Curvature and defects in liquid crystals and other soft materials: Differential geometry isn’t just for cosmology any more! – Jonathan Selinger

Date: Thu. February 27th, 2014, 4:15 pm-5:15 pm
Location: Rockefeller 301

Liquid-crystal membranes have a coupling between curvature and orientational order: Defects in the orientational order can induce curvature, and conversely, curvature leads to an effective geometrical potential acting on defects. In this colloquium, we present basic introductions to liquid-crystal physics and to differential geometry, and discuss the fundamental origin of the coupling. In particular, we show that several different types of coupling are possible, depending on whether the membranes are fluid or cross-linked, and on whether the interactions are fundamentally two- or three-dimensional. These theoretical considerations can explain experiments on lipid vesicles and liquid-crystal elastomer films, and provide opportunities to design membranes that will relax into selected shapes.