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Thesis

Some problems on the dynamics of nematic liquid crystals

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.

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Research group:
Oxford Centre for Nonlinear Partial Differential Equations (OxPDE)
Oxford college:
St Edmund Hall
Role:
Author

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Role:
Supervisor
Role:
Supervisor

Publication date:
2013
DOI:
Type of award:
DPhil
Level of award:
Doctoral
Awarding institution:
University of Oxford

Language:
English
Keywords:
Subjects:
UUID:
uuid:668f7a3b-b9f0-4126-aceb-d7bbe4230f08
Local pid:
ora:11463
Deposit date:
2015-05-18
ARK identifier:

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