Evidence of discrete scale invariance in DLA and time-to-failure by canonical averaging

International Journal of Modern Physics C

Volumn 9, Issue 3, 1998, Pages 433-447

  Johansen, A ^a   Sornette, D ^b,c  

^a UNIVERSITY OF COPENHAGEN   (Denmark)

^b UNIVERSITY OF CALIFORNIA   (United States)

^c UNIVERSITÉ CÔTE D'AZUR   (France)

Author keywords

Averaging; Complex Dimensions; Critical; Diffusion Limited Aggregation; Discrete Scale Invariance; Disorder; Log Periodicity; Power Laws; Prediction; Rupture; Scaling

Indexed keywords

EID: 0032364421     PISSN: 01291831     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0129183198000339     Document Type: Article

References (50)

1. D. Stauffer and A. Aharony, Introduction to Percolation Theory, 2nd Edn. (Taylor and Francis, London; Bristol, PA 1994).
2. C. Vanneste, A. Gilabert, and D. Sornette, Phys. Lett A155, 174 (1991).
3. M. Mézard, G. Parisi, and M. A. Virasoro, Spin Glass Theory and Beyond (World Scientific, Singapore, 1987).
4. F. Pazmandi, R. T. Scalettar, and G. T. Zimanyi, Phys. Rev. Lett. 79, 5130 (1997).
5. B. Souillard, "Waves and electrons in inhomogeneous media," in Chance and Matter, eds. J. Souletie, J. Vannimenus and R. Stora, Les Houches, Session XLVI, Elsevier, Course 5, pp. 305-380.
6. D. Sornette, Acustica 67, 251 (1989).
7. P. W. Anderson, Phys. Rev. 109, 1492 (1958).
8. R. N. Mantegna, S. V. Buldyrev, A. L. Goldberger, S. Havlin, C.-K. Peng, M. Simons, and H. E. Stanley, Phys. Rev. E52, 2939 (1995).
9. A. Arnéodo, Y. d'Aubenton-Carafa, B. Audit, E. Bacry, J. F. Muzy, and C. Thermes, Eur. Phys. J. B1, 259 (1998).
10. S. Cebrat and M. R. Dubek, "The effect of DNA phase structure on DNA walks," Eur. Phys. J. B, in press (1998).
11. S. Wiseman and E. Domany, "Lack of self-averaging and finite size scaling in critical disordered system," preprint cond-mat/9802095; "Self-averaging, distribution of pseudo-critical temperatures and finite size scaling in critical disordered systems," preprint cond-mat/9802102.
12. H. G. Ballesteros, L. A. Fernández, V. Martín-Mayor, A. Muñoz Sudupe, G. Parisi, and J. J. Ruiz-Lorenzo, "Critical exponents for the three dimensional diluted Ising model," preprint cond-mat/9802273.
13. D. Sornette, Physics Reports, 297, 239 (1998).
14. A. Johansen, Discrete Scale Invariance and Other Cooperative Phenomena in Spatially Extended Systems with Threshold Dynamics, Ph.D. Thesis, NBI, Dec. 1997.
15. D. Sornette, A. Johansen, A. Arneodo, J.-F. Muzy, and H. Saleur, Phys. Rev. Lett. 76, 251 (1996).
16. Y. Huang, G. Ouillon, H. Saleur, and D. Sornette, Phys. Rev. E55, 6433 (1997).
17. R. C. Ball and R. Blumenfeld, Phys. Rev. Lett. 65, 1784 (1990); - Reply, Phys. Rev. Lett. 68, 2254 (1992).
18. R. C. Ball and R. Blumenfeld, Phys. Rev. Lett. 65, 1784 (1990); - Reply, Phys. Rev. Lett. 68, 2254 (1992).
19. J.-C. Anifrani, C. Le Floc'h, D. Sornette, and B. Souillard, J. Phys. I France 5, 631 (1995); J.-C. Anifrani, A. Johansen, C. Le Floc'h, G. Ouillon, D. Sornette, C. Vanneste, and B. Souillard, "New approaches for exploiting acoustic emissions," Proc. 6th European Conf. on Non-Destructive Testing, October 1994, Nice, Presentation N72.
20. J.-C. Anifrani, C. Le Floc'h, D. Sornette, and B. Souillard, J. Phys. I France 5, 631 (1995); J.-C. Anifrani, A. Johansen, C. Le Floc'h, G. Ouillon, D. Sornette, C. Vanneste, and B. Souillard, "New approaches for exploiting acoustic emissions," Proc. 6th European Conf. on Non-Destructive Testing, October 1994, Nice, Presentation N72.
21. M. Sahimi and S. Arbabi, Phys. Rev. Lett. 77, 3689 (1996).
22. H. Saleur and D. Sornette, J. Phys. I France 6, 327 (1996).
23. D. Sornette and C. G. Sammis, J. Phys. I France 5, 607 (1985); A. Johansen, D. Sornette, H. Wakita, U. Tsunogai, W. I. Newman, and H. Saleur, J. Phys. I France 6, 1391 (1996).
24. D. Sornette and C. G. Sammis, J. Phys. I France 5, 607 (1985); A. Johansen, D. Sornette, H. Wakita, U. Tsunogai, W. I. Newman, and H. Saleur, J. Phys. I France 6, 1391 (1996).
25. T. A. Witten and L. M. Sander, Phys. Rev. Lett. 47, 1400 (1981).
26. L. P. Kadanoff, Physics Today, February 1986.
27. M. T. Batchelor, B. I. Henry, and A. P. Roberts, Phys. Rev. E51, 807 (1995).
28. P. Ossadnik, Physica A176, 454 (1991); Phys. Rev. A45, 1058 (1992).
29. P. Ossadnik, Physica A176, 454 (1991); Phys. Rev. A45, 1058 (1992).
30. A. Arneodo, F. Argoul, E. Bacry, and J. F. Muzy, Phys. Rev. Lett. 68, 3456 (1992).
31. D. Stauffer and D. Sornette, Physica A252, 271 (1998).
32. W. H. Press et al., Numerical Recipes (Cambridge University Press, 1992).
33. B. B. Mandelbrot, H. Kaufman, A. Vespignani, I. Yekutieli, and C.-H. Lam, Europhys. Lett. 29, 599 (1995)
34. T. C. Halsey, Europhys. Lett. 39, 43 (1997); T. C. Halsey, K. Honda, and B. Duplantier, J. Stat. Phys. 85, 681 (1996).
35. T. C. Halsey, Europhys. Lett. 39, 43 (1997); T. C. Halsey, K. Honda, and B. Duplantier, J. Stat. Phys. 85, 681 (1996).
36. A. Erzan, L. Pietronero, and A. Vespignani, Rev. Mod. Phys. 67, 545 (1995).
37. B. B. Mandelbrot, Physica A191, 95 (1992).
38. B. B. Mandelbrot, A. Vespignani, and H. Kaufman, Europhys. Lett. 32, 199 (1995)
39. L. Niemeyer, L. Pietronero, and H. J. Wiesmann, Phys. Rev. Lett. 52, 1033 (1984).
40. E. L. Hinrichsen, A. Hansen, and S. Roux, Europhys. Lett. 8, 1 (1989).
41. B. Voight, Nature 332, 125 (1988); Science 243, 200 (1989); B. Voight and R. R. Cornelius, Nature 350, 695 (1991).
42. B. Voight, Nature 332, 125 (1988); Science 243, 200 (1989); B. Voight and R. R. Cornelius, Nature 350, 695 (1991).
43. B. Voight, Nature 332, 125 (1988); Science 243, 200 (1989); B. Voight and R. R. Cornelius, Nature 350, 695 (1991).
44. A. A. Pollock, "Acoustic emission inspection," in Metal Handbook, 9th Edn., Vol. 17, (ASM International, 1989), p. 278.
45. C. Vanneste and D. Sornette, J. Phys I France 2, 1621 (1992); D. Sornette, C. Vanneste, and L. Knopoff, Phys. Rev. A45, 8351 (1992).
46. C. Vanneste and D. Sornette, J. Phys I France 2, 1621 (1992); D. Sornette, C. Vanneste, and L. Knopoff, Phys. Rev. A45, 8351 (1992).
47. L. de Arcangelis, S. Redner, and H. J. Herrmann, J. de Physique Lettres 46, L585 (1985); L. de Arcangelis, A. Hansen, H. J. Herrmann, and S. Roux, Phys. Rev. B40, 877 (1989).
48. L. de Arcangelis, S. Redner, and H. J. Herrmann, J. de Physique Lettres 46, L585 (1985); L. de Arcangelis, A. Hansen, H. J. Herrmann, and S. Roux, Phys. Rev. B40, 877 (1989).
49. L. Lamaignère, F. Carmona, and D. Sornette, Phys. Rev. Lett. 77, 2738 (1996); Physica A241, 328 (1997).
50. L. Lamaignère, F. Carmona, and D. Sornette, Phys. Rev. Lett. 77, 2738 (1996); Physica A241, 328 (1997).