HAUSDORFF DIMENSION AND SCALING NATURE OF ANISOTROPY DIFFUSION DLA CLUSTER

Abstract

In this paper,the effect of the anisotropy diffusion on the growth of diffusion-limited aggregation(DLA) clusters is discussed.Our computer simulation results verify that DLA clusters grown with anisotropic diffusion rules have a striking overall diamond shape.A new anisotropic diffusion equation of particles is derived.The Hausdorff dimension of a two-dimensional DLA cluster in the anisotropic diffusion is calculated.The results show that the effective angle β eff =min(β ix ,β iy ).In addition,the generalized dimension D q of the anisotropic diffusion DLA is also discussed and an expression of the generalized dimension D q is obtained using the modified wedge model.