SEMINAR “Contemporary Analysis and Partial Differential Equations”





Georgy Kitavtsev

Middle East Technical University, Northern Cyprus Campus

Liquid crystal defects in the Landau–de Gennes theory of liquid crystals

Tuesday, 24 January 2023 at 12:00

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In this talk I will introduce and motivate Q-tensors and the associated Landau–de Gennes energy modelling liquid crystal configurations not far from the thermodynamic equilibrium. İmposing k-radially symmetric boundary conditions I will show that the critical points consistent with the symmetry of the boundary conditions exist only in the case k=2 and identify three types of radial profiles: with two, three or full five components and numerically investigate their minimality and stability properties depending on suitable parameters. Generic bifurcation diagrams for different type solutions are then calculated numerically and justified analytically. This is a joint work with Valeriy Slastikov and Jonathan Robbins (University of Bristol) and Arghir Zarnescu (Basque Center for Applied Mathematics).