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- W4297075296 abstract "We carry out an asymptotic analysis of a thin nematic liquid crystal in which one elastic constant dominates over the others, namely begin{align} label{energyab} inf E_varepsilon(u)quadmbox{where}quad E_varepsilon(u) := frac{1}{2}int_Omega left{varepsilon,|nabla u|^2 + frac{1}{varepsilon} ,(|u|^2 - 1)^2 + L ,(mathrm{div},u)^2right} ,dx. end{align} Here $u: Omega to mathbb R^2$ is a vector field, $0 < varepsilon ll 1 $ is a small parameter, and $L > 0$ is a fixed constant, independent of $varepsilon$. We derive the $Gamma$-limit $E_0$, which is a sum of a bulk term penalizing divergence and an Aviles-Giga type wall energy involving the cube of the jump in the tangential component of the $mathbb{S}^1$-valued order parameter. We then derive criticality conditions for $E_0$ and analyze minimization of $E_0$ both rigorously and numerically for various domains $Omega$ and a variety of Dirichlet boundary conditions." @default.
- W4297075296 created "2022-09-26" @default.
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- W4297075296 date "2017-12-01" @default.
- W4297075296 modified "2023-09-25" @default.
- W4297075296 title "A Ginzburg-Landau type problem for highly anisotropic nematic liquid crystals" @default.
- W4297075296 doi "https://doi.org/10.48550/arxiv.1712.00493" @default.
- W4297075296 hasPublicationYear "2017" @default.
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