Modelling and simulating self-organised critical systems

Classical models and laws of mechanics have failed both to understand the underlying physical processes of most natural phenomena and to predict their complex macrobehaviours. A new approach to such complex systems is to consider them as self-organised critical systems. To get a better grasp on the mechanics behind self-organised critical systems, we designed and implemented GEOMAS, a simulation platform based on agents and reflection. The issue is to establish if the spatial and temporal complexity of natural phenomena emerges either from geometrical and material heterogeneity or from the chaotic behaviour related to the non-linear equations governing their behaviours at different levels. Using GEOMAS, we were able to express local microbehaviours, global macrobehaviours, the emergence of macrobehaviours out of microbehaviours, and macroconstraints coupled with the control of microbehaviours by macrobehaviours. As a concrete application of our platform, we explored the fitness of models based on statistical physics to the complexity of the eruptive behaviour of the Piton de la Foumaise volcano, which is located on La Reunion Island.