论文标题
从平面的周期性瓷砖中构建编织和多产素基序
Construction of weaving and polycatenane motifs from periodic tilings of the plane
论文作者
论文摘要
双重周期性（DP）编织和聚会烯酸是嵌入欧几里得增厚平面中的复杂纠缠结构，在两个独立方向的翻译下不变。它们的拓扑特性在定期晶格下的商空间内完全编码，我们称之为主题。在示意图上，基序是圆环上的特定类型的链接图，由DP编织的必需闭合曲线或DP聚catenanes的无效曲线组成。在本文中，我们介绍了一种组合方法，以使用多边形链接变换的概念从平面DP瓷砖中构建这些图案。我们还提出了一种预测可以从给定的DP瓷砖和选定的多边形链接方法构建的基序的方法。这种方法在材料科学和化学等各种学科中具有潜在的应用。
Doubly periodic (DP) weaves and polycatenanes are complex entangled structures embedded in the Euclidean thickened plane, invariant under translations in two independent directions. Their topological properties are fully encoded within a quotient space under a periodic lattice, which we refer to as a motif. On the diagrammatic level, a motif is a specific type of link diagram on the torus, consisting of essential closed curves for DP weaves or null-homotopic curves for DP polycatenanes. In this paper, we introduce a combinatorial methodology to construct these motifs from planar DP tilings using the concept of polygonal link transformations. We also present an approach to predict the type of motif that can be constructed from a given DP tiling and a chosen polygonal link method. This approach has potential applications in various disciplines, such as materials science and chemistry.
