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The Abelian Sand-pile Model (ASM) and Generalization to the Continuous State

Lotfi, Ehsan | 2008

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 42106 (04)
  4. University: Sharif University of Technology
  5. Department: Physics
  6. Advisor(s): Moghimi Araghi, Saman
  7. Abstract:
  8. The four-page article by Bak, Tang and Wiesenfeld in 1987 was a beginning to a new wave of physicists’ efforts to explain and describe the concept of complexity; a not-so-well-defined concept that resists against the reductionist tools and methods of physics. The Self-organized Criticality theory presented in that article via a simple model, known as sandpile model, was first of all an effort to explain the numerous occurrence of power law distribution in nature. SOC was introduced to tell us why so many natural phenomena like Earthquakes, landslides, forest fires, extinction and other seemingly non-related catastrophic events, more or less obey the scale-less power law distribution; A distribution known in equilibrium statistical mechanics as a sign for the critical phase. During the last twenty years, much effort has been put to the sandpile model and the concept of Self-Organized Criticality (SOC). People like Dhar, Majumdar, Mana, Zhang and Ramaswamy made the model definition exact and determined some of it’s static quantities. Some tried to describe the model using a field theory approach and others worked on the numerical and simulative methods. Although the SOC concept is not so stimulating for physicists as it was during the 90s and maybe no one now considers it –as Bak did- the theory of nature, but physicists still try to analyze the different models representing SOC and specially to determine analytically their dynamic quantities like critical exponents. This script is a brief review of what has been done around the Abelina Sandpile Model (ASM) plus the definition and short description of a continuous ASM .

  9. Keywords:
  10. Abelian Sandpile Model ; Self Organized Criticality

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