论文标题
渗透网络的渗透和解散
Percolation and Dissolution of Borromean Networks
论文作者
论文摘要
受拓扑链接的DNA网络的实验的启发，我们考虑了硼曲网络的连通性，在该网络中，没有两个环共享成对链接，但三个环组成的组形成了不可分割的三胞胎。具体而言，我们专注于平方晶格，每个节点都嵌入一个循环，该环路与其最近的邻居成对形成了一个浮力链路。通过将Borromean Link网络映射到晶格表示上，我们研究了这些网络的渗透阈值（巨型组件所需的占用节点的比例）以及溶解属性：如果网络溶解给Varying degrees，则将释放的拓扑链接光谱。我们发现，当大约60.75％的节点被占据时，浮游平方晶格的渗透阈值发生，略高于正方形晶格的59.27 \％\％。与HOPF连接网络的溶解相比，溶解的硼晶网络将产生更多的孤立回路，每个单个环的孤立三胞胎较少。我们的仿真结果可用于预测合成化学产生的漏洞结构的实验。
Inspired by experiments on topologically linked DNA networks, we consider the connectivity of Borromean networks, in which no two rings share a pairwise-link, but groups of three rings form inseparable triplets. Specifically, we focus on square lattices at which each node is embedded a loop which forms a Borromean link with pairs of its nearest neighbors. By mapping the Borromean link network onto a lattice representation, we investigate the percolation threshold of these networks, (the fraction of occupied nodes required for a giant component), as well as the dissolution properties: the spectrum of topological links that would be released if the network were dissolved to varying degrees. We find that the percolation threshold of the Borromean square lattice occurs when approximately 60.75\% of nodes are occupied, slightly higher than the 59.27\% typical of a square lattice. Compared to the dissolution of Hopf-linked networks, a dissolved Borromean network will yield more isolated loops, and fewer isolated triplets per single loop. Our simulation results may be used to predict experiments from Borromean structures produced by synthetic chemistry.
