Formation mechanism and size features of multiple giant clusters in generic percolation processes

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 86, Issue 5, 2012, Pages

  Zhang, Yang ^a   Wei, Wei ^a   Guo, Binghui ^a   Zhang, Renquan ^a   Zheng, Zhiming ^a  

^a BEIHANG UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

FORMATION MECHANISM; GROWTH MECHANISMS; GROWTH MODES; LARGE CLUSTERS; PERCOLATION PROCESS; RANDOM NETWORK; REAL-WORLD NETWORKS; STOCHASTIC BEHAVIOR; SUFFICIENT CONDITIONS;

MERGING; SOLVENTS;

PERCOLATION (FLUIDS);

EID: 84868378598     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.86.051103     Document Type: Article

References (40)

1. D. Stauffer and A. Aharony, Introduction to Percolation Theory (Taylor & Francis, London, 1994).
2. M. Sahimi, Applications of Percolation Theory (Taylor & Francis, London, 1994).
3. P. Erdös and A. Rényi, Publ. Math. Inst. Hungar. Acad. Sci. 5, 17 (1960).
4. S. N. Dorogovtsev, J. F. F. Mendes, and A. N. Samukhin, Phys. Rev. E 1539-3755 10.1103/PhysRevE.64.025101 64, 025101 (R) (2001).
5. J. D. Noh, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.76.026116 76, 026116 (2007). (Pubitemid 47357995)
6. Y. Berchenko, Y. Artzy-Randrup, M. Teicher, and L. Stone, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.102.138701 102, 138701 (2009).
7. D. Achlioptas, R. M. D'Souza, and J. Spencer, Science SCIEAS 0036-8075 10.1126/science.1167782 323, 1453 (2009).
8. Y. S. Cho, J. S. Kim, J. Park, B. Kahng, and D. Kim, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.103.135702 103, 135702 (2009).
9. F. Radicchi and S. Fortunato, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.103.168701 103, 168701 (2009).
10. R. M. Ziff, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.103. 045701 103, 045701 (2009).
11. R. M. Ziff, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.82.051105 82, 051105 (2010).
12. H. Chae, S. H. Yook, and Y. Kim, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.85.051118 85, 051118 (2012).
13. N. A. M. Araújo, Jose S. Andrade, Jr., R. M. Ziff, and H. J. Herrmann, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.106.095703 106, 095703 (2011).
14. J. S. Andrade, Jr., H. J. Herrmann, A. A. Moreira, and C. L. N. Oliveira, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.83.031133 83, 031133 (2011).
15. Y. S. Cho, B. Kahng, and D. Kim, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.81.030103 81, 030103 (R) (2010).
16. Y. S. Cho and B. Kahng, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.84.050102 84, 050102 (R) (2011).
17. S. S. Manna and A. Chatterjee, Physica A PHYADX 0378-4371 10.1016/j.physa.2010.10.009 390, 177 (2011).
18. N. A. M. Araújo and H. J. Herrmann, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.105.035701 105, 035701 (2010).
19. K. J. Schrenk, N. A. M. Araújo, and H. J. Herrmann, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.84.041136 84, 041136 (2011).
20. A. A. Moreira, E. A. Oliveira, S. D. S. Reis, H. J. Herrmann, and J. S. Andrade, Jr., Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.81.040101 81, 040101 (R) (2010).
21. E. J. Friedman and A. S. Landsberg, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.103.255701 103, 255701 (2009).
22. R. A. da Costa, S. N. Dorogovtsev, A. V. Goltsev, and J. F. F. Mendes, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.105.255701 105, 255701 (2010).
23. P. Grassberger, C. Christensen, G. Bizhani, S.-W. Son, and M. Paczuski, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.106.225701 106, 225701 (2011).
24. H. K. Lee, B. J. Kim, and H. Park, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.84.020101 84, 020101 (R) (2011).
25. L. Tian and D.-N. Shi, Phys. Lett. A PYLAAG 0375-9601 10.1016/j.physleta.2011.11.039 376, 286 (2012).
26. O. Riordan and L. Warnke, Science SCIEAS 0036-8075 10.1126/science. 1206241 333, 322 (2011).
27. J. Nagler, A. Levina, and M. Timme, Nat. Phys. 1745-2473 10.1038/nphys1860 7, 265 (2011).
28. H. D. Rozenfeld, L. K. Gallos, and H. A. Makse, Eur. Phys. J. B EPJBFY 1434-6028 10.1140/epjb/e2010-00156-8 75, 305 (2010).
29. T. Bohman, A. Frieze, and N. C. Wormald, Random Struct. Algorithms 1042-9832 10.1002/rsa.20038 25, 432 (2004). (Pubitemid 40031648)
30. W. Chen and R. M. D'Souza, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.106.115701 106, 115701 (2011).
31. E. Ben-Naim and P. L. Krapivsky, J. Phys. A JPHAC5 1361-6447 10.1088/0305-4470/38/23/L01 38, L417 (2005). (Pubitemid 40759138)
32. K. J. Schrenk, A. Felder, S. Deflorin, N. A. M. Araújo, R. M. D'Souza, and H. J. Herrmann, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.85. 031103 85, 031103 (2012).
33. R. M. D'Souza and M. Mitzenmacher, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.104.195702 104, 195702 (2010).
34. S. D. S. Reis, A. A. Moreira, and J. S. Andrade, Jr., Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.85.041112 85, 041112 (2012).
35. P.-S. Shim, H. K. Lee, and J. D. Noh, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.86.031113 86, 031113 (2012).
36. B. Bollobás, Random Graphs, 2nd ed. (Cambridge University Press, Cambridge, England, 2001).
37. M. E. J. Newman, S. H. Strogatz, and D. J. Watts, Phys. Rev. E 1539-3755 10.1103/PhysRevE.64.026118 64, 026118 (2001).
38. W. Chen and R. M. D'Souza, arXiv: 1106.2088.
39. O. Riordan and L. Warnke, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.86.011129 86, 011129 (2012).
40. S. Janson, T. Uczak, and A. Rucinski, Random Graphs (John Wiley & Sons, New York, 2000).