2021/05/18 by Cody D. Schimming, Jorge Viñals, Shawn W. Walker · 20 citations
Engineering · Materials Science · Mathematics · Physics and Astronomy · #Advanced Materials and Mechanics #Anisotropy #Biaxial nematic #Classical mechanics #Condensed matter physics #Disclination #Eigenvalues and eigenvectors #Elasticity (physics) #Geometry #Liquid Crystal Research Advancements #Liquid crystal #Mathematical analysis #Mathematics #Micro and Nano Robotics #Physics #Quantum mechanics #Statistical physics #Tensor (intrinsic definition) #cond-mat.soft
paper · pdf · doi:10.1016/j.jcp.2021.110441
published in Journal of Computational Physics 441, 110441 (Elsevier BV) · 37 pages, 8 figures
openalex publication_date 2021/05/18 · openalex created_date 2021/05/24 · arxiv created 2021/05/27 · arxiv updated 2021/05/28 · openalex updated_date 2026/08/05
We present a numerical method, based on a tensor order parameter description of a nematic phase, that allows fully anisotropic elasticity. Our method thus extends the Landau-de Gennes Q-tensor theory to anisotropic phases. A microscopic model of the nematogen is introduced (the Maier-Saupe potential in the case discussed in this paper), combined with a constraint on eigenvalue bounds of Q. This ensures a physically valid order parameter Q (i.e., the eigenvalue bounds are maintained), while allowing for more general gradient energy densities that can include cubic nonlinearities, and therefore elastic anisotropy. We demonstrate the method in two specific two dimensional examples in which the Landau-de Gennes model including elastic anisotropy is known to fail, as well as in three dimensions for the cases of a hedgehog point defect, a disclination line, and a disclination ring. The details of the numerical implementation are also discussed.