## Abstract

Laplacian growth models that include surface tension in a lowest approximation are simulated on the square lattice in the deterministic zero-noise limit. The models include the dielectric breakdown model with exponent η and a generalized diffusion-limited aggregation (DLA) model with local sticking probability s = α^{3-B}, where B is the number of neighbouring aggregate sites and α is a parameter. We identify two morphological transitions in the zero-noise limit for these models as the effective surface tension is increased; (i) a transition from a stable needle staircase to tip-splitting and (ii) a transition from axial growth to diagonal growth. We use a stationary contour approximation and conformal mapping methods to obtain theoretical estimates for the step lengths in the stable needle staircase for the DLA model with zero surface tension (α = 1). We further extend this formalism to describe the collapse of the needle and subsequent tip-splitting in the generalized DLA model.

Original language | English |
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Pages (from-to) | 551-574 |

Number of pages | 24 |

Journal | Physica A: Statistical Mechanics and its Applications |

Volume | 187 |

Issue number | 3-4 |

DOIs | |

Publication status | Published - 15 Sept 1992 |