Formation mechanism and size features of multiple giant clusters in generic percolation processes.
Formation mechanism and size features of multiple giant clusters in generic percolation processes.
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DOI：
10.1103/physreve.86.051103
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发表时间：
2012-11
期刊：
影响因子：
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通讯作者：
Yang Zhang;Wei Wei-Wei;Binghui Guo;Renquan Zhang;Zhiming Zheng
中科院分区：
文献类型：
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作者：
Yang Zhang;Wei Wei-Wei;Binghui Guo;Renquan Zhang;Zhiming Zheng
逾渗模型是研究最广泛的模型之一，其中一个独特的巨集团出现后，相变。近年来，在Bohman-Frieze-Wormald（BFW）模型中发现了多巨团簇现象，这一现象引起了人们的广泛关注，本文将讨论在随机网络上的一般渗流过程中如何出现多巨团簇.通过引入合并概率，考察了影响最大团簇生长的不同机制，给出了产生多个稳定巨团簇的充分条件。在此基础上，对BFW模型和我们提出的多Erdös-Rényi（ER）模型进行了分析，揭示了这两种模型的多巨星系团形成机制.此外，在许多模型中，多个巨星系团的大小都有很大的起伏，但所有巨星系团的大小之和与普通渗流中唯一巨星系团的大小一样，都表现出自平均性。此外，我们还讨论了不同巨星系团的生长模式，发现观察到的大的涨落主要是由于在临界窗口内演化的随机行为。针对上述问题，本文分别对BFW模型和多电流变模型进行了数值模拟，为我们的分析提供了有力支持。对最大团簇的合并概率和生长机制的研究有助于深入了解多个巨团簇在渗流过程中的本质，对实际网络的建模和分析具有指导意义.
Percolation is one of the most widely studied models in which a unique giant cluster emerges after the phase transition. Recently, a new phenomenon, where multiple giant clusters are observed in the so called Bohman-Frieze-Wormald (BFW) model, has attracted much attention, and how multiple giant clusters could emerge in generic percolation processes on random networks will be discussed in this paper. By introducing the merging probability and inspecting the distinct mechanisms which contribute to the growth of largest clusters, a sufficient condition to generate multiple stable giant clusters is given. Based on the above results, the BFW model and a multi-Erdös-Rényi (ER) model given by us are analyzed, and the mechanism of multiple giant clusters of these two models is revealed. Furthermore, large fluctuations are observed in the size of multiple giant clusters in many models, but the sum size of all giant clusters exhibits self-averaging as that in the size of unique giant cluster in ordinary percolation. Besides, the growth modes of different giant clusters are discussed, and we find that the large fluctuations observed are mainly due to the stochastic behavior of the evolution in the critical window. For all the discussion above, numerical simulations on the BFW model and the multi-ER model are done, which strongly support our analysis. The investigation of merging probability and the growth mechanisms of largest clusters provides insight for the essence of multiple giant clusters in the percolation processes and can be instructive for modeling or analyzing real-world networks consisting of many large clusters.