Origin of sidebranching in dendritic growth

We present mechanisms for sidebranch generation in dendritic growth, stressing the importance of nonlinear effects. One such mechanism, which we call solvability-induced sidebranching, relies on the fact that the steady states form a discrete family. In addition, time-dependent simulations of crystal growth in the boundary-layer model are performed. We find that there is a critical value of the anisotropy strength below which the needle crystals are linearly unstable to tip splitting; above this value, the needle crystals have a finite-amplitude instability.