Diffusion-limited aggregation on nonuniform substrates

• Published in: Journal of the Physical Society of Japan 2001-11, Vol.70 (11), p.3251-3254
• Main Authors: TAN, Zhi-Jie, ZOU, Xian-Wu, HUANG, Sheng-You, JIN, Zhun-Zhi
• Format: Article
• Language: English
• Subjects: Condensed matter: structure, mechanical and thermal properties; Disordered solids; Exact sciences and technology; Fractals; macroscopic aggregates (including diffusion-limited aggregates); Physics; Structure of solids and liquids; crystallography
• ISSN: 0031-9015; 1347-4073
• DOI: 10.1143/jpsj.70.3251

Diffusion-limited aggregation (DLA) on nonuniform substrates was investigated by computer simulations. The nonuniform substrates are represented by Leath percolations with the occupied probability p. p stands for the degree of nonuniformity and takes values in the range pc ≤ p≤ 1, where pc is the threshold of percolation. The DLA cluster grows up on the Leath percolation substrate. The patterns of the DLA clusters appear asymmetrical and nonuniform, and the branches are relatively few for the case that p is close to pc. In addition, the pattern depends on the shape of substrate. As p increases from pc to 1, cluster changes to pure DLA gradually. Correspondingly, the fractal dimension increases from 1.46 to 1.68. Furthermore, the random walks on Leath percolations through the range pc ≤ p ≤ 1 were examined. Our simulations show the Honda-Toyoki-Matsushita relation is still reasonable for DLA growth in fractional dimensional spaces.