Growth patterns in a channel for singular surface energy: phase-field model.

We study solidification in a two-dimensional channel for faceted materials whose facets correspond to cusps in the gamma plot. The main result is the existence of three growth modes, according to the anisotropy strength: a single faceted finger at high anisotropies, two faceted fingers in the intermediate range, and an oscillating mode at low anisotropies. Simple geometrical and dynamical models are proposed to explain the nature of the observed modes. In particular, the one-finger patterns are shown to be similar to free dendrites while the two-finger patterns correspond to confined solidification fingers.