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

[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

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

[1]	高彦丽, 徐维南, 周杰, 陈世明. 二元双层耦合网络渗流行为分析. , 2024, 73(16): 168901. doi: 10.7498/aps.73.20240454
[2]	沈力峰, 王建波, 杜占玮, 许小可. 基于社团结构和活跃性驱动的双层网络传播动力学. , 2023, 72(6): 068701. doi: 10.7498/aps.72.20222206
[3]	李新月, 祁娟娟, 赵敦, 刘伍明. 自旋-轨道耦合二分量玻色-爱因斯坦凝聚系统的孤子解. , 2023, 72(10): 106701. doi: 10.7498/aps.72.20222319
[4]	寻之朋, 郝大鹏. 含复杂近邻的二维正方格子键渗流的蒙特卡罗模拟. , 2022, 71(6): 066401. doi: 10.7498/aps.71.20211757
[5]	舒盼盼, 王伟, 唐明, 尚明生. 花簇分形无标度网络中节点影响力的区分度. , 2015, 64(20): 208901. doi: 10.7498/aps.64.208901
[6]	王凯明, 钟宁, 周海燕. 基于改进功率谱熵的抑郁症脑电信号活跃性研究. , 2014, 63(17): 178701. doi: 10.7498/aps.63.178701
[7]	张燚, 孙卫国, 付佳, 樊群超, 冯灏, 李会东. 用节点变分的代数方法研究双原子体系的完全振动能谱和离解能. , 2012, 61(13): 133301. doi: 10.7498/aps.61.133301
[8]	田立新, 贺莹环, 黄益. 一种新型二分网络类局域世界演化模型. , 2012, 61(22): 228903. doi: 10.7498/aps.61.228903
[9]	魏兵, 董宇航, 王飞, 李存志. 基于移位算子时域有限差分的色散薄层节点修正算法. , 2010, 59(4): 2443-2450. doi: 10.7498/aps.59.2443
[10]	周磊, 支蓉, 冯爱霞, 龚志强. 基于二分图的温度网络拓扑性质研究. , 2010, 59(9): 6689-6696. doi: 10.7498/aps.59.6689
[11]	陈宏斌, 樊瑛, 方锦清, 狄增如. 二元随机网. , 2009, 58(3): 1383-1390. doi: 10.7498/aps.58.1383
[12]	牛培峰, 张君, 关新平. 基于遗传算法的混沌系统二自由度比例-积分-微分控制研究. , 2007, 56(7): 3759-3765. doi: 10.7498/aps.56.3759
[13]	张海燕, GNgele, 马红孺. 二分量带电胶体悬浮系统的等效硬球模型. , 2002, 51(8): 1892-1896. doi: 10.7498/aps.51.1892
[14]	曹天德, 黄清龙. 二分量高温超导机理. , 2002, 51(7): 1600-1603. doi: 10.7498/aps.51.1600
[15]	. 二分量胶体悬浮系统的短时间动力学. , 2001, 50(9): 1810-1817. doi: 10.7498/aps.50.1810
[16]	吴克, 吴军桥, 王志军, 张金龙, 李传义, 尹道乐, 顾镇南, 周锡煌, 金朝霞. 富勒烯薄膜上二维金属渗流系统的电击穿现象. , 1996, 45(11): 1905-1912. doi: 10.7498/aps.45.1905
[17]	朱建阳. 引入“鬼”场的二维次近邻正方格点渗流模型的重整化群方法研究. , 1993, 42(6): 880-885. doi: 10.7498/aps.42.880
[18]	屈少华, 姚凯伦, 郁伯铭. 二维次近邻渗流模型. , 1991, 40(2): 169-174. doi: 10.7498/aps.40.169
[19]	谭维翰, 刘仁红. 二分岔理论的抛物线近似. , 1990, 39(7): 35-39. doi: 10.7498/aps.39.35-2
[20]	张昭庆. 自洽的关联渗流问题. , 1982, 31(11): 1576-1580. doi: 10.7498/aps.31.1576

计量

文章访问数: 8003
PDF下载量: 601
被引次数: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

搜索

留言板