Non-equilibrium Interface and Surface Dynamics

Coarsening and wavelength selection in nonlinear interface dynamics

Chaouqi Misbah

Université Joseph Fourier Grenoble I and CNRS

Nonlinear equations arising in nonequilbrium interface dynamics can be broadly classified in two important categories: (i) those which exhibit coarsening, and (ii) those which show a persistent length scale in the course of time. This talk will first describe the extension of the coarsening criterion developed few years ago in one dimension [1], to two dimensions [2]. This criterion is based on the study of the phase diffusion equation. The method will be exemplified on some prototypical nonlinear equations. We shall show that the coarsening exponent can be extracted from purely steady-state considerations. The power of this method lies in the extremely fast numerical evaluation as compared to forward time-dependent simulations. We then describe how to obtain other generic results for nonlinear equations which undergo coarsening by using heuristic arguments. Some results can be shown to hold at arbitrary dimensions.

[1] C. Misbah, O. Pierre-Louis, and Y. Saito, Crystal surfaces in and out of equilibrium: A modern view Rev. Mod. Phys. 82, 981 (2010).
[2] P. Politi and C. Misbah, When Does Coarsening Occur in the Dynamics of One-Dimensional Fronts? Phys. Rev. Lett. 92, 090601 (2004).
[3] C. Misbah and P. Poiti, Phase instability and coarsening in two dimensions, Phys. Rev. E, 030106 R (2009).