The Well Order Reconstruction Solution for three-dimensional wells, in the Landau-de Gennes theory
The Well Order Reconstruction Solution for three-dimensional wells, in the Landau-de Gennes theory
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DOI：
10.1016/j.ijnonlinmec.2019.103342
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发表时间：
2020-03-01
影响因子：
3.2
通讯作者：
Wang, Yiwei
中科院分区：
文献类型：
--
作者：
Canevari, Giacomo;Harris, Joseph;Wang, Yiwei
我们研究了三维方井的向列相平衡，重点研究了井序重构解(WORS)作为井大小的函数，用波长表征，井高用epsilon表示。Wors是Kralj和Majudar(2014)报告的正方形区域的独特平衡，没有考虑第三维，它们有两条相互垂直的缺陷线沿着正方形对角线运行，在正方形中心相交。我们证明了在任意井高的三维井上，满足(I)自然边界条件和(Ii)井顶和井底的真实表面能，以及侧面的Dirichlet条件下，WORS的存在性。此外，对于两种情况下足够小的lambda，WORS是全局稳定的，而随着Lambda的增加，WORS是不稳定的。我们数值计算了新的大波长和大波长的混合3D解，然后数值研究了表面锚定对锅的影响，举例说明了WORS解在3D环境中的相关性。
We study nematic equilibria on three-dimensional square wells, with emphasis on Well Order Reconstruction Solutions (WORS) as a function of the well size, characterized by lambda, and the well height denoted by epsilon. The WORS are distinctive equilibria reported in Kralj and Majumdar (2014) for square domains, without taking the third dimension into account, which have two mutually perpendicular defect lines running along the square diagonals, intersecting at the square center. We prove the existence of WORS on three-dimensional wells for arbitrary well heights, with (i) natural boundary conditions and (ii) realistic surface energies on the top and bottom well surfaces, along with Dirichlet conditions on the lateral surfaces. Moreover, the WORS is globally stable for lambda small enough in both cases and unstable as lambda increases. We numerically compute novel mixed 3D solutions for large lambda and epsilon followed by a numerical investigation of the effects of surface anchoring on the WOKS, exemplifying the relevance of the WORS solution in a 3D context.