Landau–De Gennes Theory of Nematic Liquid Crystals: the Oseen–Frank Limit and Beyond

By Apala Majumdar, Arghir Zarnescu. 2008

295 citations recorded by the source corpus.

We study global minimizers of a continuum Landau–De Gennes energy functional for nematic liquid crystals, in three-dimensional domains, subject to uniaxial boundary conditions. We analyze the physically relevant limit of small elastic constant and show that global minimizers converge strongly, in W1,2, to a global minimizer predicted by the Oseen–Frank theory for uniaxial nematic liquid crystals with constant order parameter. Moreover, the convergence is uniform in the interior of the domain, away from the singularities of the limiting Oseen–Frank global minimizer. We obtain results on the rate of convergence of the eigenvalues and the regularity of the eigenvectors of the Landau–De Gennes global minimizer. We also study the interplay between biaxiality and uniaxiality in Landau–De Gennes global energy minimizers and obtain estimates for various related quantities such as the biaxiality parameter and the size of admissible strongly biaxial regions.

Subfields: Applied Mathematics, Electronic, Optical and Magnetic Materials, Mechanical Engineering

View Paper: https://www.semanticscholar.org/paper/a849942fb7dd252386cf94ff2836b5ec44894c16

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In Applied Mathematics

1. Arghir Zarnescu
2. Marius Paicu
3. J. Ball
4. Bixiang Wang
5. Ping Zhang
6. José Valero
7. F. Lin
8. Alain Miranville

In Electronic, Optical and Magnetic Materials

1. Marius Paicu
2. Arghir Zarnescu
3. J. Ball

In Mechanical Engineering

1. Marius Paicu
2. Arghir Zarnescu

Citations in the corpus

• Energy Dissipation and Regularity for a Coupled Navier–Stokes and Q-Tensor System (2010, background): “We also need to assume from now on that c > 0 (5) This assumption is necessary from a modelling point of view (see [24],[25] ) so that the energy F (see next section, relation (6)) is bounded from below,”
• Orientability and Energy Minimization in Liquid Crystal Models (2010, background): “This convergence, as L → 0, was studied initially in [24] and further refined in [27].”