Mathematical Theories of Liquid Crystals

16 hour lecture course, 2.00-4.00pm Wednesdays, weeks 1-8 Hilary Term 2017 VC1 Lecture Room, Andrew Wiles Building

Outline
Liquid crystals are intermediate states of matter with a wide range of modern applications. This is because liquid crystals, as soft materials, are extremely sensitive to external stimuli. Although liquid crystals were discovered experimentally in the late 1800's, satisfactory theoretical descriptions were not developed until the early 1960's. From the very beginning, the theories that succeeded in explaining the observed behaviour of liquid crystals had a strong mathematical content and posed new mathematical questions. This course will provide an overview of the mathematical theories for liquid crystals mostly used in the physics literature. Both equilibrium and evolution problems will be treated, though primarily for the most common, nematic subphase. Both modelling subtleties and rigorous PDE results will be covered. Specific problems will be proposed in classical areas, such as topological defects and their stability. In these areas, newly discovered materials have shown that questions once considered as purely mathematical are indeed experimentally relevant.

Sources
Material for the course will be drawn from the following general books:
E.G. Virga, Variational Theories for Liquid Crystals, Chapman & Hall, London, 1994.
I.W. Stewart, The Static and Dynamic Continuum Theory of Liquid Crystals: A Mathematical Introduction, Taylor & Francis, London, 2004.
A.M. Sonnet & E.G. Virga, Dissipative Ordered Fluids: Theories for Liquid Crystals, Springer, New York, 2012.
Reference to specific research papers will be made as the course progresses.

Lecture Notes

Phenomelogy_dx.pdf

Maier_Saupe_dx.pdf

LCs & Light_vf.pdf

Onsager_BB_dx.pdf
Including 1 March a special guest lecture by Prof Peter Palffy-Muhoray (Liquid Crystal Institute, Kent State University) on Liquid Crystals and Light
Abstract.pdf