Physics of heat flow in the tails of needle crystals.

We show that the heat flow in the tail sections of needle crystal solutions of dendritic growth become increasingly anisotropic. As a result, the dominant behavior in the tails reduces to that of a very simple physical model which admits the exact Ivantsov solutions as well as a continuous family of solutions for non-zero capillary length. The model provides a useful testing ground for newly developed analytical and numerical methods for velocity selection, and highlights some of the substleties of the small Peclet number limit.