The Research Of Self-organized Criticality In One-dimensional Sandpile Model With Avalanche Probability Included

Much attention of physicists have been devoted to granular matters in the recent years. However, there are still many phenomena appearing in granular matters cannot be explained completely. In this thesis, we focus on the self-organized criticality(SOC) phenomena of one dimensional sandpile model.A classical one dimensional sandpile model was researched in this paper, the model can not explain the self-organized criticality(SOC) phenomena which appearing in one dimensional rice pile, so we did some mend on this model and make it including avalanche probability, with the new model we explained the SOC phenomena appearing in one dimensional grain pile. SOC phenomena does not appears in classical one dimensional sandpile model, but for two or three dimensional model, it does. However, some people did some experiments with rice and find the SOC existing in one dimensional rice pile, it is not fit with the classical sandpile model. Nobody explained this phenomena. We added avalanche probability to the classical model and made some computer simulation and numerical analyse on the new model. Result shows that the SOC appears in the new model, the two critical exponents are 1.50± 0.02 and 1.58 ± 0.05. The two critical exponents do not vary with avalanche probability. In real ricepile model, the rice has different status, such as plane status, upright status and tilting status. Different status corresponding to different avalanche probability. It is just the existence of avalanche probability which result in the phenomena of SOC, this is consist with our model.The innovation of our rearch:(1) A new one-dimensional sandpile model is set up, in this model avalanche probability is introduced.(2) Emulational simulation is performed with cellular automata method, and numerical analyse is carried out according the simulation result.(3) With the simulation result, We not only explained the SOC phenomena appearing in real sandpile, but also revealed a new path to SOC.