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Abstract
We have investigated on-lattice diffusion limited aggregation (DLA) involving edge diffusion and compared the results with the standard DLA model. For both cases, we observe the existence of a crossover from the fractal to the compact regime as a function of sticking coefficient. However, our modified DLA model including edge diffusion shows an extended fractal growth regime like an earlier theoretical result using realistic growth models and physical parameters [Zhang et al., Phys. Rev. Lett. 73 (1994) 1829]. While the results of Zhang et al. showed the existence of the extended fractal growth regime only on triangular but not on square lattices, we find its existence on the square lattice. There is experimental evidence of this growth regime on a square lattice. The standard DLA model cannot characterize fractal morphology as the fractal dimension (Hausdorff dimension, DH) is insensitive to morphology. It also predicts DH = DP (the perimeter dimension). For the usual fractal structures, observed in growth experiments on surfaces, the perimeter dimension can differ significantly (DH ≠ DP) depending on the morphology. Our modified DLA model shows minor sensitivity to this difference.
Highlights
Fractal structures[1] are ubiquitous in nature
According to the diffusion limited aggregation (DLA) model, the Hausdorff dimension (DH) is equal to the perimeter dimension (DP), as shown in a simulation with sticking coefficient, S = 1.0.9 In this paper we show that this is valid even when the sticking coefficient is varied over several orders of magnitude (0.00001 ≤ S ≤ 1.0)
We have presented a modified DLA model including edge diffusion
Summary
Fractal structures[1] are ubiquitous in nature. They can be produced in self-organized growth or using deterministic principles. Zhang et al considered atomic mobility along the edge of the island in realistic growth models with physical parameters[14] and concluded that essentially all the observed fractal structures in recent experimental studies have involved significant local relaxation via edge diffusion.[12,13] These fractals are distinctly different from those formed within the standard DLA model. There are other fractal structures with much wider branch width without any empty pockets within them.[16] For such structures the perimeter dimension differs from the Hausdorff dimension (DH DP). The morphology of such realistic structures can be characterized by DP
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