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

Abstract

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. Show more