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• W1978385593 abstract "In a recent paper (Bogoyavlenskiy V A 2002 JPA textbf{35} 2533), an algorithm aiming to generate isotropic clusters of the on-lattice diffusion-limited aggregation (DLA) model was proposed. The procedure consists of aggregation probabilities proportional to the squared number of occupied sites ($k^2$). In the present work, we analyzed this algorithm using the noise reduced version of the DLA model and large scale simulations. In the noiseless limit, instead of isotropic patterns, a $45^circ$ ($30^circ$) rotation in the anisotropy directions of the clusters grown on square (triangular) lattices was observed. A generalized algorithm, in which the aggregation probability is proportional to $k^nu$, was proposed. The exponent $nu$ has a nonuniversal critical value $nu_c$, for which the patterns generated in the noiseless limit exhibit the original (axial) anisotropy for $nu<nu_c$ and the rotated one (diagonal) for $nu>nu_c$. The values $nu_c = 1.395pm0.005$ and $nu_c = 0.82pm 0.01$ were found for square and triangular lattices, respectively. Moreover, large scale simulations show that there are a nontrivial relation between noise reduction and anisotropy direction. The case $nu=2$ (bogo's rule) is an example where the patterns exhibit the axial anisotropy for small and the diagonal one for large noise reduction." @default.
• W1978385593 created "2016-06-24" @default.
• W1978385593 creator A5032900093 @default.
• W1978385593 creator A5068218748 @default.
• W1978385593 date "2006-03-08" @default.
• W1978385593 modified "2023-09-27" @default.
• W1978385593 title "Is it really possible to grow isotropic on-lattice diffusion-limited aggregates?" @default.
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• W1978385593 doi "https://doi.org/10.1088/0305-4470/39/12/001" @default.
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