Crystal growth in a liquid, or by molecular beam epitaxy results in complex patterns, from periodic cellular structures to spatio-temporal chaos (such as the Kuramoto-Sivashinsky dynamics), or completely stochastic (such as the Kardar-Parisi-Zhang situation). Their understanding is of paramount technological importance, while they offer at the same time interesting examples of spontaneous morphogenesis on the fundamental level, where one is often faced with a subtle interplay between stochasticity and determinism.
We plan to study analytically and numerically the nonlinear evolution of surface morphologies on both a microscopic scale (such as step bunching and facetting), and on the mesoscale in the case of solidification. The analysis of the latter will be based on the free boundary
integrodifferential formulation and finite elements techniques. We shall focus basically on the interaction between the diffusive instability and the elastic one [see recent account by the host group: C. Misbah et al. Phys. Rev. Lett. 76, 3013 (1996)].