Oberseminar Mathematik in den Naturwissenschaften "A free-discontinuity problem for smectic liquid crystals"

Smectic liquid crystals are a phase of matter in which the constituent molecules tend to align
locally parallel to one another and to arrange themselves in layers. Experimental evidence
shows that the configuration of the layers in smectic films may be rather complex, possibly
with defects - that is, localised regions of sharp change in the orientation of the layers. Defects
may occur at isolated points, along lines or surfaces. In this talk, we discuss a free-discontinuity
variational problem for smectic A liquid crystals in two dimensions. We focus on a specific form
of the energy functional, which penalises dislocations of the layers along the defects and is lower
semicontinuous, so that minimisers exist.

The talk is based on joint work with John M. Ball (Heriot-Watt University, Edinburgh and Hong
Kong Institute of Advanced Studies) and Bianca Stroffolini (Università Federico II, Napoli).