Aggregate size distributions in migration driven growth models

Jianhong Ke (), Zhenquan Lin and Youyi Zhuang

The European Physical Journal B: Condensed Matter and Complex Systems, 2003, vol. 36, issue 3, 423-428

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 $t^{2-\mu-\nu}$ . Copyright Springer-Verlag Berlin/Heidelberg 2003

Date: 2003
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DOI: 10.1140/epjb/e2003-00362-5

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