二分网上的靴襻渗流

万宝惠; 张鹏; 张晶; 狄增如; 樊瑛

doi:10.7498/aps.61.166402

摘要

靴襻渗流最早应用于统计物理学中研究磁铁因非磁性杂质导致磁有序的降低并最终消失的现象. 随着复杂网络研究的深入, 许多学者展开网络上的靴襻渗流研究. 在自然界中, 许多系统自然呈现出二分结构, 二分网络是复杂网络中的一种重要的网络模式. 本文通过建立动力学方程和计算机仿真模拟的方法研究二分网上的靴襻渗流, 关注的参数是二分网中两类节点初始的活跃比例和活跃阈值, 分别用f1, f2和Ω1, Ω2表示, 得到二分网两类节点终态活跃比例随初始活跃比例的变化会发生相变等结论. 同时验证了动力学方程与仿真模拟的一致性.

关键词:

Abstract

Bootstrap percolation was first used in statistic physics to study the phenomenon that magnetic-order goes down and disappears because of the disturbance of nonmagnetic impurity. With the development of complex network, the application of bootstrap percolation in network has attracted much attention. In the real world, many systems naturally exhibit the two-branch structure. And bipartite network is one of important networks in complex networks. In this paper, we use the dynamics equation and computational simulation to study the bootstrap percolation in bipartite networks. The parameters we focus on are the node initial active ratios f1 and f2 and active thresholds Ω1, and Ω2. We draw the conclusion that the ratio of active nodes has discontinuous transition, which will gradually disappear with parameters varying. We also prove the consistency between the dynamic equation and simulation results.

Keywords:

作者及机构信息

1.
北京师范大学管理学院系统科学系, 北京 100875;

2.
北京邮电大学理学院, 北京 100876

基金项目: 国家自然科学基金 (批准号: 70771011, 61174150, 11147119); 教育部新世纪人才支持计划 (批准号: NCET-09-0228)和中央高校基本科研业务费 (批准号: G470422)资助的课题.

Authors and contacts

1.
Department of Systems Science, School of Management, Beijing Normal University, Beijing 100875, China;

2.
School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 70771011, 61174150, 11147119), the Program for New Century Excellent Talents in University of Ministry of Education of China (Grant No. NCET-09-0228), and the Fundamental Research Fund for the Central Universities, China (Grant No. G470422).

参考文献

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[11]	Ertel W, Frobose K, Jackle J 1988 J. Chem. Phys. 88 5027
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[15]	Ma Z F, Zhang P, Wu Y, Li W H, Zhuang Y Q, Du L 2010 Chin. Phys. B 19 7201
[16]	Holroyd A E 2003 Probab. Theory Relat. Fields 125 195
[17]	Holroyd A E 2006 Electron. J. Probab. 11 418
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[26]	Latapy M, Magnien C, Vecchio N D 2008 Soc. Networks 30 31

施引文献

[1]	Chalupa J, Leath P L, Reich G R 1979 J. Phys. C 12 L31
[2]	Wu K, Gu Z N 1996 Acta Phys. Sin. 45 1905 (in Chinese) [吴克,顾镇南 1996 45 1905]
[3]	Yi L, Xiao Y, Yao K L 1993 Acta Phys. Sin. (Overseas Ed.) 2 458
[4]	Zheng M S, Liu Y P 1993 Acta Phys. Sin. 42 304 (in Chinese) [郑茂盛,刘云鹏 1993 42 304]
[5]	Ye G X, Xu Y Q, Wang J S, Zhang Q R 1994 Acta Phys. Sin. 43 4 (in Chinese) [叶高翔,许宇庆,王劲松,张其瑞 1994 43 4]
[6]	Eckmann J P, Feinerman O, Gruendlinger L, Moses E, Soriano J, Tlusty T 2007 Phys. Rep. 449 54
[7]	Soriano J, Marttnez M R, Tlusty T, Moses E 2008 Proc. Natl. Acad. Sci. 105 13758
[8]	Goltsev A V, Abreu F V de, Dorogovtsev S N, Mendes J F F 2010 Phys. Rev. E 81 1921
[9]	Adler J, Palmer R G, Meyer H M 1987 Phys. Rev. Lett. 58 882
[10]	Nakanishi H, Takano H 1986 Phys. Lett. ll5A 117
[11]	Ertel W, Frobose K, Jackle J 1988 J. Chem. Phys. 88 5027
[12]	Sellitto M, Biroli G, Toninell C 2005 Europhys. Lett. 69 496
[13]	Toninelli C, Biroli G, Fisher D S 2006 Phys. Rev. Lett. 96 5702
[14]	Chalupa J, Leath P L, Reich G R 1981 J. Phys. C: Solid State Phys. 14 3187
[15]	Ma Z F, Zhang P, Wu Y, Li W H, Zhuang Y Q, Du L 2010 Chin. Phys. B 19 7201
[16]	Holroyd A E 2003 Probab. Theory Relat. Fields 125 195
[17]	Holroyd A E 2006 Electron. J. Probab. 11 418
[18]	Balogh J, Bollobas B 2006 Probab. Theory Relat. Fields 134 624
[19]	Balogh J, Pittel B G 2007 Random Struct. Alg. 30 257
[20]	Fontes L R G, Schonmann R H 2008 J. Stat. Phys. 132 839
[21]	Watts D J 2002 PNAS 99 5766
[22]	Baxter G J, Dorogovtsev S N, Goltsev A V Mendes J F F 2010 Phys. Rev. E 82 1103
[23]	Chen H B, Fan Y, Fang J Q, Di Z R 2007 Acta Phys. Sin. 58 1383 (in Chinese) [陈宏斌,樊瑛,方锦清,狄增如 2007 58 1383]
[24]	Fan Y, Suo L N, Shen X S, Hu Y Q 2008 J. BNU (Natural Science) 44 103 (in Chinese) [樊瑛, 索丽娜, 沈晓松, 胡延庆 2008 北京师范大学学报 (自然科学版) 44 103]
[25]	Ma W D, Wang L, Li R P, Shui H S, Zhou M T 2008 Acta Phys. Sin. 57 1381 (in Chinese) [马卫东,王磊,李幼平,水鸿寿,周明天 2008 57 1381]
[26]	Latapy M, Magnien C, Vecchio N D 2008 Soc. Networks 30 31

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