Scaling and finite-size effects for the critical backbone

Fractals

Volumn 11, Issue SUPPL., 2003, Pages 19-27

  Barthelemy, M ^a   Buldyrev, S V ^a   Havlin, S ^b   Stanley, H E ^a  

^a BOSTON UNIVERSITY   (United States)

^b BAR ILAN UNIVERSITY   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0037311942     PISSN: 0218348X     EISSN: None     Source Type: Journal    
DOI: 10.1142/s0218348x03001689     Document Type: Conference Paper

References (34)

1. A. Bunde and S. Havlin (eds.), Fractals and Disordered Systems, 2nd ed. (Springer, Berlin, 1996), and refs. therein.
2. D. Stauffer and A. Aharony, Introduction to Percolation Theory (Taylor and Francis, London, 1992).
3. M. Sahimi, Applications of Percolation Theory (Taylor and Francis, London, 1992).
4. S. Kirkpatrick, AIP Conf. Proc. 40, 99 (1978); G. Shlifer, W. Klein, P. J. Reynolds and H. E. Stanley, J. Phys. A12, L169 (1979).
5. S. Kirkpatrick, AIP Conf. Proc. 40, 99 (1978); G. Shlifer, W. Klein, P. J. Reynolds and H. E. Stanley, J. Phys. A12, L169 (1979).
6. H. J. Herrmann and H. E. Stanley, Phys. Rev. Lett. 53, 1121 (1984).
7. H. E. Stanley, J. Phys. A10, L211 (1977)
8. A. Coniglio, Phys. Rev. Lett. 46, 250 (1981).
9. R. Rammal, C. Tannous, P. Breton and A. M. S. Tremblay, Phys. Rev. Lett 54, 1718 (1985).
10. L. de Arcangelis, A. Coniglio and S. Redner, Phys. Rev. B36, 5631 (1987).
11. H. Herrmann and S. Roux (eds.), Statistical Models for the Fracture of Disordered Media (North-Holland, 1990).
12. P. Grassberger, Physica A262, 251 (1999).
13. Y. Lee, J. S. Andrade Jr, S. V. Buldyrev, S. Havlin, P. R. King, G. Paul and H. E. Stanley, preprint Cond-Mat 9903066.
14. M. Barthélémy, S. V. Buldyrev, S. Havlin and H. E. Stanley, Phys. Rev. E60, R1123 (1999).
15. H. J. Herrmann, D. Hong and H. E. Stanley, J. Phys. A17, L261 (1984).
16. A. Coniglio and M. Zannetti, Physica D38, 37 (1989).
17. R. Landauer, in Proceedings of the 1st Conference on Electrical and Optical Properties of In-homogeneous Media (Ohio State University, 1977), AIP Conf. Proc. No. 40, eds. J. C. Garland and D. B. Tanner (AIP, New York, 1978).
18. D. J. Bergman and D. Stroud, Solid State Physics 46, 147 (1992).
19. R. Rammal, C. Tannous and A.-M. S. Tremblay, Phys. Rev. A31, 2662 (1985).
20. R. Rammal, C. Tannous, P. Breton and A.-M. S. Tremblay, Phys. Rev. Lett. 54, 1718 (1985).
21. L. de Arcangelis, S. Redner and A. Coniglio, Phys. Rev. B34, 4656 (1986).
22. B. B. Mandelbrot, J. Fluid Mech. 62, 331 (1974)
23. See, e.g., J. Lee et al., Phys. Rev. A39, 6545 (1989).
24. P. Ch. Ivanov et al., Nature 399, 461 (1999).
25. G. Batrouni, A. Hansen and S. Roux, Phys. Rev. A38, 3820 (1988).
26. A. Aharony, R. Blumenfeld and A. B. Harris, Phys. Rev. B47, 5756 (1993).
27. M. Barthélémy, S. V. Buldyrev, S. Havlin and H. E. Stanley, Phys. Rev. E61, R3283 (2000).
28. Y. Lee et al., Phys. Rev. E60, 3425 (1999).
29. A. Coniglio, J. Phys. A15, 3829 (1982).
30. In the "two injection points" configuration, the large currents are controlled by the small loops between A and B. The fluctuation of the length of the shortest path between A and B gives thus rise to the region of power law behavior for large currents we observe in Fig. 5.
31. G. Batrouni, A. Hansen and B. Larson, Phys. Rev. B53, 2292 (1998).
32. H. E. Daniels, Ann. Math. Stat. 25, 631 (1954).
33. B. B. Mandelbrot and C. J. G. Evertsz, Physica A168, 95 (1990).
34. B. B. Mandelbrot, C. J. G. Evertsz and Y. Hayakawa, Phys. Rev. B42, 4528 (1990).