DLA Clusters Research Articles

Topological and geometrical properties of DLA clusters

Three new exponents are calculated for diffusion limited aggregates in two dimensions via computer simulation. The 1/N=0 limit gives zeta =1.52, nu =0.91 and dw=2.56. These results confirm Martin's conjecture D= zeta / nu , and are consistent with previous work indicating that topological rather than geometrical properties of random fractals are responsible for variations in fractal dimension. Diffusion on DLA clusters is anomalous with an exponent that is consistent with the Alexander-Orbach conjecture and satisfies the Einstein relation.

Anisotropy and cluster growth by diffusion-limited aggregation.

We describe a simple theory of diffusion-limited-aggregation cluster growth which relates the large-scale shape of the cluster to its fractal dimension. We present results of computer simulation for DLA clusters grown with anisotropic sticking rules which provide strong confirmation of our model in two dimensions. New universal exponents are predicted and found. We are also able to obtain good estimates for the fractal dimension of ordinary DLA.