ABSTRACT

Nematic liquid crystals are classical examples of mesogenic materials that are intermediate in physical character between solids and conventional liquids. Nematic liquid crystals exhibit a degree of long-range orientational order i.e. there are locally preferred directions of averaged molecular alignment referred to as "directors". We briefly review two popular continuum theories for nematic liquid crystals: the OseenFrank theory for uniaxial nematics with constant order and the Landau-de Gennes theory which can account for uniaxiality, biaxiality and variable order. We model two multistable systems: annular chambers filled with fd-viruses or nematic-like materials and nematic-filled square chambers. Both systems are multistable in the sense that they can support multiple stable equilibria, in some cases stabilised by interior and boundary defects, as a function of the geometry, boundary conditions and temperature. We compare the Oseen-Frank and Landau-de Gennes results in both cases and give examples of new stable spatial patterns captured by the Landau-de Gennes theory, outside the scope of the Oseen-Frank approach. We use a combination of methods from calculus of variations, singular perturbation theory, bistable reaction diffusion equations and powerful numerical methods for partial differential equations. This is joint work with a number of collaborators who will be acknowledged throughout the talk.