Continuum models for surface growth
Abstract
Description
As an introductory lecture to the workshop an overview is given over continuum models for homoepitaxial surface growth using partial differential equations (PDEs). Their {\em heuristic derivation} makes use of inherent symmetries in the physical process (mass conservation, crystal symmetry, ...) which determines their {\em structure}. Two examples of applications are given, one for large scale properties, one including crystal lattice discreteness. These are: (i) a simplified model for {\em mound coarsening} and (ii) for the transition from {\em layer-by-layer} to {\em rough growth}. Virtues and shortcomings of this approach is discussed in a concluding section.
Lecture held at Oberwolfach Workshop "Multiscale modeling in epitaxial growth", submitted to Birkhauser Internatinal Series in Numerical Mathematics, 13 pages Latex
Lecture held at Oberwolfach Workshop "Multiscale modeling in epitaxial growth", submitted to Birkhauser Internatinal Series in Numerical Mathematics, 13 pages Latex