Tip Oscillation of Dendritic Patterns in a Phase Field Model
  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. 
Hidetsugu Sakaguchi and Seiji Tokunaga