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Watersheds and Explosive percolation

Authors
Journal
Physics Procedia
1875-3892
Publisher
Elsevier
Publication Date
Volume
15
Identifiers
DOI: 10.1016/j.phpro.2011.05.057
Keywords
  • Explosive Percolation
  • Discontinuous Phase Transitions
  • Percolation Threshold
  • Watershed
  • Fractal Interface
Disciplines
  • Mathematics

Abstract

Abstract 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 di_ering 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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