Diffusion, annihilation, and chemical reactions in complex networks with spatial constraints

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

Volumn 86, Issue 4, 2012, Pages

  Emmerich, Thorsten ^a   Bunde, Armin ^a   Havlin, Shlomo ^b  

^a JUSTUS LIEBIG UNIVERSITY   (Germany)

^b BAR ILAN UNIVERSITY   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

ANNIHILATION PROCESS; AVERAGE DISTANCE; CHEMICAL REACTION PROCESS; COMPLEX NETWORKS; DISORDERED LATTICES; EMBEDDED NETWORK; EMBEDDING DIMENSIONS; EUCLIDEAN SPACES; FUNCTION OF TIME; LONG-RANGE LINKS; NETWORK DIMENSIONS; RANDOM WALK; RANDOM WALKERS; SPATIAL CONSTRAINTS; TIME STEP;

RANDOM PROCESSES;

CHEMICAL REACTIONS;

EID: 84867437128     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.86.046103     Document Type: Article

References (35)

1. R. Albert, H. Jeong, and A. L. Barabási, Nature NATUAS 0028-0836 10.1038/43601 401, 130 (1999). (Pubitemid 29436307)
2. R. Albert and A. L. Barabási, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.74.47 74, 4797 (2002).
3. M. E. J. Newman, D. J. Watts, and S. H. Strogatz, Proc. Natl. Acad. Sci. USA PNASA6 0027-8424 10.1073/pnas.012582999 99, 2566 (2002). (Pubitemid 34165067)
4. S. N. Dorogovtsev, Evolution of Networks: From Biological Nets to the Internet and WWW (Oxford University Press, Oxford, 2003).
5. J. Goldberg and M. Levy, arXiv: 0906.3202 (2009).
6. R. Cohen and S. Havlin, Complex Networks: Structure Robustness and Function (Cambridge University Press, Cambridge, UK, 2010).
7. R. P. Satorras and A. Vespignani, Evolution and Structure of the Internet: A Statistical Physics Approach (Cambridge University Press, Cambridge, UK, 2004).
8. D. Liben-Nowell, J. Novak, R. Kumar, P. Raghavan, and A. Tomkins, Proc. Natl. Acad. Sci. USA PNASA6 0027-8424 10.1073/pnas.0503018102 102, 11623 (2005). (Pubitemid 41170776)
9. D. Brockmann, L. Hufnagel, and T. Geisel, Nature NATUAS 0028-0836 10.1038/nature04292 439, 462 (2006). (Pubitemid 43152835)
10. A. Barrat, M. Barthélmy, R. Pastor-Satorras, and A. Vespignani, Proc. Natl. Acad. Sci. USA PNASA6 0027-8424 10.1073/pnas.0400087101 101, 3747 (2004). (Pubitemid 38381049)
11. A. Barrat, M. Barthélmy, and A. Vespignani, Dynamical Processes on Complex Networks (Cambridge University Press, Cambridge, 2008).
12. R. Lambiotte, V. D. Blondel, C. de Kerchove, E. Huens, C. Prieur, Z. Smoreda, and P. Van Dooren, Physica A PHYADX 0378-4371 10.1016/j.physa.2008.05. 014 387, 5317 (2008).
13. M. Barthélmy, Phys. Rep. PRPLCM 0370-1573 10.1016/j.physrep.2010. 11.002 499, 1 (2010).
14. K. Kosmidis, S. Havlin, and A. Bunde, Europhys. Lett. EULEEJ 0295-5075 10.1209/0295-5075/82/48005 82, 48005 (2008).
15. Li Daqing, Li Guanliang, K. Kosmidis, H. E. Stanley, A. Bunde, and S. Havlin, Europhys. Lett. EULEEJ 0295-5075 10.1209/0295-5075/93/68004 93, 68004 (2011).
16. Li Daqing, K. Kosmidis, A. Bunde, and S. Havlin, Nat. Phys. 1745-2473 10.1038/nphys1932 7, 481 (2011).
17. T. Emmerich, A. Bunde, S. Havlin, Li Guanlian and Li Daqing, arXiv: 1206.5710 (2012).
18. P. Erdös and A. Rényi, Publ. Math. Inst. Hung. Acad. Sci. 5, 17 (1960).
19. P. Erdös and A. Rényi, Publ. Math. Debrecen 6, 290 (1959).
20. B. Bollobás, Random Graphs (Cambridge University Press, Cambridge, UK, 2001).
21. D. Toussaint and F. Wilczek, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.445022 78, 2642 (1983).
22. K. Kang and S. Redner, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.52.955 52, 955 (1984).
23. L. Peliti, J. Phys. A 1361-6447 10.1088/0305-4470/19/6/012 19, L365 (1986).
24. D. Ben-Avraham and S. Havlin, Diffusion and Reactions in Fractals and Disordered Systems (Cambridge University Press, Cambridge, UK, 2000).
25. S. Havlin and D. Ben-Avraham, Adv. Phys. ADPHAH 0001-8732 10.1080/00018730110116353 51, 187 (2002). (Pubitemid 34590201)
26. D. Ben-Avraham and S. Redner, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.34.501 34, 501 (1986).
27. L. K. Gallos and P. Argyrakis, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.92.138301 92, 138301 (2004).
28. M. Catanzaro, M. Boguñá, and R. Pastor-Satorras, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.71.056104 71, 056104 (2005). (Pubitemid 41480993)
29. J. M. Kleinberg, Nature NATUAS 0028-0836 10.1038/35022643 406, 845 (2000). (Pubitemid 30664249)
30. A. Bunde and S. Havlin (eds.), Fractals and Disordered Systems (Springer, Berlin, 1991).
31. G. H. Weiss, Aspects and Applications of the Random Walk (North-Holland Press, Amsterdam, 1994).
32. J. Klafter and I. M. Sokolov First Steps in Random Walks (Oxford University Press, Oxford, 2011).
33. J. Klafter, M. F. Shlesinger, and G. Zumofen, Phys. Today PHTOAD 0031-9228 10.1063/1.881487 49, 33 (1996).
34. R. Metzler and J. Klafter, Phys. Rep. PRPLCM 0370-1573 10.1016/S0370-1573(00)00070-3 339, 1 (2000).
35. K. Kang and S. Redner, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.32. 435 32, 435 (1985).