Effect of Dissipation and Perturbation in Sandpile Model

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Sebtosheikh, Mahmood | 2015

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 46776 (04)
University: Sharif University of Technology
Department: Physics
Advisor(s): Moghimi Araghi, Saman
Abstract:
Sandpile models are the simplest models to study self organized criticality (SOC). In these phenomena, system reaches its critical state and shows power law behavior without fine tuning of any external parameters. In nature, many examples of such phenomena has been observed such as earthquakes, rainfalls and heights of mountains. In SOC systems, always there is an input and an out put of energy. In sandpile models the dissipative sites that play the role of energy dissipation, are usualy put on the boundary. In this study we have considered sandpile models which have dissipative site in the bulk. We have controled the ratio of the dissipative sites to the number of whole sites and have shown that the critical exponents slightly depend on this ratio. Such dependece was previously assigned to the finite lenght of the system. Also we have considered a system in which dissipative and ”anti-dissipative” pairs
exist. We have numerically shown that such a perturbation takes the system to a new fixed point. The observation is supported with a conformal-field-theoretical RG calculation
Keywords:
Perturbation Method ; Self Organized Criticality ; Bulk Dissipation ; Sand Pile Model