Aggregate size distributions in migration driven growth models

Abstract.

The kinetics of aggregate growth through reversible migrations between any two aggregates is studied. We propose a simple model with the symmetrical migration rate kernel $K(k;j)\propto (kj)^\upsilon$ at which the monomers migrate from the aggregates of size k to those of size j. The results show that for the $\upsilon \leq 3/2$ case, the aggregate size distribution approaches a conventional scaling form; moreover, the typical aggregate size grows as $t^{1 / (3 - 2\upsilon )}$ in the $\upsilon < 3/2$ case and as $\exp(C_1 t)$ in the $\upsilon = 3/2$ case. We also investigate another simple model with the asymmetrical rate kernel $K(k;j)\propto k^\mu j^\nu$ ($\mu \neq \nu$), which exhibits some scaling properties quite different from the symmetrical one. The aggregate size distribution satisfies the conventional scaling form only in the case of $\mu < \nu$ and $\mu + \nu < 2$, and the typical aggregate size grows as $t^{2-\mu-\nu}$.