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Department of Mathematical Sciences

Seminar Archives

On this page you can find information about seminars in this and previous academic years, where available on the database.

Applied Mathematics Seminars: Mathematical Models for Faceted Crystals

Presented by Hala AH Shehadeh, James Madison University

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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