Fractal dimension of the accessible perimeter of diffusion-limited aggregation

The growth simulation of pine-needle like structure with diffusion-limited aggregation and oriented attachment

A growth model combined with diffusion-limited aggregation (DLA) and oriented attachment (OA) is developed for deducing quantitative understanding of the growth process of pine-needle like structures. We define the completely random parameters for describing the realistic Brownian motion in DLA. The results indicate that the cluster by DLA changes from random branches to regular needles by the introduction of OA. And the cluster of DLA and OA has a fractal dimensionality of about 1.0 during the whole growth process. The maximum length of needels (L_max) depends on the number of particles (N_p). They satisfy the relation L_max = aN_p^b (a and b are constant) over the whole range. The model has also been used to describe the formation of needles on a line, plane and sphere. The growth of needles has obvious steric hindrance from the outer needles. In particular, only one needle grows in the later period in the plane.

A growth model combined with diffusion-limited aggregation and oriented attachment is developed for deducing the growth process of pine-needle like structure.

Linear relationship statistics in diffusion limited aggregation

We show that various surface parameters in two-dimensional diffusion limited aggregation (DLA) grow linearly with the number of particles. We find the ratio of the average length of the perimeter and the accessible perimeter of a DLA cluster together with its external perimeters to the cluster size, and define a microscopic schematic procedure for attachment of an incident new particle to the cluster. We measure the fractal dimension of the red sites (i.e., the sites such that cutting each of them splits the cluster) as equal to that of the DLA cluster. It is also shown that the average number of dead sites and the average number of red sites have linear relationships with the cluster size.

Scaling and multiscaling behavior of the perimeter of a diffusion-limited aggregation generated by the Hastings-Levitov method

In this paper, we analyze the scaling behavior of a diffusion-limited aggregation (DLA) simulated by the Hastings-Levitov method. We obtain the fractal dimension of the clusters by direct analysis of the geometrical patterns, in good agreement with one obtained from an analytical approach. We compute the two-point density correlation function and we show that, in the large-size limit, it agrees with the obtained fractal dimension. These support the statistical agreement between the patterns and DLA clusters. We also investigate the scaling properties of various length scales and their fluctuations, related to the boundary of the cluster. We find that all of the length scales do not have a simple scaling with the same correction to scaling exponent. The fractal dimension of the perimeter is obtained equal to that of the cluster. The growth exponent is computed from the evolution of the interface width equal to β = 0.557(2). We also show that the perimeter of the DLA cluster has an asymptotic multiscaling behavior.