Avalanches and surface roughening of granular piles

Introduction

We use avalanches on a granular pile as a model system for generic avalanches such as: mudslides, snow avalanches, forest fires, stock market fluctuations etc. All these systems have in common that the size distribution of events is a power law. Normally, the size distribution of things, e.g. the length of men above 20 years of age, is given by a Gaussian: a bell shape curve with a clear peak and tails that decay exponentially. There is an extremely small chance to find a man taller than 4 meters. Power law distributed events have tails that are power laws. As a consequence to probability for events in these tails is still significant. The probability for an earthquake that is 10 times more devastating is only 10 times smaller. The result of all this is that events that have a power law size distribution can lead to very large disasters. The purpose of our research is to try and find out what causes a system to obey power law statistics and to find out what we can do to prevent a system from entering this class.

Our work

We study extensively avalanches in granular piles. One of our main aims is to try and understand what are the key ingredients for the occurrence of power law distributed avalanches. For this purpose we have collected a large data set of avalanches on a rice pile with a floor area of 1 x 1 m² and a height of roughly 1 m. We observe:

• That the boundary of the pile is important: with the foot of the pile on a horizontal plane, powerlaw distributed avalanches are observed over more than 3 orders of magnitude, while if the foot coincides with a ledge, we observe quasi-periodic avalanches as discussed further in our paper Phys. Rev. E 76 (2007) 040301(R).
• That quite some of the scaling relations of Packzuski, Maslow and Bak between avalanche exponents and surface roughness exponents hold for the experimental rice pile. This supports the conclusion that our rice pile is well described by the concept of Self-Organized Criticality (SOC). For a discussion see our paper "Nonlinear Dynamics and Fractal Avalanches in a Pile of Rice" published in: M. Ausloos and M. Dirickx (Eds.), The Logistic Map and the Route to Chaos:From The Beginnings to Modern Applications (Springer 2005) p. 317-335 preprint and also Phys. Rev. E 67(2003) 051306 
• That temporal multiscaling is observed. The observation of temporal multiscaling is claimed by Packzuski as disciminating SOC behavior from Langevin dynamics. Also this supports the conclusion that our rice pile is well described by SOC.  See further our paper Europhys. Lett. 67 (2004) 342-348 (preprint)
• That, starting from a rather flat pile, the pile approaches the critical state in a very specific manner, consistent with SOC. See further our paper Phys. Rev. Lett. 92 (2004) 058702