Proves existence of weak solutions to the surface Beris-Edwards model on C^{2,1} closed hypersurfaces via Faedo-Galerkin scheme with tangent Stokes and Laplace-Beltrami eigenfunctions plus compactness.
Introduction to Q-tensor theory
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abstract
This paper aims to provide an introduction to a basic form of the ${\bf Q}$-tensor approach to modelling liquid crystals, which has seen increased interest in recent years. The increase in interest in this type of modelling approach has been driven by investigations into the fundamental nature of defects and new applications of liquid crystals such as bistable displays and colloidal systems for which a description of defects and disorder is essential. The work in this paper is not new research, rather it is an introductory guide for anyone wishing to model a system using such a theory. A more complete mathematical description of this theory, including a description of flow effects, can be found in numerous sources but the books by Virga and Sonnet and Virga are recommended. More information can be obtained from the plethora of papers using such approaches, although a general introduction for the novice is lacking. The first few sections of this paper will detail the development of the ${\bf Q}$-tensor approach for nematic liquid crystalline systems and construct the free energy and governing equations for the mesoscopic dependent variables. A number of device surface treatments are considered and theoretical boundary conditions are specified for each instance. Finally, an example of a real device is demonstrated.
years
2026 2verdicts
UNVERDICTED 2representative citing papers
Equivariant neural networks for 2D Q-tensor prediction in nematic liquid crystals achieve lower errors and better generalization than non-equivariant models while satisfying symmetry constraints.
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Existence of weak solutions of the surface Beris-Edwards model
Proves existence of weak solutions to the surface Beris-Edwards model on C^{2,1} closed hypersurfaces via Faedo-Galerkin scheme with tangent Stokes and Laplace-Beltrami eigenfunctions plus compactness.