Growth and form in the zero-noise limit of discrete Laplacian growth processes with inherent surface tension

M.T. Batchelor and B.I. Henry

Physica A: Statistical Mechanics and its Applications, 1992, vol. 187, issue 3, 551-574

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 = α3−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.

Date: 1992
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:187:y:1992:i:3:p:551-574

DOI: 10.1016/0378-4371(92)90010-N

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