We study dendritic growth numerically with a phase field model. Tip oscillation and regular side-branching are observed in a parameter region where the anisotropies of the surface tension and the kinetic effect compete. The transition from a needle pattern to a dendritic pattern is conjectured to be a supercritical Hopf bifurcation.
@article{arxiv.nlin/0212040,
title = {Tip Oscillation of Dendritic Patterns in a Phase Field Model},
author = {Hidetsugu Sakaguchi and Seiji Tokunaga},
journal= {arXiv preprint arXiv:nlin/0212040},
year = {2009}
}