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利用Monte-Carlo模拟研究了全局耦合网络上扩散限制的不可逆聚集-湮没过程的动力学行为. 在系统中, 同种类集团相遇, 将发生聚集反应; 不同种类的集团相遇, 则发生部分湮没反应. 模拟结果表明:1) 当两种粒子初始浓度相等时, 系统长时间演化后, 集团浓度c(t)和粒子浓度g(t)呈现幂律形式, c(t)～t- 和g(t)～t-, 其中幂指数和满足=2的关系, 且=2/(2 + q); 集团大小分布随时间的演化满足标度律, ak(t)=k-t-(k/tz), 其中-1.27q, (3 + 1.27q)/(2 + q), z=/2=1/(2 + q); 2) 当两种粒子初始浓度不相等时, 系统经长时间演化后, 初始浓度较小的种类完全湮没, 而初始浓度较大的那个种类的集团浓度cA(t)仍具有幂律形式, cA(t)～t-, 其中=1/(1+q), 其集团大小分布随时间的演化也满足标度律, 标度指数为-1.27q, (2 + 1.27q)/(1 + q)和z==1/(1 + q). 模拟结果与已报道的理论分析结果相符得很好.
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关键词:
- 全局耦合网络 /
- 聚集-湮没 /
- Monte-Carlo模拟 /
- 标度律
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.-
Keywords:
- globally coupled network /
- aggregation-annihilation /
- Monte Carlo simulation /
- scaling law
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[45] -
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[2] Krapivsky P L 1993 Physica A 198 135
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[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 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 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 59 6681]
[44] Vicsek T,Family F 1984 Phys.Rev.Lett.52 1669
[45]
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