Watersheds and Explosive percolation

Details Watersheds and Explosive percolation Watersheds and Explosive percolation

2011-03-03

arxiv.org/abs/1103.0765v1

Physics Procedia 15, 37 (2011)

Physics

Condensed Matter

Statistical Mechanics

to appear in the Proceedings of the 24th Annual CSP Workshop

Scientific paper

10.1016/j.phpro.2011.05.057

The recent work by Achlioptas, D'Souza, and Spencer opened up the possibility of obtaining a discontinuous (explosive) percolation transition by changing the stochastic rule of bond occupation. Despite the active research on this subject, several questions still remain open about the leading mechanism and the properties of the system. We review the largest cluster and the Gaussian models recently introduced. We show that, to obtain a discontinuous transition it is solely necessary to control the size of the largest cluster, suppressing the growth of a cluster differing significantly, in size, from the average one. As expected for a discontinuous transition, a Gaussian cluster-size distribution and compact clusters are obtained. The surface of the clusters is fractal, with the same fractal dimension of the watershed line.

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