Velocity selection in the symmetric model of dendritic crystal growth

We present an analytic solution of the problem of velocity selection in a fully nonlocal model of dendritic crystal growth. Our analysis uses a WKB technique to derive and evaluate a solvability condition for the existence of steady-state needlelike solidification fronts in the limit of small undercooling Δ. For the two-dimensional symmetric model with a capillary anisotropy of strength α, we find that the velocity is proportional to ${\Delta }^4$ ${\alpha }^{7/4}$. We also describe the application of our method in three dimensions.