In this course I will introduce a geometric approach recently developed for the description of complex fluids, including liquid crystals and superfluids. This approach is based on various tools from geometric mechanics such as reduction by symmetries and variational principles, exploited in an infinite dimensional setting. This geometric framework allows us to solve an open problem concerning two competing descriptions of nematic liquid crystal dynamics: the Ericksen-Leslie theory and the Eringen micropolar theory. We will show that these theories are compatible, the latter being an extension of the former.
Monday 13 April : 10h00 - 12h00
Wednesday 15 April : 10h00 - 12h00