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- W2044127515 abstract "This work was inspired by a paper of Lonberg and Meyer [Phys. Rev. Lett. 55, 718 (1985)], who observed a Fr'eedericksz threshold different from the usual one, ${mathit{U}}_{mathrm{Fred}}$=ensuremath{pi} ensuremath{surd}${mathit{K}}_{1}$/ensuremath{Delta}ensuremath{varepsilon}, which results from a one-dimensional (1D) stability analysis and which underlies measurement techniques of the Frank elastic constant ${mathit{K}}_{1}$. The new threshold occurs in polymer constituent nematic liquid crystals, which possess, compared to the usual low-molecular-weight nematic mixtures, an unusually large ratio of ${mathit{K}}_{1}$/${mathit{K}}_{2}$. It is accompanied by a periodic splay-twist distortion parallel to the director field. The stability estimations given by Lonberg and Meyer were later confirmed by Cohen and Luskin [in Nematics: Mathematical and Physical Aspects, Vol. 332 of 2 NATO Advanced Study Institute, Series C: Mathematical and Physical Sciences, edited by J. F. Coron, F. Helein, and J. M. Ghidaglia (Kluwer, Dordrecht, 1991), p. 261], who used a new variation method to determine ``weak stability.'' Due to the fundamental role of Fr'eedericksz transitions not only in measurement techniques, but also in the operation of many electro-optical devices, I found that the problem of stability in 3D deserves systematic investigation. Since there is not much hope of obtaining analytical solutions of the respective Euler-Lagrange equations in 3D, I programmed a scheme that simulates the measurement process of elastic constants at different geometries. As a result, I could first reconfirm the known effect, and second, predict a new instability mode that should occur in nematic liquid crystals with a negative dielectric anisotropy subjected to homeotropic anchoring. Analytical expressions for the 3D threshold values support the numerical results." @default.
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- W2044127515 date "1994-11-01" @default.
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- W2044127515 title "New Fréedericksz thresholds in three dimensions" @default.
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- W2044127515 doi "https://doi.org/10.1103/physreve.50.3774" @default.
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