Is it really possible to grow isotropic on-lattice diffusion-limited aggregates?
| dc.creator | Alves, S. G. | |
| dc.creator | Ferreira Jr, S. C. | |
| dc.date | 2006-03-08 | |
| dc.date.accessioned | 2026-07-07T07:02:16Z | |
| dc.date.available | 2026-07-07T07:02:16Z | |
| dc.description | 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 $k^ν$, was proposed. The exponent $ν$ has a nonuniversal critical value $ν_c$, for which the patterns generated in the noiseless limit exhibit the original (axial) anisotropy for $ν<ν_c$ and the rotated one (diagonal) for $ν>ν_c$. The values $ν_c = 1.395\pm0.005$ and $ν_c = 0.82\pm 0.01$ 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 $ν=2$ (\bogo's rule) is an example where the patterns exhibit the axial anisotropy for small and the diagonal one for large noise reduction. | |
| dc.description | 12 pages, 8 figures | |
| dc.identifier | https://arxiv.org/abs/cond-mat/0603218 | |
| dc.identifier | http://arxiv.org/abs/cond-mat/0603218 | |
| dc.identifier | J. Phys. A: Math. Gen. 39 (2006) 2843-2852 | |
| dc.identifier | doi:10.1088/0305-4470/39/12/001 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/108541 | |
| dc.subject | Statistical Mechanics | |
| dc.title | Is it really possible to grow isotropic on-lattice diffusion-limited aggregates? | |
| dc.type | text |