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

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.