Cluster aggregation model for discontinuous percolation transitions

被引:81
作者
Cho, Y. S. [1 ]
Kahng, B. [1 ]
Kim, D. [1 ]
机构
[1] Seoul Natl Univ, Dept Phys & Astron, Seoul 151747, South Korea
来源
PHYSICAL REVIEW E | 2010年 / 81卷 / 03期
关键词
KINETICS; GELATION;
D O I
10.1103/PhysRevE.81.030103
中图分类号
O35 [流体力学]; O53 [等离子体物理学];
学科分类号
070204 ; 080103 ; 080704 ;
摘要
The evolution of the Erdos-Renyi (ER) network by adding edges is a basis model for irreversible kinetic aggregation phenomena. Such ER processes can be described by a rate equation for the evolution of the cluster-size distribution with the connection kernel K-ij similar to ij, where ij is the product of the sizes of two merging clusters. Here we study that when the giant cluster is discouraged to develop by a sublinear kernel K-ij similar to (ij)(omega) with 0 <= omega < 1/2, the percolation transition (PT) is discontinuous. Such discontinuous PT can occur even when the ER dynamics evolves from proper initial conditions. The obtained evolutionary properties of the simple model sheds light on the origin of the discontinuous PT in other nonequilibrium kinetic systems.
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页数:4
相关论文
共 21 条
  • [1] Explosive Percolation in Random Networks
    Achlioptas, Dimitris
    D'Souza, Raissa M.
    Spencer, Joel
    [J]. SCIENCE, 2009, 323 (5920) : 1453 - 1555
  • [2] Network robustness and fragility: Percolation on random graphs
    Callaway, DS
    Newman, MEJ
    Strogatz, SH
    Watts, DJ
    [J]. PHYSICAL REVIEW LETTERS, 2000, 85 (25) : 5468 - 5471
  • [3] Percolation Transitions in Scale-Free Networks under the Achlioptas Process
    Cho, Y. S.
    Kim, J. S.
    Park, J.
    Kahng, B.
    Kim, D.
    [J]. PHYSICAL REVIEW LETTERS, 2009, 103 (13)
  • [4] Percolation critical exponents in scale-free networks
    Cohen, R
    ben-Avraham, D
    Havlin, S
    [J]. PHYSICAL REVIEW E, 2002, 66 (03): : 1 - 036113
  • [5] ERDOS P, 1960, B INT STATIST INST, V38, P343
  • [6] Family F., 1984, KINETICS AGGREGATION
  • [7] Molecular size distribution in three dimensional polymers. I. Gelation
    Flory, PJ
    [J]. JOURNAL OF THE AMERICAN CHEMICAL SOCIETY, 1941, 63 : 3083 - 3090
  • [8] Construction and Analysis of Random Networks with Explosive Percolation
    Friedman, Eric J.
    Landsberg, Adam S.
    [J]. PHYSICAL REVIEW LETTERS, 2009, 103 (25)
  • [9] Evolution of scale-free random graphs: Potts model formulation
    Lee, DS
    Goh, KI
    Kahng, B
    Kim, D
    [J]. NUCLEAR PHYSICS B, 2004, 696 (03) : 351 - 380
  • [10] Scaling theory and exactly solved models in the kinetics of irreversible aggregation
    Leyvraz, F
    [J]. PHYSICS REPORTS-REVIEW SECTION OF PHYSICS LETTERS, 2003, 383 (2-3): : 95 - 212