TIP LENGTHS AND WHISKERING IN NOISE-REDUCED DIFFUSION-LIMITED AGGREGATION

We examine the nature of the tunable family of patterns obtained from the discrete eta-DLA model in the deterministic zero-noise limit. The eta-DLA model is a variant of the standard diffusion-limited aggregati on (DLA) model in which the DLA growth probabilities are raised to the power eta. The observed morphologies, which range from compact Eden c lusters for eta = 0 through to sharp needle-like clusters with increas ing eta, can be characterized by a sequence of step lengths in a stabl e staircase structure proceeding back from the tip. Side-branch whiske rs, which are found on the triangular lattice but not on the square la ttice, occur closer to the tip as eta is increased. Beyond a value eta (c), whiskers are found immediately behind the tip. We derive the leng th of the exposed tip as a function of eta using a stationary contour approximation and conformal mapping methods. A theoretical estimate fo r eta(c) is derived by refining this approach to incorporate the possi ble shielding of surface sites by aggregate sites. Our theoretical res ults are in excellent agreement with the numerical results on both lat tices.