随机纳米线网络：使用改进的墙跟随器算法识别载流导线子集
Random nanowire networks: Identification of a current-carrying subset of wires using a modified wall follower algorithm
摘要：
我们模仿随机纳米线网络的均匀，各向同性，和随机沉积的导电零宽度棒到绝缘基板上。这些棒的数量密度（每单位面积表面的物体数量）应该超过渗透阈值，即，所考虑的系统是导体。为了识别任何载流部分（骨干）的渗流集群，我们提出并实现了一个修改的著名的墙跟随算法-一种类型的迷宫求解算法。改进算法的优点是不需要访问所有的边就能识别出整个主干。该算法的复杂性很大程度上取决于图的结构，并且从$O\left(\sqrt{N_\text{V}}\right)$到$Θ(N_\text{V})$不等。该算法已被应用于不同数目密度的导电棒网络的骨干识别。我们已经发现，（i）对于高于逾渗阈值的棒数密度，随着棒数密度的增加，逾渗簇的强度迅速接近1;（ii）同时，逾渗簇变得与其主链加上最简单的死端相同，即，与度为1的顶点关联的边。该行为与所提供的分析评价一致。
英文摘要：
We mimic random nanowire networks by the homogeneous, isotropic, and random deposition of conductive zero-width sticks onto an insulating substrate. The number density (the number of objects per unit area of the surface) of these sticks is supposed to exceed the percolation threshold, i.e., the system under consideration is a conductor. To identify any current-carrying part (the backbone) of the percolation cluster, we have proposed and implemented a modification of the well-known wall follower algorithm -- one type of maze solving algorithm. The advantage of the modified algorithm is its identification of the whole backbone without visiting all the edges. The complexity of the algorithm depends significantly on the structure of the graph and varies from $O\left(\sqrt{N_\text{V}}\right)$ to $Θ(N_\text{V})$. The algorithm has been applied to backbone identification in networks with different number densities of conducting sticks. We have found that (i) for number densities of sticks above the percolation threshold, the strength of the percolation cluster quickly approaches unity as the number density of the sticks increases; (ii) simultaneously, the percolation cluster becomes identical to its backbone plus simplest dead ends, i.e., edges that are incident to vertices of degree 1. This behavior is consistent with the presented analytical evaluations.
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