Dimension Reduction for the Landau-de Gennes Model on Curved Nematic Thin Films
作者: Dmitry GolovatyJosé Alberto MonteroPeter Sternberg
作者单位: 1The University of Akron
2Pontificia Universidad Católica de Chile
3Indiana University Bloomington
刊名: Journal of Nonlinear Science, 2017, Vol.27 (6), pp.1905-1932
来源数据库: Springer Nature Journal
DOI: 10.1007/s00332-017-9390-5
关键词: NematicLandau-de GennesGamma-convergenceThin film35J6249J45
英文摘要: We use the method of \(\Gamma \) -convergence to study the behavior of the Landau-de Gennes model for a nematic liquid crystalline film attached to a general fixed surface in the limit of vanishing thickness. This paper generalizes the approach in Golovaty et al. (J Nonlinear Sci 25(6):1431–1451, 2015 ) where we considered a similar problem for a planar surface. Since the anchoring energy dominates when the thickness of the film is small, it is essential to understand its influence on the structure of the minimizers of the limiting energy. In particular, the anchoring energy dictates the class of admissible competitors and the structure of the limiting problem. We assume general weak anchoring conditions on the top and the bottom surfaces of the film and strong Dirichlet boundary...
原始语种摘要: We use the method of \(\Gamma \) -convergence to study the behavior of the Landau-de Gennes model for a nematic liquid crystalline film attached to a general fixed surface in the limit of vanishing thickness. This paper generalizes the approach in Golovaty et al. (J Nonlinear Sci 25(6):1431–1451, 2015 ) where we considered a similar problem for a planar surface. Since the anchoring energy dominates when the thickness of the film is small, it is essential to understand its influence on the structure of the minimizers of the limiting energy. In particular, the anchoring energy dictates the class of admissible competitors and the structure of the limiting problem. We assume general weak anchoring conditions on the top and the bottom surfaces of the film and strong Dirichlet boundary...
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影响因子:1.566 (2012)

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关键词翻译
关键词翻译
  • Landau 兰多牌汽车
  • frustum 平截头体
  • curvature 曲率
  • vanishing 消失
  • understand 理解
  • convergence 汇合
  • lateral 侧面的
  • anchoring 系泊
  • energy 能量
  • thickness 厚度