Steady-state dendritic crystal growth

We study the problem of velocity and shape selection in the growth of dendritic crystals. We demonstrate that the presence of surface tension destroys the Ivantsov family of solutions at all but a single velocity. This occurs at all undercoolings and for both two-dimensional and axisymmetric three-dimensional dendrites. The lack of a continuous family of solutions is due to a mismatch of terms exponentially small in velocity, in agreement with the mechanism of microscopic solvability previously derived for geometrical growth models.