On Some Properties of the Sandpile Model of Self–Organized Critical Systems

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

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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.

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