Sub-shaped Aggregation Of Numerical And Theoretical Studies Of The Growth Process

The effects of the external environments on the scaling properties of the growing clusters have been analyzed, by means of the mean-field theories. It was found that for constant external field, the density of the growing cluster, ρ, initially dropping as 1/r, finally became a constant; for the external field of type 1/r^α, it was found that the aggregates exhibited very complicated, non-trivial scaling behaviors with varying control parameter a. To study the effect of anisotropic diffusion on the srowth of DIA clusters, we presented a coordinate transformation approach. For the two dimensional square lattice, we calculate analytically the fractal dimension of the Aniso— tropically—Diffusion-Limited Aggregation, and show that the fractal dimension D varies continuously with the anisotropic diffusion probability p, with D_max=5/3 and D_min =3/2. We also discuss the generalized dimensions D_q for such anisotropic DLA clusters. It is found that our analytical estimates are in agreement with the corresponding computer simulation results.We study the screening effect on the structure of growing clusters by introducing a new growth model, called Screened Eden Model. Our Monte Carlo simulations show that this model can produce growing clusters belonging to different universal classes, including Eden cluster and DLA cluster, by varying...