Discrete surface growth process as a synchronization mechanism for scale-free complex networks

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

Volumn 76, Issue 4, 2007, Pages

  Pastore Y Piontti, A L ^a   MacRi, P A ^a   Braunstein, L A ^a,b  

^a UNIVERSIDAD NACIONAL DE MAR DEL PLATA   (Argentina)

^b BOSTON UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CRYSTAL LATTICES; RELAXATION PROCESSES; SURFACE ROUGHNESS; SYNCHRONIZATION;

EUCLIDEAN LATTICES; SURFACE GROWTH; WILKINSON PROCESSES;

LARGE SCALE SYSTEMS;

EID: 35648952300     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.76.046117     Document Type: Article

References (27)

1. R. Albert and A.-L. Barabási, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.74.47 74, 47 (2002).
2. S. N. Dorogovtsev and J. F. F. Mendes, Evolution of Networks (Oxford University Press, Oxford, 2003).
3. P. Erdos and A. Rényi, Publ. Math. (Debrecen) PUMAAR 0033-3883 6, 290 (1959).
4. P. Erdos and A. Rényi, Publ. Math. Inst. Hung. Acad. Sci. 2, 17 (1960).
5. B. Bollobás, Random Graphs (Academic, London, 1985).
6. R. Cohen, K. Erez, D. ben-Avraham, and S. Havlin, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.85.4626 85, 4626 (2000).
7. D. S. Callaway, M. E. J. Newman, S. H. Strogatz, and D. J. Watts, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.85.5468 85, 5468 (2000).
8. R. Cohen and S. Havlin, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.90.058701 90, 058701 (2003).
9. E. López, S. V. Buldyrev, S. Havlin, and H. E. Stanley, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.94.248701 94, 248701 (2005).
10. D. J. Watts and S. H. Strogatz, Nature (London) NATUAS 0028-0836 10.1038/30918 393, 440 (1998).
11. R. Albert and A.-L. Barabási, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.74.47 74, 47 (2002).
12. R. Cohen, S. Havlin, and D. ben-Avraham, in Handbook of Graphs and Networks, edited by, S. Bornholdt, and, H. G. Shuster, (Wiley-VCH, New York, 2002), Chap..
13. S. Valverde and R. V. Sole, Eur. Phys. J. B EPJBFY 1434-6028 10.1140/epjb/e2004-00117-x 38, 245 (2004).
14. Y. Rabani, A. Sinclair, and R. Wanka, Proceedings of the 39th Symp. on Foundations of Computer Science (FOCS), 694 (1998).
15. G. Korniss, Z. Toroczkai, M. A. Novotny, and P. A. Rikvold, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.84.1351 84, 1351 (2000).
16. S. F. Edwards and D. R. Wilkinson, Proc. R. Soc. London, Ser. A PRLAAZ 0950-1207 10.1103/PhysRevLett.56.889 381, 17 (1982).
17. G. Korniss, M. B. Hastings, K. E. Bassler, M. J. Berryman, B. Kozma, and D. Abbot, Phys. Lett. A PYLAAG 0375-9601 10.1016/j.physleta.2005.09.081 350, 324 (2006).
18. B. Kozma, M. B. Hastings, and G. Korniss, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.92.108701 92, 108701 (2004).
19. B. Kozma, M. B. Hastings, and G. Korniss, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.018701 95, 018701 (2005).
20. A.-L. Barabási and H. E. Stanley, Fractal Concepts in Surface Growth (Cambridge University Press, New York, 1995)
21. P. Meakin, Fractals, Scaling and Growth Far from Equilibrium (Cambridge University Press, Cambridge, 1998).
22. F. Family, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/19/8/006 19, L441 (1986).
23. M. Molloy and B. Reed, Random Struct. Algorithms 6, 161 (1995) 1042-9832
24. M. Molloy and B. Reed, Combinatorics, Probab. Comput. CPCOFG 0963-5483 10.1017/S0963548398003526 7, 295 (1998).
25. If the initial configuration is flat, the second rule of Eq. 4 is the following: if there are m/v minimum and j is one of them hj = hj +1 with probability 1/m.
26. G. Korniss, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.75.051121 75, 051121 (2007).
27. M. Boguna, R. Pastor-Satorras, and A. Vespignani, Eur. Phys. J. B EPJBFY 1434-6028 10.1140/epjb/e2004-00038-8 38, 205 (2004).