Random nanowire networks: Identification of a current-carrying subset of wires using a modified wall follower algorithm

TL;DR

This paper introduces a modified wall follower algorithm to efficiently identify the current-carrying backbone in random nanowire networks, improving understanding of their conductive properties.

Contribution

A novel modification of the wall follower algorithm is proposed for backbone identification, reducing the need to visit all edges in nanowire network analysis.

Findings

Percolation cluster strength approaches unity with increasing wire density.

The backbone becomes nearly identical to the entire cluster plus simple dead ends.

Algorithm complexity varies from square root to linear in the number of vertices.

Abstract

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 $\Theta(N_\text{V})$. 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.