Explosive Percolation in Random Networks by Wei Chen

By Wei Chen

This thesis is dedicated to the learn of the Bohman-Frieze-Wormald percolation version, which shows a discontinuous transition on the serious threshold, whereas the section transitions in random networks are initially thought of to be strong non-stop part transitions. The underlying mechanism that results in the discontinuous transition during this version is thoroughly analyzed and lots of attention-grabbing severe behaviors, together with a number of monstrous parts, a number of section transitions, and risky significant parts are printed. those findings must also be worthwhile with reference to functions in different disciplines equivalent to physics, chemistry and biology.

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1. Then, in the second regime of n 1/3 < k < n 1/2 , S(n) is larger and has large fluctuations. 99 , so C1 merges with other essentially macroscopic components. As shown inset, T (n) is essentially independent of regimes, with T (n) ≥ 5 in the first regime and in the third, with T (n) ∅ 1, but fluctuating in the second (not shown). The analogous three regimes and behaviors for β = 3 are shown in Fig. 3a. 01 . 93 4 10 5 10 6 10 n 7 10 8 10 Fig. 3 a The analogous plot to Fig. 0102 ). b Bounding the critical window from above and below to estimate tc .

103, 135702 (2009) 7. : Explosive percolation in scale-free networks. Phys. Rev. Lett. 103, 168701 (2009) 8. : Explosive growth in biased dynamic percolation on two-dimensional regular lattice networks. Phys. Rev. Lett. 103, 045701 (2009) 9. : Scaling behavior of explosive percolation on the square lattice. Phys. Rev. E 82, 051105 (2010) 10. : Local cluster aggregation models of explosive percolation. Phys. Rev. Lett. 104, 195702 (2010) 11. : Cluster aggregation model for discontinuous percolation transitions.

Percolation under ER-like processes is considered a robust continuous phase transition with a unique giant component emerging at the percolation threshold [13]. Thus, altering the location and nature of the percolation phase transition has been a long-standing challenge. Three years ago, Achlioptas et al. proposed a modified ER model in which two random edges are sampled simultaneously, but only the edge connecting two components with smaller product of their sizes is added, while the other edge is discarded.

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