Occurrence of Finite-Time Singularities in Epidemic Models of Rupture, Earthquakes, and Starquakes

Physical Review Letters

Volumn 89, Issue 15, 2002, Pages

  Sornette, D ^a,b   Helmstetter, A ^c  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b LABORATOIRE DE PHYSIQUE DE LA MATIÈRE CONDENSÉE   (France)

^c UNIVERSITÉ GRENOBLE ALPES   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ACCELERATION; APPROXIMATION THEORY; CRACK PROPAGATION; EARTHQUAKES; VORTEX FLOW;

EPIDEMIC MODELS; EULER EQUATIONS; FINITE-TIME SINGULARITIES; SELF-ORGANIZED CRITICALITY;

SEISMIC PROSPECTING;

EID: 3342946273     PISSN: 00319007     EISSN: 10797114     Source Type: Journal    
DOI: 10.1103/PhysRevLett.89.158501     Document Type: Article

References (52)

1. D. Sornette and C.G. Sammis, J. Phys. I (France)JPGCE8 5, 607 (1995);
2. H. Saleur, C.G. Sammis, and D. Sornette, J. Geophys. Res.JGREA2 101, 17?661 (1996).
3. A. Sornette and D. Sornette, Europhys. Lett. 9, 197 (1989);
4. P. Bak and C. Tang, J. Geophys. Res.JGREA2 94, 15?635 (1989).
5. L.R. Sykes and S. Jaumé, Nature (London) 348, 595 (1990).
6. C.G. Bufe and D.J. Varnes, J. Geophys. Res.JGREA2 98, 9871 (1993).
7. R.A. Harris and R.W. Simpson, Geophys. Res. Lett. 23, 229 (1996);
8. Leon Knopoff et al, J. Geophys. Res.JGREA2 101, 5779 (1996);
9. L.M. Jones and E. Hauksson, Geophys. Res. Lett. 24, 469 (1997).
10. D.D. Bowman et al, J. Geophys. Res.JGREA2 103, 24?359 (1998);
11. D.J. Brehm and L.W. Braile, Bull. Seismol. Soc. Am. 88, 564 (1998);
12. S.C. Jaumé and L.R. Sykes, Pure Appl. Geophys.10.1007/s000240050266 155, 279 (1999);
13. G. Ouillon and D. Sornette, Geophys. J. Int.10.1046/j.1365-246X.2000.01257.x 143, 454 (2000).
14. G. Zoller, S. Hainzl, and J. Kurths, J. Geophys. Res.JGREA2 106, 2167 (2001).
15. X-C. Yin, report, 2001.
16. D. Sornette and C. Vanneste, Phys. Rev. Lett.10.1103/PhysRevLett.68.612 68, 612 (1992);
17. C. Vanneste and D. Sornette, J. Phys. I (France)JPGCE8 2, 1621 (1992);
18. D. Sornette, C. Vanneste, and L. Knopoff, Phys. Rev. A10.1103/PhysRevA.45.8351 45, 8351 (1992);
19. M. Sahimi and S. Arbabi, Phys. Rev. Lett.10.1103/PhysRevLett.77.3689 77, 3689 (1996);
20. J.V. Andersen, D. Sornette, and K.-T. Leung, Phys. Rev. Lett.10.1103/PhysRevLett.78.2140 78, 2140 (1997).
21. J.-C. Anifrani, C. Le Floc’h, D. Sornette, and B. Souillard, J. Phys. I (France)JPGCE8 5, 631 (1995);
22. L. Lamaignère, F. Carmona, and D. Sornette, Phys. Rev. Lett.10.1103/PhysRevLett.77.2738 77, 2738 (1996);
23. A. Garcimartin, A. Guarino, L. Bellon, and S. Ciliberto, Phys. Rev. Lett.10.1103/PhysRevLett.79.3202 79, 3202 (1997);
24. A. Johansen and D. Sornette, Eur. Phys. J. B 18, 163 (2000).
25. M. Anghel et al, EOS Trans. Am. Geophys. Union 80, F923 (1999);
26. M. Anghel
27. J.S.S. Martins et al, Phys. Rev. EPLEEE810.1103/PhysRevE.64.056117 64, 056117 (2002).
28. Y. Huang et al, Europhys. Lett. 41, 43 (1998);
29. C.G. Sammis and S.W. Smith, Pure Appl. Geophys.10.1007/s000240050267 155, 307 (1999).
30. P. Mora et al, in Geocomplexity and the Physics of Earthquakes, edited by J.B. Rundle, D.L. Turcotte, and W. Klein (American Geophysical Union, Washington, D.C., 2000); P. Mora and D. Place, Pure Appl. Geophys. (to be published).
31. M. Heimpel, Nature (London)10.1038/42232 388, 865 (1997).
32. D.D. Bowman and G.C.P. King, Geophys. Res. Lett. 28, 4039 (2001).
33. Y. Ben-Zion and V. Lyakhovsky, Pure Appl. Geophys. (to be published).
34. S.G. Sammis and D. Sornette, Proc. Natl. Acad. Sci. U.S.A.PNASA6 99, 2501 (2002).
35. S. Das and C.H. Scholz, J. Geophys. Res.JGREA2 86, 6039 (1981).
36. D. Krajcinovic, Damage Mechanics, North-Holland Series in Applied Mathematics and Mechanics (Elsevier, Amsterdam, 1996).
37. Y.Y. Kagan and L. Knopoff, J. Geophys. Res.JGREA2 86, 2853 (1981);
38. Y.Y. KaganL. KnopoffScience 236, 1563 (1987).
39. Y. Ogata, J. Am. Stat. Assoc. 83, 9 (1988).
40. D. Vere-Jones, Math. Geol. 9, 455 (1977).
41. A. Sornette and D. Sornette, Geophys. Res. Lett. 6, 1981 (1999).
42. A. Helmstetter and D. Sornette, cond-mat/0109318 [J. Geophys. Res.JGREA2 (to be published)].
43. G. Drakatos and J. Latoussakis, J. Seismol. 5, 137 (2001).
44. Z. Guo and Y. Ogata, J. Geophys. Res.JGREA2 102, 2857 (1997).
45. Y. Ogata, Tectonophysics 169, 159 (1989).
46. J.-P. Bouchaud and A. Georges, Phys. Rep. 195, 127 (1990);
47. D. Sornette, Critical Phenomena in Natural Sciences, Springer Series in Synergetics (Springer, Heidelberg, 2000).
48. D. Sornette et al, J. Geophys. Res.JGREA2 101, 13?883 (1996).
49. L. Jones and P. Molnar, Nature (London) 262, 677 (1976);
50. L. JonesP. MolnarJ. Geophys. Res.JGREA2 84, 3596 (1979);
51. Y.Y. Kagan and L. Knopoff, Geophys. J. R. Astron. Soc. 55, 67 (1978).
52. V.G. Kossobokov, V.I. Keilis-Borok, and B.L. Cheng, Phys. Rev. EPLEEE810.1103/PhysRevE.61.3529 61, 3529 (2000).