Finite element analysis of a nematic liquid crystal Landau-de Gennes model with quartic elastic terms

Jacob Elafandi, Franziska Weber
{"title":"Finite element analysis of a nematic liquid crystal Landau-de Gennes model with quartic elastic terms","authors":"Jacob Elafandi, Franziska Weber","doi":"arxiv-2409.09837","DOIUrl":null,"url":null,"abstract":"In arXiv:1906.09232v2, Golovaty et al. present a $Q$-tensor model for liquid\ncrystal dynamics which reduces to the well-known Oseen-Frank director field\nmodel in uniaxial states. We study a closely related model and present an\nenergy stable scheme for the corresponding gradient flow. We prove the\nconvergence of this scheme via fixed-point iteration and rigorously show the\n$\\Gamma$-convergence of discrete minimizers as the mesh size approaches zero.\nIn the numerical experiments, we successfully simulate isotropic-to-nematic\nphase transitions as expected.","PeriodicalId":501162,"journal":{"name":"arXiv - MATH - Numerical Analysis","volume":"18 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Numerical Analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.09837","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0

Abstract

In arXiv:1906.09232v2, Golovaty et al. present a $Q$-tensor model for liquid crystal dynamics which reduces to the well-known Oseen-Frank director field model in uniaxial states. We study a closely related model and present an energy stable scheme for the corresponding gradient flow. We prove the convergence of this scheme via fixed-point iteration and rigorously show the $\Gamma$-convergence of discrete minimizers as the mesh size approaches zero. In the numerical experiments, we successfully simulate isotropic-to-nematic phase transitions as expected.
查看原文
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
带有四次弹性项的向列液晶 Landau-de Gennes 模型的有限元分析
在 arXiv:1906.09232v2 中,Golovaty 等人提出了液晶动力学的 $Q$ 张量模型,该模型可还原为单轴状态下著名的奥森-弗兰克导演场模型。我们研究了一个密切相关的模型,并提出了相应梯度流的能量稳定方案。我们通过定点迭代证明了该方案的收敛性,并严格证明了当网格尺寸趋近于零时离散最小值的伽马收敛性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 去求助
来源期刊
自引率
0.00%
发文量
0
期刊最新文献
A Lightweight, Geometrically Flexible Fast Algorithm for the Evaluation of Layer and Volume Potentials Adaptive Time-Step Semi-Implicit One-Step Taylor Scheme for Stiff Ordinary Differential Equations Conditions aux limites fortement non lin{é}aires pour les {é}quations d'Euler de la dynamique des gaz Fully guaranteed and computable error bounds on the energy for periodic Kohn-Sham equations with convex density functionals A novel Mortar Method Integration using Radial Basis Functions
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 联系我们:info@booksci.cn
Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。
Copyright © 2023 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1