Morphological diagram of diffusion driven aggregate growth in plane: competition Reference: COMPHY4276

Anton Yu. Menshutin, Lev. N. Shchur

arXiv:1008.3449v1 [cond-mat.stat-mech]

Computer Physics Communications 182 (2011), pp. 1819-1823

DOI: 10.1016/j.cpc.2010.10.028

Abstract:

Two-dimensional structures grown with Witten and Sander algorithm are investigated. We analyze clusters grown off-lattice and clusters grown with antenna method with $N_{fp}=3,4,5,6,7$ and 8 allowed growth directions. With the help of variable probe particles technique we measure fractal dimension of such clusters $D(N)$ as a function of their size $N$. We propose that in the thermodynamic limit of infinite cluster size the aggregates grown with high degree of anisotropy ($N_{fp}=3,4,5$) tend to have fractal dimension $D$ equal to 3/2, while off-lattice aggregates and aggregates with lower anisotropy ($N_{fp}>6$) have $D \approx 1.710$. Noise-reduction procedure results in the change of universality class for DLA. For high enough noise-reduction value clusters with $N_{fp} \ge 6$ have fractal dimension going to $3/2$ when $N\rightarrow\infty$.

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