Diffusion-Limited Aggregation with Anisotropic Sticking Probability: A Tentative Model for River Networks

抄録

Diffusion-limited aggregation (DLA) model with anisotropic sticking probability P_s is computer-simulated on two dimensional square lattice. The cluster grows from a seed particle at the origin in the positive y area with the absorption-type boundary along x-axis. The cluster is found to grow anisotropically as R_⁄⁄∼N^ν_⁄⁄ and R_⊥∼N^ν_⊥, where R_⊥ and R_⁄⁄ are the radii of gyration of the cluster along x- and y-axes, respectively, and N is the particle number constituting the cluster. The two exponents are shown to become assymptotically ν_⁄⁄=2⁄3, ν_⊥=1⁄3 whenever the sticking anisotropy exists. It is also found that the present model is fairly consistent with Hack’s law of river networks, suggesting that it is a good candidate of a prototype model for the evolution of the river network.