Stability of dendritic crystals

We present an integrodifferential-operator formulation of the problem of linear stability around the selected needle crystal pattern in dendritic crystal growth. We show by explicit computation that (a) all members of the discrete set of allowed steady states aside from the fastest are unstable and (b) the fastest such shape is linearly stable at least for large enough anisotropy. We comment on the implications of our work for the issue of side-branch wavelength determination.