Cluster aggregation model for discontinuous percolation transitions

Department of Physics and Astronomy, Seoul National University, Seoul 151-747, Korea.
Physical Review E (Impact Factor: 2.31). 03/2010; 81(3 Pt 1):030103. DOI: 10.1103/PhysRevE.81.030103
Source: PubMed

ABSTRACT The evolution of the Erdos-Rényi (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 Kij approximately 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 Kij approximately (ij)omega with 0<or=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.

  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: We present a simple model of network growth and solve it by writing the dynamic equations for its macroscopic characteristics such as the degree distribution and degree correlations. This allows us to study carefully the percolation transition using a generating functions theory. The model considers a network with a fixed number of nodes wherein links are introduced using degree-dependent linking probabilities pk. To illustrate the techniques and support our findings using Monte Carlo simulations, we introduce the exemplary linking rule pk∝k-α, with α between -1 and +∞. This parameter may be used to interpolate between different regimes. For negative α, links are most likely attached to high-degree nodes. On the other hand, in case α>0, nodes with low degrees are connected and the model asymptotically approaches a process undergoing explosive percolation.
    Physical Review E 04/2014; 89(4-1):042815. DOI:10.1103/PhysRevE.89.042815 · 2.31 Impact Factor
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: Percolation refers to the emergence of a giant connected cluster in a disordered system when the number of connections between nodes exceeds a critical value. The percolation phase transitions were believed to be continuous until recently when, in a new so-called "explosive percolation" problem for a competition-driven process, a discontinuous phase transition was reported. The analysis of evolution equations for this process showed, however, that this transition is actually continuous, though with surprisingly tiny critical exponents. For a wide class of representative models, we develop a strict scaling theory of this exotic transition which provides the full set of scaling functions and critical exponents. This theory indicates the relevant order parameter and susceptibility for the problem and explains the continuous nature of this transition and its unusual properties.
    Physical Review E 08/2014; 90(2-1):022145. DOI:10.1103/PhysRevE.90.022145 · 2.33 Impact Factor
  • [Show abstract] [Hide abstract]
    ABSTRACT: How clusters is aggregated have great effect on the function and dynamic of complex network. A percolation transition model is introduced in this paper which can be described with the clusters aggregated probability p(Ci)~1-Ci / (Cmax + α), where Ci is the size of the cluster, Cmax is the size of the largest cluster and α is disturbance parameter. This model respectively introduce weakly and strongly discontinuous percolation transition underlying the different α and reveal the strongly impact of clusters' aggregated probability.
    2013 IEEE International Conference on Applied Superconductivity and Electromagnetic Devices (ASEMD); 10/2013


Available from