论文标题
在六角形上减少Landau-De Gennes模型的解决方案景观
Solution landscape of a reduced Landau-de Gennes model on a hexagon
论文作者
论文摘要
我们研究了在固定温度下，在二维六边形上降低的landau-de Gennes模型的溶液景观，这是$λ$ ---边缘长度的函数。这是用于降低常规多边形方法的通用示例。我们将基于高指数优化的缩小二聚体方法应用于系统地构建由多个缺陷解决方案及其之间的关系组成的解决方案景观。我们报告了一个新的稳定t状态，该状态具有索引-0 $，其内部$ -1/2 $缺陷；具有多个内部缺陷的高索引鞍点的新类别称为H类和TD类；用$λ^2 $的马鞍点的摩尔斯索引变化，以及可以控制和转移动态途径的高索引鞍点介导的新型途径。这些鞍点提供的缺陷的拓扑度，位置和多样性的范围可用于浏览列液晶和其他相关软物质系统的复杂解决方案景观。
We investigate the solution landscape of a reduced Landau--de Gennes model for nematic liquid crystals on a two-dimensional hexagon at a fixed temperature, as a function of $λ$---the edge length. This is a generic example for reduced approaches on regular polygons. We apply the high-index optimization-based shrinking dimer method to systematically construct the solution landscape consisting of multiple defect solutions and relationships between them. We report a new stable T state with index-$0$ that has an interior $-1/2$ defect; new classes of high-index saddle points with multiple interior defects referred to as H class and TD class; changes in the Morse index of saddle points with $λ^2$ and novel pathways mediated by high-index saddle points that can control and steer dynamical pathways. The range of topological degrees, locations and multiplicity of defects offered by these saddle points can be used to navigate through complex solution landscapes of nematic liquid crystals and other related soft matter systems.
