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Sandpile Model on Height Parameters

Safdari, Mohammad Amin | 2016

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 49546 (04)
  4. University: Sharif University of Technology
  5. Department: Physics
  6. Advisor(s): Moghimi Araghi, Saman
  7. Abstract:
  8. Many statistical systems such as earthquakes, road trafcs, forest fres, neurocortical avalanches etc. exhibit self-organized criticality (SOC). In such systems without tuning extrenal parameters, the system arrives at criticality. During recent decades, a number of models are introduced which show the same charactristics. These models have made a platform to investigate the physics of self-organized criticality. Among them, sandpile models are the best known models. They exhibit critical behaviour such as scaling laws. Also in some of them conformal invariance is checked nummerically.Most of sandpile models deal with slope parameters, that is, the main dynamical parameters are the local slopes. However these models have failed to describe quantitatively the experimetal data on rice, bean, etc. Therefore models that deal with the heights of the pile have proposed and these models show a better description of the experiment. However the conformal invariance in these models is not checked. In this thesis we investigate a height model to see if the model has conformal invariance or not. Through usual methods like box-counting and properties of gyration radious we fnd that the geometrical object defend in the theory has scale invariance, yet the SLE technique shows the these objects do not have full conformal invariance
  9. Keywords:
  10. Self Organized Criticality ; Sand Pile Model ; BTW Sandpile Model ; Conformal Mapping ; Schramm-Loewner Evolution (SLE)

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