论文标题
部分可观测时空混沌系统的无模型预测
A Reduced Landau-de Gennes Study for Nematic Equilibria in Three-Dimensional Prisms
论文作者
论文摘要
我们在三维棱镜内部建模了夜间液晶构型，并在所有棱镜表面上具有多边形的横截面和差异的边界条件。我们在减少的Landau-De Gennes框架中工作，顶部和底部表面的Dirichlet条件在某种意义上是特殊的，它们是多边形横截面上减少的Landau-De Gennes能量的关键点。边界条件的选择使我们能够在多边形横截面上的二维Landau-de Gennes解决方案景观上的三维Landau-de Gennes临界点和途径之间进行直接对应关系。我们通过渐近分析和数值示例探索这个概念，重点是立方体和六角形棱镜，重点是由二维解决方案景观量身定制的三维多稳定性。
We model nematic liquid crystal configurations inside three-dimensional prisms, with a polygonal cross-section and Dirichlet boundary conditions on all prism surfaces. We work in a reduced Landau-de Gennes framework, and the Dirichlet conditions on the top and bottom surfaces are special in the sense, that they are critical points of the reduced Landau-de Gennes energy on the polygonal cross-section. The choice of the boundary conditions allows us to make a direct correspondence between the three-dimensional Landau-de Gennes critical points and pathways on the two-dimensional Landau-de Gennes solution landscape on the polygonal cross-section. We explore this concept by means of asymptotic analysis and numerical examples, with emphasis on a cuboid and a hexagonal prism, focusing on three-dimensional multistability tailored by two-dimensional solution landscapes.
