Sobre Algunas Propiedades del Modelo de la Pila de los Sistemas Críticamente Auto Organizados
Juan Carlos Chimal Eguía
Departamento de Posgrado, Escuela Superior de Cómputo Instituto Politécnico Nacional, U. P. Zacatenco C.P. 07738, México D.F., Mexico e–mail : jchimale@ipn.mx
Article received on January 21, 2004
Accepted on August 10, 2004
Abstract
In this paper we analyze the sandpile model proposed by Bak, Tang and Wiesenfeld as the canonical example of self–organized critical systems. We find that the sandpile–model can reproduce staircase graphics and also that the distribution of large avalanches recurrence times in this model is log–normal. We also find that the slope of cumulative activity characterize a "province" of generation of avalanches in the same way as the seismic or evolutionary provinces do.
Keywords: Sandpile, criticality, self–organization.
Resumen
En este artículo se analiza el modelo de la pila de arena propuesto por Bak, Tang y Weinselfed como ejemplo canónico de los sistemas críticamente auto–organizados. Encontramos que la pila de arena puede reproducir gráficas tipo escalera, así como que la distribución de tiempos de recurrencia en este modelo es log–normal. Hemos también encontrado que existe una pendiente característica de la actividad acumulada que caracteriza a una "provincia" de generación de avalanchas de la misma manera que se hace para provincias sísmicas o evolutivas.
Palabras Clave: Pila de arena, criticalidad, auto–organización.
PACS: 89.75.Da; 05.65.+b
]]>DESCARGAR ARTÍCULO EN FORMATO PDF
Acknowledgments
I thank to Dr. F. Angulo–Brown for his valuable opinions and helpful discussions during the elaboration of this work and Rodrigo Velasco Pacheco for his computational support. Also this work was supported by COFAA–IPN.
References
1. Chao Tang, Kurt Weisenfeld, Per Bak, Susan Coppersmith and Peter Littlewood. Phys. Rev., Lett. 58 (1987),1161. [ Links ]
2. Steven H. Strogatz. Non Linear Dynamics. Adison Wesley, 1994. [ Links ]
3. Manfred Schoeder. Fractals, Chaos, Power Laws. W.H. Freeman and Company 1990. [ Links ]
4. Per Bak, Chao Tang, Kurt Weisenfeld. Phys. Rev., Lett. 59 (1987), 381. [ Links ]
5. Per Bak. How Nature Works. Springer–Verlag, 1996. [ Links ]
6. P. Bak and Chao Tang. J. Geophys. Res., 94(1989), 15635. [ Links ]
7. G. Nicolis. The New Physics. Cambridge University Press, 1989. [ Links ]
8. Benoit B. Mandelbrot. The fractal Geometry of Nature. W.H. Freeman and Company 1983. [ Links ]
9. Henrik Jeldtoft Jensen. Self–Organized Criticality. Cambridge University Press, 1998. [ Links ]
10. Jaeger H.M. and Nagel S.R. Science, 255(1992), 1523. [ Links ]
11. Held G.A. and Solina II D.H. et al. Phys. Rev., Lett. 65 (1990), 1120. [ Links ]
12. Frette V. Christensen K. et al., Science, 379(1996), 49. [ Links ]
13. K. Ito and M. Matzuzaki. J. Geophys. Res., 95(1990), 6853. [ Links ]
14. A. Sornette and D. Sornette. Europhys. Lett. 9(1989), 197. [ Links ]
15. J. M. Carlson and J.S. Langer. Phys. Rev., Lett. 62 (1989), 2632. [ Links ]
16. H.J.S. Feder and J. Feder. Phys. Rev., Lett. 66 (1991), 2669. [ Links ]
17. H.J.S. Feder, Z. Olami and K. Christensen. Phys. Rev., Lett. 68 (1992), 1244. [ Links ]
18. R. Burridge and L. Knopoff. Bull. Seismol. Soc. Am. 57(1967), 341. [ Links ]
19. P. Bak and K. Sneppen. Phys. Rev., Lett. 71 (1993),4083. [ Links ]
20. S. Kauffman. The Origin of the Order. Oxford University Press, 1993. [ Links ]
21. Newman M.E.J. and Palmer R.G. Models of extinction: A review. Santa Fe Institute, 1993. [ Links ]
22. Boettcher S. and Paczuski M. Phys. Rev., Lett. 76 (1996), 3348. [ Links ]
23. Vandewalle N. and Ausloos M., Europhys. Lett., 37(1997), 1. [ Links ]
24. Head D.A. and Rodgers G.J. Phys. Rev. E: Stat. Phys. Plasmas Fluids Relat. Interdicip. Top., 55(1997), 3312. [ Links ]
25. A. Muñoz Diosdado and F. Angulo Brown. Rev. Mex. Fis.,45(1999), 393. [ Links ]
26. F. Angulo Brown and A. Muñoz Diosdado. Geophys. J. Int., 139(1999), 410. [ Links ]
27. J. Chimal Eguia, O. Chavoya Aceves and F. Angulo Brown. Can. J. Phys. 80 (2002), 1675. [ Links ]
28. H. Nakanishi. Phys. Rev. A., 41(1990), 7086. [ Links ]
29. K. Christensen and Z. Olami., Phys. Rev. A., 46(1992), 1829. [ Links ]
30. S.R. Brown C.H.Scholz and J.B. Rundle. Geophys. Res. Lett., 18(1991), 215. [ Links ]
31. Pedro L. Garrido Third Granada Lectures in Computational Physics. Springer Verlag., 1995. [ Links ]
32. K. C. McNally. "Plate Subduction and Prediction of earthquakes along the middle American Trench, in earthquake prediction. D.W. Simpson and P.G. Richards editors., 1981. [ Links ]
33. Pablo M. Gleiser, Sergio A. Cannas and Francisco A. Tamarit. Phys. Rev. E., 63(2001), 2301. [ Links ]
34. S.P. Nishenko and R. Bulland. Bull. Seis. Soc. Am., 77(1987), 1382. [ Links ]
35. P. Bak and M. Paczuski. Complexity, Contingency and Criticality. Brookhaven National Laboratory, 1994. [ Links ] ]]>