Tip lengths and whiskering in noise-reduced diffusion-limited aggregation

The authors 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 aggregation (DLA) model in which the DLA growth probabilities are raised to the power eta . The observed morphologies, which range from compact Eden clusters for eta =0 through to sharp needle-like clusters with increasing eta , can be characterized by a sequence of step lengths in a stable staircase structure proceeding back from the tip. Side-branch whiskers, which are found on the triangular lattice but not on the square lattice, occur closer to the tip as eta is increased. Beyond a value eta _c, whiskers are found immediately behind the tip. They derive the length of the exposed tip as a function of eta using a stationary contour approximation and conformal mapping methods. A theoretical estimate for eta _c is derived by refining this approach to incorporate the possible shielding of surface sites by aggregate sites. Their theoretical results are in excellent agreement with the numerical results on both lattices.