Sand pile models are dynamical systems emphasizing the phenomenon of Self Organized Criticality (SOC). From N stacked grains, iterating evolution rules leads to some critical configuration where a small disturbance has deep consequences on the system, involving numerous steps of grain fall. Physicists L. Kadanoff et al inspire KSPM, a model presenting a sharp SOC behavior, extending the well known Sand Pile Model. In KSPM with parameter D we start from a pile of N stacked grains and apply the rule: grains can fall from column i onto the adjacent columns to the right if the difference of height between columns i and is greater or equal to D. We propose an iterative study of KSPM evolution where one single grain addition is repeated on a heap of sand. The sequence of grain falls following a single grain addition is called an avalanche. From a certain column precisely studied for D = 3, we provide a plain process describing avalanches. We hope that this process is a first stone toward the study of KSPM fixed points structure. © 2011 Springer-Verlag.
CITATION STYLE
Perrot, K., & Rémila, E. (2011). Avalanche structure in the Kadanoff sand pile model. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 6638 LNCS, pp. 427–439). Springer Verlag. https://doi.org/10.1007/978-3-642-21254-3_34
Mendeley helps you to discover research relevant for your work.