Non universal DLA and exact fractal dimensions
Abstract
In analogy to recent results on non-universal roughening in surface growth [Lam and Sander, Phys. Rev. Lett. {\bf 69}, 3338 (1992)], we propose a variant of diffusion-limited aggregation (
DLA
) in which the radii of the particles are chosen from a power law distribution. For very broad distributions, the huge particles dominate and the fractal dimension is calculated exactly using a scaling theory. For narrower distributions, it crosses back to DLA. We simulated
1200
clusters containing up to
200,000
particles. The fractal dimensions obtained are in reasonable agreement with our theory.