论文标题
具有远距离相互作用的异质空间网络中的渗透
Percolation in heterogeneous spatial networks with long-range interactions
论文作者
论文摘要
我们研究了一个巨型组件在空间网络中的出现，在空间网络中，节点之间的度量距离的分布是比例不变的，并且节点之间的相互作用具有远程幂律行为。节点使用征费的飞行过程将节点定位在公制空间中，并具有关联的比例不变的步长概率密度函数，然后是将每对节点与概率函数连接的过程，该过程取决于它们之间的距离。分析该系统的一种自然方法是考虑到其可能的位置来考虑其索引之间的边缘之间的总概率。通过这样做，在该模型和具有长距离相互作用的一维晶格中发现了对应关系，这允许识别渗透过渡的条件。我们发现，巨型成分和渗透转变的出现取决于复杂的相图，该相位图表现出从弱远程相互作用到强远程相互作用的过渡。
We study the emergence of a giant component in a spatial network where the distribution of the metric distances between the nodes is scale-invariant, and the interaction between the nodes has a long-range power-law behavior. The nodes are positioned in the metric space using a Levy flight procedure, with an associated scale-invariant step probability density function, and is then followed by a process of connecting each pair of nodes with a probability function that depends on the distance between them. A natural way to analyze the system is to consider the total probability for an edge between steps in term of their indexes, by summing over their possible positions. By doing so, a correspondence is found between this model and a model of percolation in a one-dimensional lattice with long-range interactions, which allows the identification of the conditions for which a percolation transition is possible. We find that the emergence of a giant component and percolation transitions is determined by a complicated phase diagram, that exhibits a transition from weak long-range interactions to strong long-range interactions.
