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Explosive Percolation via Control of the Largest Cluster

N. A. M. Araújo and H. J. Herrmann
Phys. Rev. Lett. 105, 035701 – Published 14 July 2010

Abstract

We show that considering only the largest cluster suffices to obtain a first-order percolation transition. As opposed to previous realizations of explosive percolation, our models obtain Gaussian cluster distributions and compact clusters as one would expect at first-order transitions. We also discover that the cluster perimeters are fractal at the transition point, yielding a fractal dimension of 1.23±0.03, close to that of watersheds.

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  • Received 14 May 2010

DOI:https://doi.org/10.1103/PhysRevLett.105.035701

©2010 American Physical Society

Authors & Affiliations

N. A. M. Araújo1,* and H. J. Herrmann1,2,†

  • 1Computational Physics for Engineering Materials, IfB, ETH Zurich, Schafmattstrasse 6, 8093 Zurich, Switzerland
  • 2Departamento de Física, Universidade Federal do Ceará, Campus do Pici, 60451-970 Fortaleza, Ceará, Brazil

  • *nuno@ethz.ch
  • hans@ifb.baug.ethz.ch

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Vol. 105, Iss. 3 — 16 July 2010

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