The geometry of topological defects
Presenter
July 23, 2008
Keywords:
- Topological
MSC:
- 74P15
Abstract
The theory of smectic liquid crystals is notoriously difficult to study. Thermal fluctuations render them disordered through
the Landau-Peierls instability, lead to anomalous momentum dependent elasticity, and make the nematic to smectic-A transition
enigmatic, at best. I will discuss recent progress in studying large deformations of smectics which necessitate the use of nonlinear
elasticity in order to preserve the underlying rotational symmetry. By recasting the problem of smectic configurations geometrically
it is often possible to exploit toplogical information or, equivalently, boundary conditions, to confront these highly nonlinear problems.
Specifically, I will discuss edge dislocations, disclination networks in three-dimensionally modulated smectics, and large angle twist
grain boundary phases. Fortuitously, it is possible to make intimate comparison with experimental systems!