Dynamic scaling of migration-driven aggregate growth

We study the kinetic behaviour of the growth of aggregates driven by reversible migration between any two aggregates. For a simple model with the migration rate K(i;j)=K′(i;j)∝i^uj^v at which the monomers migrate from the aggregates of size i to those of size j, we find that the aggregate size distribution in the system with u+v≤3 and u<2 approaches a conventional scaling form, which reduces to the Smoluchovski form in the u=1 case. On the other hand, for the system with u<2, the average aggregate size S(t) grows exponentially in the u+v=3 case and as (tlnt)^{1/(5-2u)} in another special case of v=u-2. Moreover, this typical size S(t) grows as t^{1/(3-u-v)} in the general u-2