In this course, an overview over different theoretical approaches to modeling problems in Materials Sciences will be given. We will discuss different approaches that are appropriate for different time and length scales. In particular, we will cover density-functional theory, kinetic Monte Carlo simulations, and continuum models. The mathematical and theoretical foundation of these methods will be discussed. Also, examples how these methods are used for problems in Materials Sciences will be given. Many (but not all) of the examples will be related to modeling and simulation of thin film growth, as this is a major area of research in the Applied Math group here at UCLA.
This is a seminar-style course. There will be (at least) 3 blocks within this course that are fairly self contained: We will spend a number of classes to discuss density-functional theory. We will start with the basic theory that has been formulated by Hohenberg and Kohn, and Kohn and Sham, will discuss modern implementations, and discuss a number of expamples. In the second and third block, we will discuss kinetic Monte Carlo methods and continuum models. There will be a number of guest-lecturers in this course, with special expertise in a particular area.
This course is designed for graduate Math students who specialize in Applied Mathematics.
It is, however, also designed to be an appropriate course for students in Materials
Sciences, Physics, and Chemistry, who are interested in computational methods for
materials science problems. Please feel free to contact me of you are uncertain whether
this is an appropriate course for you.
Prerequisites: A basic (undergraduate) background in Math, Physics, and Materials Science, and an interest to learn about the subject. Expertise in computation and numerics is not needed.