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- 2018
初始条件对网络渗流变换的影响
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Abstract:
近年来，不同添边规则下的网络渗流特征得到了广泛研究，但系统初始条件对渗流变换的影响少有关注。该文研究了初始分支尺度服从指数分布条件下的经典ER（Er？ds-Rényi）渗流过程，通过分支凝聚过程的斯莫洛科夫斯基方程解析分析发现，与经典ER渗流过程相比，尽管渗流仍然连续，但在相变点附近，分支尺度分布不再服从幂律分布，同时，敏感度在相变点也不再满足居里-外斯定律。
| [1] | HENLEY C L. Statics of a ‘self-organized’ percolation model[J]. Phys Rev Lett, 1993, 71(1):2741-2744. |
| [2] | ACHLIOPTAS D, D'SOUZA R M, SPENCER J. Explosive percolation in random networks[J]. Science, 2009, 323(5920):1453-1555. |
| [3] | CHEN Xiao-long, YANG Chun, ZHONG Lin-feng, et al. Crossover phenomena of percolation transition in evolution networks with hybrid attachment[J]. Chaos, 2016, 26:083114. |
| [4] | da COSTA R A, DOROGOVTSEV S N, GOLTSEV A V, et al. Solution of the explosive percolation quest Ⅱ. Infinite-order transition produced by the initial distributions of clusters[J]. Phys Rev E, 2015, 91(3):032140. |
| [5] | SMOLUCHOWSKI M V, DIFFUSION D V U. Brownsche bewegung und koagulation von kolloidteilchen[J]. Phys Zeits, 1916, 17:557-585. |
| [6] | Lü L, CHEN D, REN X L, et al. Vital nodes identification in complex networks[J]. Physics Reports, 2016, 650:1-63. |
| [7] | MORONE F, MAKSE H A. Influence maximization in complex networks through optimal percolation[J]. Nature, 2015, 524:65-68. |
| [8] | STAUFFER D, AHARONY A. Introduction to percolation theory[M]. London:Taylor & Francis, 1994. |
| [9] | DOROGOVTSEV S N. Lectures on complex networks[M]. Oxford, UK:Oxford University Press, 2010. |
| [10] | BROADBENT S R, HAMMERSLY J M. Percolation processes I crystals and mazes[J]. Proceedings of the Cambridge Philosophical Society, 1957, 53(3):629-641. |
| [11] | ERD？S P, RéNYI A. On the evolution of random graphs[J]. Publ Math Inst Hungar Acad Sci, 1960, 5(1):17-61. |
| [12] | MOORE C, NEWMAN M E J. Epidemics and percolation in small-world networks[J]. Phys Rev E, 2000, 61(5):5678-5682. |
| [13] | PAN R K, KIVELA M, SARAMAKI J, et al. Using explosive percolation in analysis of real-world networks[J]. Phys Rev E, 2011, 83(4):046112. |
| [14] | ERD？S P, RéNYI A. On the evolution of random graphs Ⅱ[J]. Bull Inst Int Stat, 1961, 38(4):343-347. |
| [15] | de ARCANGELIS L, REDNER L, CONIGLIO A. Anomalous voltage distribution of random resistor networks and a new model for the backbone at the percolation threshold[J]. Phys Rev B, 1985, 31(7):4725-4727. |
| [16] | ROZENFELD H D, GALLOS L K, MAKSE H A. Explosive percolation in the human protein homology network[J]. Eur Phys J B, 2010, 75(3):305-310. |
| [17] | 陈小龙, 杨春, 李志鹏, 等. 复杂网络爆炸渗流研究综述[J]. 电子科技大学学报, 2015, 44(1):12-21. CHEN Xiao-long, YANG Chun, LI Zhi-peng, et al. Review of explosive percolation of the complex networks[J]. Journal of University of Electronic Science and Technology of China, 2015, 44(1):12-21. |
| [18] | da COSTA R A, DOROGOVTSEV S N, GOLTSEV A V, et al. Mendes solution of the explosive percolation quest Ⅱ. infinite-order transition produced by the initial distributions of clusters[J]. Phys Rev E, 2015, 91(3):032140. |
| [19] | KRAOIVSKY P L, REDNER S, BEN-NAIM E. A kinetic view of statistical physics[M]. Cambridge, UK:Cambridge University Press, 2010. |
| [20] | da COSTA R A, DOROGOVTSEV S N, GOLTSEV A V, et al. Inverting the Achlioptas rule for explosive percolation[J]. Phys Rev E, 2015, 91(4):042130. |
