Growth and form in the zero-noise limit of discrete Laplacian growth processes with inherent surface tension: II. The triangular lattice

Abstract

Laplacian growth models that include surface tension in a lowest approximation are simulated on the triangular lattice in the deterministic zero-noise limit. In the absence of surface tension the zero-noise clusters are needle-star-shaped objects with the star tips directed along the lattice axes. The star tips are characterized by a needle staircase with constant step lengths independent of cluster size. Further back from the tip the star arms can develop side-branch whiskers.As an effective surface tension is introduced and increased in these models the step lengths in the staircases become shorter and the needle arms become wider. Depending on the details of the model, tip-splitting may occur as the surface tension is increased still further. Typically, in the limit where surface tension dominates, the growth becomes regular and compact. The essential properties of the Laplacian growth models considered here are derived algebraically by combining a stationary contour approximation with conformal mapping methods.Comparisons are drawn between the growth and form arising from these Laplacian models on the square (paper I) and triangular lattices.