论文标题
三维立方体上Landau-de Gennes自由能的关键点的层次结构
Hierarchies of Critical Points of a Landau-de Gennes Free Energy on Three-Dimensional Cuboids
论文作者
论文摘要
我们研究了三维（3D）立方体中Landau-De Gennes（LDG）自由能的临界点，该临界点是模拟列表平衡的模型。我们开发了一种基于混合鞍动力学的算法，以有效计算这些3D系统的解决方案景观。我们的主要结果涉及（a）从2D LDG临界点数据库中构建3D LDG临界点以及（b）研究横截面尺寸和Cuboid高度对溶液景观的影响。在这样做的过程中，我们发现了通过将3D临界点堆叠在彼此之上的多层3D LDG临界点，这是由3D LDG临界点介导的不同能量最小值与新型可稳态的Escable Escapated Solutions介导的新型途径，所有这些都可以调整为量身定制的静态静态液体液体晶体系统的量身定制的静态和动态性能。
We investigate critical points of a Landau-de Gennes (LdG) free energy in three-dimensional (3D) cuboids, that model nematic equilibria. We develop a hybrid saddle dynamics-based algorithm to efficiently compute solution landscapes of these 3D systems. Our main results concern (a) the construction of 3D LdG critical points from a database of 2D LdG critical points and (b) studies of the effects of cross-section size and cuboid height on solution landscapes. In doing so, we discover multiple-layer 3D LdG critical points constructed by stacking 3D critical points on top of each other, novel pathways between distinct energy minima mediated by 3D LdG critical points and novel metastable escaped solutions, all of which can be tuned for tailor-made static and dynamic properties of confined nematic liquid crystal systems in 3D.
