Calculus of Variations and Geometric Measure Theory

G. Di Fratta - J. Robbins - V. Slastikov - A. Zarnescu

Landau-de Gennes corrections to the Oseen-Frank theory of nematic liquid crystals

created by difratta on 30 Apr 2021


Published Paper

Inserted: 30 apr 2021
Last Updated: 30 apr 2021

Journal: Archive for Rational Mechanics and Analysis
Volume: 236
Year: 2020

ArXiv: 1904.02410 PDF


We study the asymptotic behavior of the minimisers of the Landau-de Gennes model for nematic liquid crystals in a two-dimensional domain in the regime of small elastic constant. At leading order in the elasticity constant, the minimum-energy configurations can be described by the simpler Oseen-Frank theory. Using a refined notion of $\Gamma$-development we recover Landau-de Gennes corrections to the Oseen-Frank energy. We provide an explicit characterisation of minimizing $Q$-tensors at this order in terms of optimal Oseen-Frank directors and observe the emerging biaxiality. We apply our results to distinguish between optimal configurations in the class of conformal director fields of fixed topological degree saturating the lower bound for the Oseen-Frank energy.