2004/05/07 by Martin Rost, M. Rost, Rost, Martin
Engineering · Materials Science · Physics and Astronomy · #Adhesion, Friction, and Surface Interactions #FOS: Physical sciences #Fluid Dynamics and Thin Films #Materials Science (cond-mat.mtrl-sci) #Solidification and crystal growth phenomena #Statistical Mechanics (cond-mat.stat-mech) #cond-mat.mtrl-sci #cond-mat.stat-mech
paper · pdf · doi:10.48550/arxiv.cond-mat/0405142
Lecture held at Oberwolfach Workshop "Multiscale modeling in epitaxial growth", submitted to Birkhauser Internatinal Series in Numerical Mathematics, 13 pages Latex
arxiv created 2004/05/07 · openalex publication_date 2004/05/07 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.