One of the most common modes of growth of a solid phase from a metastable liquid is the dendritic one where a nearly parabolic front advances at a constant velocity. The possibility of a steady-state growth of a parabolic front was first demonstrated by Ivantsov and was supplemented by the determination of the anisotropy of surface tension as a selection mechanism for the velocity. Recently, selection mechanisms such as the presence of a triple junction or of elastic effects were reported.
Another classical mode of solidification is the lamellar growth in eutectic alloys. The pioneering work of Jackson and Hunt on this topic refers to directional solidification and especially consists of finding the temperature of the solidification front. In opposition to dendritic growth, no unique solution exists for this process. A range of lamellae spacing is stable and bifurcations toward a broad range of oscillatory regimes or tilted patterns have been evidenced. It is worthwhile to mention the recent observation of a three-dimensional spiral dendrite in eutectics.