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• W3165369416 abstract "We study the effects of elastic anisotropy on the Landau-de Gennes critical points for nematic liquid crystals, in a square domain. The elastic anisotropy is captured by a parameter, $L_2$, and the critical points are described by three degrees of freedom. We analytically construct a symmetric critical point for all admissible values of $L_2$, which is necessarily globally stable for small domains i.e., when the square edge length, $lambda$, is small enough. We perform asymptotic analyses and numerical studies to discover at least $5$ classes of these symmetric critical points - the $WORS$, $Ring^{pm}$, $Constant$ and $pWORS$ solutions, of which the $WORS$, $Ring^+$ and $Constant$ solutions can be stable. Furthermore, we demonstrate that the novel $Constant$ solution is energetically preferable for large $lambda$ and large $L_2$, and prove associated stability results that corroborate the stabilising effects of $L_2$ for reduced Landau-de Gennes critical points. We complement our analysis with numerically computed bifurcation diagrams for different values of $L_2$, which illustrate the interplay of elastic anisotropy and geometry for nematic solution landscapes, at low temperatures." @default.
• W3165369416 created "2021-06-07" @default.
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• W3165369416 date "2021-05-21" @default.
• W3165369416 modified "2023-09-23" @default.
• W3165369416 title "Elastic anisotropy of nematic liquid crystals in the two-dimensional Landau-de Gennes model" @default.
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• W3165369416 doi "https://doi.org/10.48550/arxiv.2105.10253" @default.
• W3165369416 hasPublicationYear "2021" @default.
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