## Graduate Seminar Course Math 285J, Winter 2002:

Mathematical Aspects of Computational Materials Science

**Instructor:** Christian Ratsch, MS7619c

**Phone: **825-4127;
**E-mail:** cratsch@math.ucla.edu

**Class Webpage:** www.math.ucla.edu/~cratsch/285j.1.02w/index.html

**Meeting Time and Place:** M,W 11:00 - 12:20, MS6221

**Textbook:** There will be no textbook for this class. However, books and research papers
used for preparation of this course will be announced.

## Course Description

Many problems in Materials and all of Physical Sciences occur on
time and length scales that are the macroscopic, continuum scales, while the
underlying physical processes occur on a microscopic, atomistic scale.
Thus, the biggest challenge in modeling problems in Materials Sciences
is to properly use and link the hierarchy of theoretical models that are
appropriate for the different time and length scales. This is a concept that
is often referred to as **multiscale modeling**.
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.