Year: 2013
Type: dissertation
Abstract: In this thesis, we consider two problems in the Q-tensor theory of nematic liquid crystals. The first concerns eigenvalue constraints on the Q-tensor order parameter. In particular, by employing a singular potential constructed by Ball and Majumdar, we consider the existence, regularity and "strict physicality" of weak solutions to the Beris-Edwards equations of nemato-hydrodynamics. In the second part of the thesis, we consider a gradient flow of the well-studied Landau-de Gennes energy. We prove some rigorous results on the average long-time statistical behaviour of its solutions, which are in agreement with experimental observations in the condensed matter physics literature.
Author: Wilkinson, Mark
Institution: University of Oxford
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W915474948