Cluster-Size Distribution in the Incremental Growth of DLA Clusters

Abstract

Large-scale computer simulation results are presented for the cluster-size distributions N_s in the incremental growth of on-lattice and off-lattice DLA clusters in the spatial dimensions d=2–5. The clusters are first grown to a size of s₁ particles and additional s₂ particles are added. Then the number N_s of clusters or “trees” of size s in the incremental growth consisting of the last s₂ particles added is obtained to investigate the s-dependence of N_s. It is found that N_s can be approximately described by the power-law form, N_s∼s^−τ with the apparent values of the exponent τ≅1.65, 1.76, 1.70 for hypercubic lattice DLA and τ≅1.68, 1.77, 1.71 for off-lattice DLA in d=2–4, respectively. A value of about 1.66 was obtained for τ from five-dimensional off-lattice simulations. These exponents are related to the fractal dimensionality of the old growth/new growth interface.