2017/10/08 by Apala Majumdar, Yiwei Wang, Majumdar, Apala +1
Biochemistry, Genetics and Molecular Biology · Engineering · Materials Science · Mathematics · Physics and Astronomy · #Advanced Materials and Mechanics #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Liquid Crystal Research Advancements #Plant Reproductive Biology #Soft Condensed Matter (cond-mat.soft) #cond-mat.soft #math.AP
paper · pdf · doi:10.48550/arxiv.1710.02783
openalex publication_date 2017/10/08 · arxiv created 2017/10/25 · arxiv updated 2017/10/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study uniaxial solutions of the Euler-Lagrange equations for a Landau-de Gennes free energy for nematic liquid crystals, with a fourth order bulk potential, with and without elastic anisotropy. In the elastic isotropic case, we show that (i) all uniaxial solutions of the Euler-Lagrange equations, with a director field of certain symmetry, necessarily have the radial-hedgehog structure modulo an orthogonal transformation, (ii) the "escape into third dimension" director cannot correspond to a purely uniaxial solution of the Landau-de Gennes Euler-Lagrange equations and we do not use artificial assumptions on the scalar order parameter and (iii) there are no non-trivial uniaxial solutions that have ez as an eigenvector. In the elastic anisotropic case, we prove that all uniaxial solutions of the corresponding Euler-Lagrange equations, with a certain symmetry, are strictly of the radial-hedgehog type, i.e. the elastic anisotropic case enforces the radial-hedgehog structure (or the degree +1-vortex structure) more strongly than the elastic isotropic case and the associated partial differential equations are technically far more difficult than in the elastic isotropic case.