Paper Info
Title
Avalanche structure in the kadanoff sand pile model
Abstract
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: D-1 grains can fall from column i onto the D-1 adjacent columns to the right if the difference of height between columns i and i+1 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.
Year
DOI
Venue
2011
10.1007/978-3-642-21254-3_34
language and automata theory and applications
Keywords
DocType
Volume
single grain addition,grain fall,d-1 adjacent column,discrete dynamical system,sand pile model.,d-1 grain,kspm fixed points structure,columns i,kadanoff sand pile model,kspm evolution,avalanche structure,self-organized criticality,parameter d,sand pile model,column i
Conference
abs/1101.5940
ISSN
Citations 
PageRank 
LATA 2011, LNCS Springer-Verlag, volume 6638, pages 427-439
4
0.48
References 
Authors
9
2
Name
Order
Citations
PageRank
Kévin Perrot1138.36
Eric Rémila232945.22