Applied Mathematics Seminars: Mathematical Models for Faceted Crystals
14 October 2016 14:00 in CG93
This talk is in the area of mathematical modeling of materials science. We discuss the continuum limit of two discrete models for crystalline structures evolving on a flat substrate. The first model is based on microscopic Burton-Cabrera-Frank (BCF) models for stepped surfaces, and the second one is based on atomistic Solid-on-Solid (SOS) models. We prove that the BCF model is a finite difference scheme for a continuum PDE, and describe the macroscopic long term behavior and self similar solutions. For the SOS model, we use statistical mechanics techniques to prove that, in the discrete setting, a facet (flat face of the crystal) emerges as a consequence of the model. We hope to carry this over to the continuum setting.
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This seminar series is the continuation of the Numerical Analysis Seminar series that ran until August 2016. This change of name reflects the broader interests of the Applied Mathematics group (note that the Mathematical and Theoretical Particle Physics group also has a seminar series).