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Kinetics of two-species aggregation-annihilation processes on globally coupled networks

Zhu Biao Li Ping-Ping Ke Jian-Hong Lin Zhen-Quan

Kinetics of two-species aggregation-annihilation processes on globally coupled networks

Zhu Biao, Li Ping-Ping, Ke Jian-Hong, Lin Zhen-Quan
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  • Kinetics of diffusion-limited aggregation-annihilation process on globally coupled networks is investigated by the Monte Carlo simulation. In the system, when two clusters of the same species meet at the same node, they will aggregate and form a larger one; while if two clusters of different species meet at the same node, they will annihilate each other. The simulation results show that, (i) if the two species have equal initial concentrations, the concentration of clusters c(t) and the concentration of particles g(t) follow power laws at large time, c(t)~t- and g(t)~t-, with the exponents and satisfying =2 and =2/(2 + q); meanwhile, the cluster size distribution can take the scaling form ak(t)=k-t-(k/tz), where -1.27q, (3 + 1.27q)/(2 + q) and z=/2=1/(2 + q); (ii) if the two species have different initial concentrations, the cluster concentration of the heavy species cA(t) follows the power law at large time, cA (t)~t-, where =1/(1 + q), and the cluster size distribution of the heavy species can obey the scaling law at large time, ak(t)=k-t-\varPhi (k/tz), with the scaling exponents -1.27q, (2 + 1.27q)/(1 + q) and z==1/(1 + q). The simulation results accord well with the reported theoretic analyses.
      Corresponding author: Ke Jian-Hong, kejianhong@yahoo.com.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos.11175131 10775104,10875086,10305009).
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    Ke J,Lin Z,Zheng Y,Chen X,Lu W 2006 Phys.Rev.Lett.97 028301

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    Shi H P,Ke J H,Sun C,Lin Z Q 2009 Acta Phys.Sin.58 1 (in Chinese) [施华萍,柯见洪,孙策,林振权 2009 物理学报 58 1]

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    Laguna M F,Aldana M,Larralde H,Parris P E,Kenkre V M 2005 Phys.Rev.E 72 026102

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    Gallos L K,Argyrakis P 2004 Phys.Rev.Lett.92 138301

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    Tang M,Liu Z,Zhou J 2006 Phys.Rev.E 74 036101

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    Liang X M,Ma L J,Tang M 2009 Acta Phys.Sin.58 83 (in Chinese) [梁小明,马丽娟,唐明 2009 物理学报 58 83]

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    Hua D Y 2009 Chin.Phys.Lett.26 018901

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    Kwon S,Kim Y 2009 Phys.Rev.E 79 041132

    [42]
    [43]

    Shen W W,Li P P,Ke J H 2010 Acta Phys.Sin.59 6681 (in Chinese) [沈伟维,李萍萍,柯见洪 2010 物理学报 59 6681]

    [44]

    Vicsek T,Family F 1984 Phys.Rev.Lett.52 1669

    [45]
  • [1]

    Vicsek T 1992 Fractal Growth Phenomena (Singapore:World Scientific)

    [2]

    Krapivsky P L 1993 Physica A 198 135

    [3]
    [4]

    Krapivsky P L 1993 Physica A 198 150

    [5]
    [6]

    Ben-Naim E,Krapivsky P L 1995 Phys.Rev.E 52 6066

    [7]
    [8]
    [9]

    Argyrakis P,Kopelman R 1993 Phys.Rev.E 47 3757

    [10]

    Ke J,Lin Z 2002 Phys.Rev.E 65 051107

    [11]
    [12]

    Privman V,Cadilhe A M R,Glasser M L 1996 Phys.Rev.E 53 739

    [13]
    [14]

    Zhang L,Yang Z R 1997 Physica A 237 444

    [15]
    [16]

    Zhang L,Yang Z R 1997 Phys.Rev.E 55 1442

    [17]
    [18]
    [19]

    Frachebourg L,Krapivsky P L,Redner S 1998 J.Phys.A:Math.Gen.31 2791

    [20]
    [21]

    Balboni D,Rey P A,Droz M 1995 Phys.Rev.E 52 6220

    [22]
    [23]

    Ke J,Lin Z,Zheng Y,Chen X,Lu W 2006 Phys.Rev.Lett.97 028301

    [24]

    Shi H P,Ke J H,Sun C,Lin Z Q 2009 Acta Phys.Sin.58 1 (in Chinese) [施华萍,柯见洪,孙策,林振权 2009 物理学报 58 1]

    [25]
    [26]
    [27]

    Sokolov I M,Blumen A 1994 Phys.Rev.E 50 2335

    [28]

    Catanzaro M,Bogu M,Pastor-Satorras R 2005 Phys.Rev.E 71 056104

    [29]
    [30]

    Laguna M F,Aldana M,Larralde H,Parris P E,Kenkre V M 2005 Phys.Rev.E 72 026102

    [31]
    [32]

    Gallos L K,Argyrakis P 2004 Phys.Rev.Lett.92 138301

    [33]
    [34]

    Tang M,Liu Z,Zhou J 2006 Phys.Rev.E 74 036101

    [35]
    [36]
    [37]

    Liang X M,Ma L J,Tang M 2009 Acta Phys.Sin.58 83 (in Chinese) [梁小明,马丽娟,唐明 2009 物理学报 58 83]

    [38]

    Hua D Y 2009 Chin.Phys.Lett.26 018901

    [39]
    [40]
    [41]

    Kwon S,Kim Y 2009 Phys.Rev.E 79 041132

    [42]
    [43]

    Shen W W,Li P P,Ke J H 2010 Acta Phys.Sin.59 6681 (in Chinese) [沈伟维,李萍萍,柯见洪 2010 物理学报 59 6681]

    [44]

    Vicsek T,Family F 1984 Phys.Rev.Lett.52 1669

    [45]
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  • Received Date:  21 April 2011
  • Accepted Date:  26 July 2011
  • Published Online:  20 March 2012

Kinetics of two-species aggregation-annihilation processes on globally coupled networks

    Corresponding author: Ke Jian-Hong, kejianhong@yahoo.com.cn
  • 1. College of Physics and Electronic Information Engineering, Wenzhou University, Wenzhou 325035, China
Fund Project:  Project supported by the National Natural Science Foundation of China (Grant Nos.11175131 10775104,10875086,10305009).

Abstract: Kinetics of diffusion-limited aggregation-annihilation process on globally coupled networks is investigated by the Monte Carlo simulation. In the system, when two clusters of the same species meet at the same node, they will aggregate and form a larger one; while if two clusters of different species meet at the same node, they will annihilate each other. The simulation results show that, (i) if the two species have equal initial concentrations, the concentration of clusters c(t) and the concentration of particles g(t) follow power laws at large time, c(t)~t- and g(t)~t-, with the exponents and satisfying =2 and =2/(2 + q); meanwhile, the cluster size distribution can take the scaling form ak(t)=k-t-(k/tz), where -1.27q, (3 + 1.27q)/(2 + q) and z=/2=1/(2 + q); (ii) if the two species have different initial concentrations, the cluster concentration of the heavy species cA(t) follows the power law at large time, cA (t)~t-, where =1/(1 + q), and the cluster size distribution of the heavy species can obey the scaling law at large time, ak(t)=k-t-\varPhi (k/tz), with the scaling exponents -1.27q, (2 + 1.27q)/(1 + q) and z==1/(1 + q). The simulation results accord well with the reported theoretic analyses.

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