We will start this course by first discussing numerical and mathematical tools used to study problems in Material Sciences. Modeling and analysis of polycrystalline materials will be of particular interest in this course. Most technologically useful materials are polycrystalline microstructures composed of a myriad of small monocrystalline grains separated by grain boundaries. Grain boundaries are dynamic, driven by an interfacial energy that forces some grains to shrink and disappear, others to grow. The result is a general coarsening process of a large metastable network that is a rich subject of research for mathematicians and materials scientists. Different approaches to the problem, as well as the recent progress and open questions in the area will be presented as a part of this module.
Lecture 2: Role of the Interfacial Energy during Coarsening, Grain Boundary Character Distribution (GBCD), 2D Large Scale Simulations - Set up of the Computational Model
Lectures 3, 4, 5: GBCD, Simplified 1D Critical Events Model, Different Aspects of the Critical Events Model; Introduction to Monte Carlo Method and Grain Growth Modeling using Monte Carlo Idea
Lectures 5, 6: Students Final Project: Presentations of the Selected Papers (about 15 minutes each)