Carlos J. García-Cervera.
South Hall, Room 6707.
Office Phone: (805) 893 3681
Office Fax: (805) 893 2385
Office Hours: Tuesday and Thursday, 12:30-2:00pm.

Course description: Liquid crystals are a state of matter intermediate between an isotropic liquid and a crystalline solid. They possess mechanical properties of a liquid, such as high fluidity and inability to support shear, and at the same time they have properties similar to a crystalline solid. In this course we will do an introduction to the different mathematical theories for liquid crystals presented in the last 50 years. Applications and numerical issues will also be considered. A tentative syllabus follows:

1. Introduction to Thermodynamics.
2. Introduction to the Calculus of Variations.
3. Statistical Theories of Liquid Crystals.
4. Continuum Theory of the Nematic State.
5. The Leslie-Ericksen and Landau-de Gennes Theories.
6. Smectic Liquid Crystals: de Gennes model.
7. The Doi-Marrucci-Greco Kinetic Theory.
8. Numerical Approaches: Fokker-Planck equation, Stochastic models, Closure Approximations, and Molecular Dynamics.

Prerequisites: Basic knowledge of ODEs and PDEs (at the level of the Mat 214 and 215 series for non-math majors, and the level of Mat 243 and 246 for math majors). Numerical background at the level of Mat 206.

References: Although some of the material will be extracted from published research articles, we will use some of the following references:

1. Liquid Crystals, by S. Chandrasekhar.
2. The Physics of Liquid Crystals, by P.G. de Gennes.
3. The Theory of Polymer Dynamics, by Doi and Edwards.
4. Dynamics of Polymeric Liquids, by Bird et al..
5. Variational Theories for Liquid Crystals, by E. Virga.

1. Partial Differential Equations, by L.C. Evans.
2. Stochastic differential equations: an introduction, by B.K. Øksendal.
3. Variational methods, by M. Struwe.
4. Thermal Physics, by C. Kittel.
5. Understanding Molecular Simulation, by Frenkel and Smit.