Dynamic Scaling for Aggregation of Clusters

Abstract

The model of cluster growth by diffusion-limited aggregation of clusters is studied in two dimensions and the cluster size distribution $n_s\mathrm{}\left(t\right)\mathrm{}$ is determined as a function of the cluster size $s$ and the time $t$. A dynamic scaling function of the form $n_s\mathrm{}\left(t\right)\mathrm{}\sim t^{-w}{s}^{-\tau }f\left(\frac{s}{t^z}\right)$ is proposed and is shown to lead to the scaling relation $w=(2-\tau )z$ among the critical exponents. The simulation results support this scaling law.