搜索

x

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

Erds Rnyi随机网络上爆炸渗流模型相变性质的数值模拟研究

李炎 唐刚 宋丽建 寻之朋 夏辉 郝大鹏

引用本文:
Citation:

Erds Rnyi随机网络上爆炸渗流模型相变性质的数值模拟研究

李炎, 唐刚, 宋丽建, 寻之朋, 夏辉, 郝大鹏

Numerical simulations of the phase transition property of the explosive percolation model on Erds Rnyi random network

Li Yan, Tang Gang, Song Li-Jiang, Xun Zhi-Peng, Xia Hui, Hao Da-Peng
PDF
导出引用
  • 基于改进的Newman和Ziff算法以及有限尺寸标度理论, 通过对表征渗流相变特征物理量的序参量、平均集团尺寸、二阶矩、标准偏差及尺寸不均匀性的数值模拟, 分析研究了Erds Rnyi随机网络上Achlioptas爆炸渗流模型的相变性质.研究表明: 尽管序参量表现出了不连续相变的特征, 但序参量以及其他特征物理量仍具有连续相变的幂律标度行为.因此严格地说, Erds Rnyi随机网络中的爆炸渗流相变是一种奇异相变, 它既不是标准的不连续相变, 又与常规随机渗流表现出的连续相变处于不同的普适类.
    Based on the modified Newman and Ziff algorithm combined with the finite-size scaling theory, in this present work we analytically study the phase transition property of the explosive percolation model induced by Achlioptas process on the Erds Rnyi random network via numerical simulations for the basic percolation quantities including the order parameter, the average cluster size, the moments, the standard deviation and the cluster heterogeneity. It is explicitly shown that all these relevant quantities display a typical power-law scaling behavior, which is the characteristic of continuous phase transition at the percolation threshold despite the fact that the order parameter presents a certain feature of discontinuous transition at the same time. Strictly, the explosive percolation transition during the Erds Rnyi random network is a singular transition, which means that it is neither a standard discontinuous phase transition nor the continuous transition in the regular random percolation model.
    • 基金项目: 中央高校基本科研业务费(批准号:2012LWB45)资助的课题.
    • Funds: Project supported by the Fundamental Research Fund for the Central Universities, China (Grant No. 2012LWB45).
    [1]

    Zalle R (translated by Huang Y) 1998 Amorphous Solid State Physics (Beijing: Peking University Press) (in Chinese) [Zalle著 (黄畇译) 1998 非晶态固体物理学 (北京:北京大学出版社)]

    [2]

    de Arcangelis L, Redner L, Coniglio A 1985 Phys. Rev. B 31 4725

    [3]

    Henley C L 1993 Phys. Rev. Lett. 71 2741

    [4]

    Moore C, Newman M E J 2000 Phys. Rev. E 61 5678

    [5]

    Jovanovi\’c B, Buldyrev S V, Havlin S, Stanley H E 1994 Phys. Rev. E 50 2403

    [6]

    Solomon S, Weisbuch G, de Arcangelis L, Jan N, Stauffer D 2000 Physica (Amsterdam) 277A 239

    [7]

    Stauffer D, Aharony A 1991 Introduction to Percolation Theory (2nd Ed.) (London: Taylor and Francis)

    [8]

    Erdös P, Rényi A 1960 Publ. Math. Inst. Hungar. Acad. Sci. 5 17

    [9]

    Callaway D, Hopcroft J, Kleinberg J, Newman M, Strogatz S 2001 Phys. Rev. E 64 041902

    [10]

    Kim J, Krapivsky P, Kahng B, Redner S 2002 Phys. Rev. E 66 055101

    [11]

    Achlioptas D, Souza R M D, Spencer J 2009 Science 323 1453

    [12]

    Ziff R M 2009 Phys. Rev. Lett. 103 045701

    [13]

    Ziff R M 2010 Phys. Rev. E 82 051105

    [14]

    Radicchi F, Fortunato S 2009 Phys. Rev. Lett. 103 168701

    [15]

    Cho Y S, Kim J S, Park J, Kahng B, Kim D 2009 Phys. Rev. Lett. 103 135702

    [16]

    Araújo N A M, Herrmann H J 2010 Phys. Rev. Lett. 105 035701

    [17]

    Moreira A A, Oliveira E A, Reis S D S, Herrmann H J, Andrade Jr J S 2010 Phys. Rev. E 81 040101(R)

    [18]

    Friedman E J, Landsberg A S 2009 Phys. Rev. Lett. 103 255701

    [19]

    Souza R M D, Mitzenmacher M 2010 Phys. Rev. Lett. 104 195702

    [20]

    Araújo N A M, Andrade Jr J S, Ziff R M, Herrmann Jr H 2011 Phys. Rev. Lett. 106 095703

    [21]

    Manna S S, Chatterjee A 2011 Physica (Amsterdam) 390A 177

    [22]

    Pan R K, Kivela M, Saramaki J, Kaski K, Kertesz K 2011 Phys. Rev. Lett. 83 046112

    [23]

    Grassberger P, Christensen C, Bizhani G, Son S W, Paczuski M 2011 Phys. Rev. Lett. 106 255701

    [24]

    Riordan O, Warnke L 2011 Science 333 322

    [25]

    Lee H K, Kim B J, Park H 2011 Phys. Rev. E 84 020101

    [26]

    da Costa R A, Dorogovtsev S N, Goltsev A V, Mendes J F F 2010 Phys. Rev. Lett. 105 255701

    [27]

    Newman M E J, Ziff R M 2000 Phys. Rev. Lett. 85 4104

    [28]

    Newman M E J, Ziff R M 2001 Phys. Rev. E 64 016706

    [29]

    Radicchi F, Fortunato S 2010 Phys. Rev. E 81 036110

    [30]

    Landau D P, Binder K 2000 A Guide to Monte Carlo Simulations in Statistical Physics (England: Cambridge University Press)

    [31]

    Ódor G 2004 Rev. Mod. Phys. 76 663

    [32]

    Cohen R, ben-Avraham D, Havlin S 2002 Phys. Rev. E 66 036113

    [33]

    Noh J D, Lee H E, Park H 2011 Phys. Rev. E 84 010101

  • [1]

    Zalle R (translated by Huang Y) 1998 Amorphous Solid State Physics (Beijing: Peking University Press) (in Chinese) [Zalle著 (黄畇译) 1998 非晶态固体物理学 (北京:北京大学出版社)]

    [2]

    de Arcangelis L, Redner L, Coniglio A 1985 Phys. Rev. B 31 4725

    [3]

    Henley C L 1993 Phys. Rev. Lett. 71 2741

    [4]

    Moore C, Newman M E J 2000 Phys. Rev. E 61 5678

    [5]

    Jovanovi\’c B, Buldyrev S V, Havlin S, Stanley H E 1994 Phys. Rev. E 50 2403

    [6]

    Solomon S, Weisbuch G, de Arcangelis L, Jan N, Stauffer D 2000 Physica (Amsterdam) 277A 239

    [7]

    Stauffer D, Aharony A 1991 Introduction to Percolation Theory (2nd Ed.) (London: Taylor and Francis)

    [8]

    Erdös P, Rényi A 1960 Publ. Math. Inst. Hungar. Acad. Sci. 5 17

    [9]

    Callaway D, Hopcroft J, Kleinberg J, Newman M, Strogatz S 2001 Phys. Rev. E 64 041902

    [10]

    Kim J, Krapivsky P, Kahng B, Redner S 2002 Phys. Rev. E 66 055101

    [11]

    Achlioptas D, Souza R M D, Spencer J 2009 Science 323 1453

    [12]

    Ziff R M 2009 Phys. Rev. Lett. 103 045701

    [13]

    Ziff R M 2010 Phys. Rev. E 82 051105

    [14]

    Radicchi F, Fortunato S 2009 Phys. Rev. Lett. 103 168701

    [15]

    Cho Y S, Kim J S, Park J, Kahng B, Kim D 2009 Phys. Rev. Lett. 103 135702

    [16]

    Araújo N A M, Herrmann H J 2010 Phys. Rev. Lett. 105 035701

    [17]

    Moreira A A, Oliveira E A, Reis S D S, Herrmann H J, Andrade Jr J S 2010 Phys. Rev. E 81 040101(R)

    [18]

    Friedman E J, Landsberg A S 2009 Phys. Rev. Lett. 103 255701

    [19]

    Souza R M D, Mitzenmacher M 2010 Phys. Rev. Lett. 104 195702

    [20]

    Araújo N A M, Andrade Jr J S, Ziff R M, Herrmann Jr H 2011 Phys. Rev. Lett. 106 095703

    [21]

    Manna S S, Chatterjee A 2011 Physica (Amsterdam) 390A 177

    [22]

    Pan R K, Kivela M, Saramaki J, Kaski K, Kertesz K 2011 Phys. Rev. Lett. 83 046112

    [23]

    Grassberger P, Christensen C, Bizhani G, Son S W, Paczuski M 2011 Phys. Rev. Lett. 106 255701

    [24]

    Riordan O, Warnke L 2011 Science 333 322

    [25]

    Lee H K, Kim B J, Park H 2011 Phys. Rev. E 84 020101

    [26]

    da Costa R A, Dorogovtsev S N, Goltsev A V, Mendes J F F 2010 Phys. Rev. Lett. 105 255701

    [27]

    Newman M E J, Ziff R M 2000 Phys. Rev. Lett. 85 4104

    [28]

    Newman M E J, Ziff R M 2001 Phys. Rev. E 64 016706

    [29]

    Radicchi F, Fortunato S 2010 Phys. Rev. E 81 036110

    [30]

    Landau D P, Binder K 2000 A Guide to Monte Carlo Simulations in Statistical Physics (England: Cambridge University Press)

    [31]

    Ódor G 2004 Rev. Mod. Phys. 76 663

    [32]

    Cohen R, ben-Avraham D, Havlin S 2002 Phys. Rev. E 66 036113

    [33]

    Noh J D, Lee H E, Park H 2011 Phys. Rev. E 84 010101

  • [1] 郭灿, 康晨瑞, 高莹, 张一弛, 邓英远, 马超, 徐春杰, 梁淑华. 金属基复合材料原位反应相场模型. 物理学报, 2022, 71(9): 096401. doi: 10.7498/aps.71.20211737
    [2] 田城, 蓝剑雄, 王苍龙, 翟鹏飞, 刘杰. BaF 2高压相变行为的第一性原理研究. 物理学报, 2022, 71(1): 017102. doi: 10.7498/aps.71.20211163
    [3] 田城, 蓝剑雄, 王苍龙, 翟鹏飞, 刘杰. BaF2高压相变行为的第一性原理研究. 物理学报, 2021, (): . doi: 10.7498/aps.70.20211163
    [4] 韩伟涛, 伊鹏, 马海龙, 张鹏, 田乐. 异质弱相依网络鲁棒性研究. 物理学报, 2019, 68(18): 186401. doi: 10.7498/aps.68.20190761
    [5] 韩伟涛, 伊鹏. 相依网络的条件依赖群逾渗. 物理学报, 2019, 68(7): 078902. doi: 10.7498/aps.68.20182258
    [6] 蒋招绣, 王永刚, 聂恒昌, 刘雨生. 极化状态与方向对单轴压缩下Pb(Zr0.95Ti0.05)O3铁电陶瓷畴变与相变行为的影响. 物理学报, 2017, 66(2): 024601. doi: 10.7498/aps.66.024601
    [7] 任国武, 张世文, 范诚, 陈永涛. 预应力对多晶铁冲击行为影响的微观模拟研究. 物理学报, 2016, 65(19): 196203. doi: 10.7498/aps.65.196203
    [8] 刘洪涛, 孙光爱, 王沿东, 陈波, 汪小琳. 冲击诱发NiTi形状记忆合金相变行为研究. 物理学报, 2013, 62(1): 018103. doi: 10.7498/aps.62.018103
    [9] 罗植, 杨冠琼, 狄增如. 具有空间因素的社会网络上的舆论形成. 物理学报, 2012, 61(19): 190509. doi: 10.7498/aps.61.190509
    [10] 王参军. 随机基因选择模型中的延迟效应. 物理学报, 2012, 61(5): 050501. doi: 10.7498/aps.61.050501
    [11] 韩秀琴, 姜虹, 石玉仁, 刘妍秀, 孙建华, 陈建敏, 段文山. 一维 Frenkel-Kontorova(FK)模型原子链的相变研究. 物理学报, 2011, 60(11): 116801. doi: 10.7498/aps.60.116801
    [12] 汪志刚, 吴亮, 张杨, 文玉华. 面心立方铁纳米粒子的相变与并合行为的分子动力学研究. 物理学报, 2011, 60(9): 096105. doi: 10.7498/aps.60.096105
    [13] 陈永涛, 唐小军, 李庆忠. Fe基α相合金的冲击相变及其对层裂行为的影响研究. 物理学报, 2011, 60(4): 046401. doi: 10.7498/aps.60.046401
    [14] 王建伟, 荣莉莉. 基于负荷局域择优重新分配原则的复杂网络上的相继故障. 物理学报, 2009, 58(6): 3714-3721. doi: 10.7498/aps.58.3714
    [15] 樊华, 李理, 袁坚, 山秀明. 互联网流量控制的朗之万模型及相变分析. 物理学报, 2009, 58(11): 7507-7513. doi: 10.7498/aps.58.7507
    [16] 马卫东, 王 磊, 李幼平, 水鸿寿, 周明天. 用户需求行为对互联网动力学整体特性的影响. 物理学报, 2008, 57(3): 1381-1388. doi: 10.7498/aps.57.1381
    [17] 王 磊, 周淑华, 袁 坚, 任 勇, 山秀明. 虚拟网络行为对互联网整体特性的影响. 物理学报, 2007, 56(1): 36-42. doi: 10.7498/aps.56.36
    [18] 刘 锋, 山秀明, 任 勇, 张 军, 马正新. 计算机网络的长程相关特性. 物理学报, 2004, 53(2): 373-378. doi: 10.7498/aps.53.373
    [19] 石筑一, 吉世印. 微观核芯+两准粒子模型中热核148—158Sm的比热容及其相变. 物理学报, 2003, 52(1): 42-47. doi: 10.7498/aps.52.42
    [20] 袁坚, 任勇, 刘锋, 山秀明. 复杂计算机网络中的相变和整体关联行为. 物理学报, 2001, 50(7): 1221-1225. doi: 10.7498/aps.50.1221
计量
  • 文章访问数:  7162
  • PDF下载量:  866
  • 被引次数: 0
出版历程
  • 收稿日期:  2012-09-01
  • 修回日期:  2012-09-17
  • 刊出日期:  2013-02-05

/

返回文章
返回