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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Hunter–Saxton equation ： ウィキペディア英語版 Hunter–Saxton equation In mathematical physics, the Hunter–Saxton equation〔Hunter & Saxton 1991〕 :$$ (u_t + u u_x)_x = \frac \, u_x^2 is an integrable PDE that arises in the theoretical study of nematic liquid crystals. If the molecules in the liquid crystal are initially all aligned, and some of them are then wiggled slightly, this disturbance in orientation will propagate through the crystal, and the Hunter–Saxton equation describes certain aspects of such orientation waves. == Physical background == In the models for liquid crystals considered here, it is assumed that there is no fluid flow, so that only the ''orientation'' of the molecules is of interest. Within the elastic continuum theory, the orientation is described by a field of unit vectors n(''x'',''y'',''z'',''t''). For nematic liquid crystals, there is no difference between orienting a molecule in the n direction or in the −n direction, and the vector field n is then called a ''director field''. The potential energy density of a director field is usually assumed to be given by the Oseen–Frank energy functional 〔de Gennes & Prost 1994 (Ch. 3)〕 :$$ W(\mathbf,\nabla\mathbf) = \frac12 \left( \alpha (\nabla \cdot \mathbf)^2 + \beta (\mathbf \cdot (\nabla \times \mathbf))^2 + \gamma | \mathbf \times (\nabla \times \mathbf)|^2 \right), where the positive coefficients $\backslash alpha$, $\backslash beta$, $\backslash gamma$ are known as the elastic coefficients of splay, twist, and bend, respectively. The kinetic energy is often neglected because of the high viscosity of liquid crystals. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Hunter–Saxton equation」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.