We obtain explicit predictions for velocity selection in two- and three-dimensional, symmetric, and one-sided models of dendritic solidification. We do this by using WKB techniques to derive a solvability condition, which is then solved numerically, for the existence of steady-state needle crystals. The comparison with available numerical results is reasonably good. We also discuss the comparison with experiments.

• Received 22 August 1988

DOI:https://doi.org/10.1103/PhysRevA.39.5314