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An Overview of the Oseen-Frank elastic model and some symmetry aspects of the Straley Mean-Field model for Biaxial Nematic liquid crystals

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If you have a question about this talk, please contact Mustapha Amrani.

The Mathematics of Liquid Crystals

In this (mostly) expository talk, we will present a brief overview of two independent topics: (1) the Oseen-Frank model for the spatially varying orientational properties of confined uniaxial nematic liquid crystals and (2) the mean-field model of Straley for the bulk phase behavior of biaxial nematic liquid crystals. The Oseen-Frank elastic model is a phenomenological variational model for equilibrium orientational properties characterized by a unit-length vector field. It is a macroscopic continuum model that has been very successful in modeling liquid crystals at the typical scales of experiments and devices. We will discuss the development of the model, its range of applicability, its relation to other models, and its strengths and weaknesses. The mean-field model of Straley was put forward almost 40 years ago as an attempt to describe the bulk phases and transitions for molecules of an architecture that would promote the development of spontaneous biaxial order. The model has received an intensive re-examination in recent years. Some of the symmetry properties of the model arise in unconventional ways, such as through degeneracies in the representations of the states of the system. We will discuss the symmetries of this model and the multiple symmetry-breaking bifurcations encountered in the numerical exploration of its equilibrium phases.

This talk is part of the Isaac Newton Institute Seminar Series series.

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