SIMPLIFIED DIFFUSION-LIMITED AGGREGATION MODELS

Computer simulations have been used to explore two-dimensional diffusion-limited aggregation models in which growth is allowed only at the tips of needle shaped arms that are directed away from the origin. For the case of two adsorbing needles with growth velocities equal to the rate at which the needle tips capture random walkers the critical angle, theta(c) (between the two needles) for stable growth is about 30-degrees-33-degrees (in good agreement with the theoretical value of pi[1 - (2/3)1/2] or about 33.03-degrees obtained by Derrida and Hakim (preprint, 1992). For the growth of n symmetrically directed arms with the same boundary conditions all n arms grow in a stable pattern for n less-than-or-equal-to 6. For n greater-than-or-equal-to 7 the growth of n needles is not stable. Quite different results are reported for other needle growth models with different boundary conditions.