Cluster size distribution in irreversible aggregation at large times

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Abstract
It is assumed that the size distribution ck(t) satisfies Smoluchowski's coagulation equation with rate coefficients K(i, j), behaving as K(i, j) approximately imu jnu (ik(t) approaches for t to infinity the exact solution Cbk/t(k=1, 2, . . .), where the bk's are independent of the initial conditions ck(0), and can be determined from a recursion relation. In class II systems ( mu =0), ck(t)/c1(t) to bk (t to infinity , k=1, 2, . . .), but the bk's depend on ck(0). Only in the scaling limit (k to infinity , s(t) to infinity with k/s(t)=finite; s(t) is the mean cluster size) does ck(t) approach a form independent of the initial distribution. Class III, where ck(t)/c1(t) to infinity (t to infinity , k=2, 3, . . .), has not been considered here.

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