Velocity selection in the symmetric model of dendritic crystal growth

An analytic solution of the problem of velocity selection in a fully nonlocal model of dendritic crystal growth is presented. The analysis uses a WKB technique to derive and evaluate a solvability condition for the existence of steady-state needle-like solidification fronts in the limit of small under-cooling Delta. For the two-dimensional symmetric model with a capillary anisotropy of strength alpha, it is found that the velocity is proportional to (Delta to the 4th) times (alpha exp 7/4). The application of the method in three dimensions is also described.