Velocity selection in the symmetric model of dendritic crystal growth

Abstract

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 \ensuremath{\Delta}. For the two-dimensional symmetric model with a capillary anisotropy of strength \ensuremath{\alpha}, we find that the velocity is proportional to ${\ensuremath{\Delta}}^{4}$${\ensuremath{\alpha}}^{7/4}$. We also describe the application of our method in three dimensions.