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Continuous Transition from Self-organized Criticality to Self-organized Bistability

Ali Akbarian, Mohammad Navid | 2023

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 56558 (04)
  4. University: Sharif University of Technology
  5. Department: Physics
  6. Advisor(s): Moghimi Araghi, Saman
  7. Abstract:
  8. ”Self-organized criticality” is a conceptual term that has helped us describe cer- tain critical behaviors in nature over the past approximately thirty years. In systems exhibiting this characteristic, critical behavior emerges without the need for external parameter adjustments. The necessary mechanism to observe such phenomena is for the critical point to be a dynamical attractor. Based on this, other phenomena have been proposed in which the critical point is not an attractor; instead, a stable cycle forms around it. This mechanism has led to the emergence of a new concept known as ”self- organized bistability.” The primary model proposed for such a phenomenon is based on a sandpile model, in which each avalanche can facilitate subsequent avalanches. In this thesis, we have considered variations of this model with a continuously ad- justable parameter, so that the transition from self-organized criticality to self-organized bistability can be continuously achieved. We have demonstrated that at least in this model, there is no self-organized bistability in the limit of large systems. We have inves- tigated the changes of parameter adjustments in terms of changes in length. By using equations similar to renormalization equations, we have observed that this parameter approaches the self-organization criticality in the limit of large scales.
  9. Keywords:
  10. Self Organized Criticality ; Sand Pile Model ; Critical Phenomena ; Self-Organized Bistability

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