Watersheds and Explosive percolation
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 me...
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| Published in | Physics procedia Vol. 15; pp. 37 - 43 |
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| Format | Journal Article |
| Language | English |
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2011
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| 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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| AbstractList | 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. |
| Author | Herrmann, Hans J. Araujo, Nuno A.M. |
| Author_xml | – sequence: 1 givenname: Hans J. surname: Herrmann fullname: Herrmann, Hans J. organization: Computational Physics for Engineering Materials, IfB, ETH Zurich, Schafmattstr. 6, 8093 Zurich, Switzerland – sequence: 2 givenname: Nuno A.M. surname: Araujo fullname: Araujo, Nuno A.M. organization: Computational Physics for Engineering Materials, IfB, ETH Zurich, Schafmattstr. 6, 8093 Zurich, Switzerland |
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| CitedBy_id | crossref_primary_10_20473_amnt_v2i1_2018_59_65 crossref_primary_10_1103_PhysRevE_86_061131 crossref_primary_10_1103_PhysRevE_85_031103 crossref_primary_10_1016_j_physrep_2015_03_003 crossref_primary_10_1080_00018732_2019_1650450 crossref_primary_10_20473_amnt_v2i1_2018_97_105 crossref_primary_10_1103_PhysRevE_93_042315 |
| Cites_doi | 10.1103/RevModPhys.76.663 10.1103/PhysRevB.30.1477 10.1142/S0129183192000683 10.1103/PhysRevLett.105.035701 10.1103/PhysRevE.81.036110 10.1103/PhysRevLett.103.168701 10.1103/PhysRevLett.106.048501 10.1007/BF01293604 10.1103/PhysRevE.60.R2448 10.1103/PhysRevLett.103.255701 10.1103/PhysRevE.82.051105 10.1109/MCSE.2011.16 10.1103/PhysRevE.81.030103 10.1126/science.1167782 10.1103/PhysRevLett.72.2320 10.1017/S0305004100032680 10.1103/PhysRevLett.105.255701 10.1103/PhysRevLett.104.195702 10.1103/PhysRevLett.103.045701 10.1016/j.physa.2010.10.009 10.1103/PhysRevLett.103.135702 10.1103/PhysRevE.81.040101 10.1103/PhysRevLett.103.225503 10.1103/PhysRevLett.59.454 10.1140/epjb/e2010-00156-8 10.1051/rphysap:01988002302011100 |
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| Keywords | discontinuous phase transitions watershed fractal interface explosive percolation percolation threshold |
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| SubjectTerms | discontinuous phase transitions explosive percolation fractal interface percolation threshold watershed |
| Title | Watersheds and Explosive percolation |
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