Percolation and dissolution of Borromean networks
Percolation and dissolution of Borromean networks
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DOI：
10.1103/physreve.107.024304
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发表时间：
2023-02-07
影响因子：
2.4
通讯作者：
Klotz, Alexander R.
中科院分区：
文献类型：
--
作者：
Ferschweiler, Donald G.;Blair, Ryan;Klotz, Alexander R.
受拓扑连接DNA网络实验的启发，我们考虑了Borroean网络的连通性，在该网络中，没有两个环共享两两链接，但三个环组成的组形成了不可分的三元组。具体地说，我们将重点放在正方形格子上，在正方形格子上，每个节点嵌入一个循环，该循环与其最近的邻居对形成Borroean链接。通过将Borroean链接网络映射到格子表示上，我们研究了这些网络的渗流阈值(一个巨大分量所需的占用节点的比例)，以及它的溶解性质：如果网络被不同程度地溶解，将释放的拓扑链的谱。我们发现，当大约60.75%的节点被占据时，Borroean正方形晶格的渗流阈值出现，略高于正方形晶格的59.27%。与分解Hopf连接的网络相比，溶解的Borroean网络将产生更多的孤立环，而每个单个环产生更少的孤立三联体。我们的模拟结果可以用来预测由合成化学产生的Borromean型结构的实验。
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.