribution function, where as the monomer decays regardless of the initial velocity distribution. We study also the case in which the mean velocity is infinite. In thi s case it is found that the predictions of the Smoluchovski equation t heory are completely inconsistent with the numerical results in one di mension.