Project 6

Sandpile models were introduced almost twenty years ago as a paradigmatic example of self-organized criticality (SOC) [1], the tendency of slowly driven dissipative systems to display a scale free avalanche response. Such ideas have had an enormous impact in different fields, ranging from magnetic systems [2], superconductors [3] and mechanics [4, 5], to geophysics and plasma physics, including in particular the magnetosphere [6, 8]. 4 The influence also extends beyond physics, to for example biology [9], human (heart) physiology [10] and cognitive processes or neuroscience [11]. The reason for this success lies in the wide variety of non-equilibrium systems displaying an avalanche response to an external driving. One of the primary aims of SOC was, originally, to explain the wide occurrence of 1/f α noise in natural phenomena, through a direct relation between avalanche scaling and spectral properties [1].

References

• [1] P. Bak, C. Tang, and K. Wiesenfeld, Self-organized criticality, Phys. Rev. A 38, 364 (1988). [PDF]

• [2] S. K. Grumbacher, K. M. McEwen, D. A. Halverson, D. T. Jacobs, and J. Lindner, Self‐organized criticality: An experiment with sandpiles, Am. J. Phys. 61, 329 (1993). [PDF]

• [3]