McAndrew Thomas C, Danforth Christopher M, Bagrow James P
Department of Mathematics and Statistics, University of Vermont, Burlington, Vermont 05405, USA and Vermont Complex Systems Center, University of Vermont, Burlington, Vermont 05405, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2015 Apr;91(4):042813. doi: 10.1103/PhysRevE.91.042813. Epub 2015 Apr 29.
Power lines, roadways, pipelines, and other physical infrastructure are critical to modern society. These structures may be viewed as spatial networks where geographic distances play a role in the functionality and construction cost of links. Traditionally, studies of network robustness have primarily considered the connectedness of large, random networks. Yet for spatial infrastructure, physical distances must also play a role in network robustness. Understanding the robustness of small spatial networks is particularly important with the increasing interest in microgrids, i.e., small-area distributed power grids that are well suited to using renewable energy resources. We study the random failures of links in small networks where functionality depends on both spatial distance and topological connectedness. By introducing a percolation model where the failure of each link is proportional to its spatial length, we find that when failures depend on spatial distances, networks are more fragile than expected. Accounting for spatial effects in both construction and robustness is important for designing efficient microgrids and other network infrastructure.
输电线、道路、管道及其他物理基础设施对现代社会至关重要。这些结构可被视为空间网络，其中地理距离在链路的功能和建设成本中发挥作用。传统上，网络鲁棒性研究主要考虑大型随机网络的连通性。然而对于空间基础设施而言，物理距离在网络鲁棒性方面也必定发挥作用。随着对微电网（即非常适合使用可再生能源的小区域分布式电网）的兴趣日益浓厚，了解小型空间网络的鲁棒性尤为重要。我们研究小型网络中链路的随机故障，其功能取决于空间距离和拓扑连通性。通过引入一种渗流模型，其中每条链路的故障与其空间长度成正比，我们发现当故障取决于空间距离时，网络比预期更脆弱。在建设和鲁棒性方面考虑空间效应对于设计高效的微电网及其他网络基础设施很重要。
