Fluctuations in the order of System Size in the Avalanche-Size Distribution of Sandpiles Model

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Saadat, Elaheh | 2019

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 52357 (04)
University: Sharif University of Technology
Department: Physics
Advisor(s): Moghimi Araghi, Saman
Abstract:
Since the concept of Self-Organized Criticality was introduced in terms of BTW Sandpiles model, its major features have been known as broad power law distributions without any tuning parameters. In some selforganized critical systems like brain and neural networks, some evidences and experiments show a periodic or non-power law distribution of avalanches in addition to the power-law distributions of avalanches. In this thesis we try to observe the same phenomenon in the well-known SOC models, namely the BTW and Manna sandpile models. We have considered small lattice sizes with periodic boundary conditions and a small amount of dissipation. Within such conditions we observe a periodic-like distribution of avalanches, togheter with the original powerlaw behavior in BTW sandpile model. In the case of the Manna model, although there exists no periodic-like distribution, a non power-law distribution of avalanches is observed. At the end, we conclude that this periodic-like and non power-law distribution is relying on the lattice size and scale of sands dissipation. Moreover, we study how the lattice size and scale of sands dissipation can affect this behavior
Keywords:
Self Organized Criticality ; Power Law Model ; Sand Pile Model ; Periodic Boundary Condition ; Dissipation ; Deflection