Parity-Broken Dendrites

We show that the problem of crystal growth in a channel is closely related to the Saffman-Taylor problem in a sector. By using this analogy we obtain the family of zero-surface-tension solutions for small P\'eclet numbers and extend them to infinite geometry. We focus on the existence of parity-broken double fingers, which are found to appear with fully isotropic surface tension even in the range of small undercooling. We derive the scaling law for the selected velocity of double-fingering structures which is very different from the scaling law of free dendrites with anisotropy.