Geometric methods in the elastic theory of membranes in liquid crystal phases
Geometric methods in the elastic theory of membranes in liquid crystal phases
复制标题
DOI：
10.1142/10645
复制
发表时间：
1999-03
期刊：
影响因子：
--
通讯作者：
O. Zhong-can;Jixing Liu;Yuzhang Xie
中科院分区：
文献类型：
--
作者：
O. Zhong-can;Jixing Liu;Yuzhang Xie
包含对膜的机械平衡和变形作为微分几何中的表面问题的全面描述。继 W. Helfrich 的开创性工作之后，流体膜被视为向列相或近晶相 - 液晶膜，其弹性能量形式正是从液晶的曲率弹性理论推导出来的。随着表面变化，固定渗透压和表面张力下能量的最小化给出了几何中的表面方程，这涉及数学的潜在兴趣。本文介绍了作者对方程的解进行的研究结果。
Contains a comprehensive description of the mechanical equilibrium and deformation of membranes as a surface problem in differential geometry. Following the pioneering work by W. Helfrich, the fluid membrane is seen as a nematic or smectic - a liquid crystal film and its elastic enegy form is deduced exactly from the curvature elastic theory of the liquid crystals. With surface variation, the minimization of the energy at the fixed osmotical pressure and surface tension gives a surface equation in geometry that involves potential interest in mathematics. This text presents the results of the investigation into the solution of the equation that have been carried out by the authors.