Deterministic Abelian Sandpile Models and Patterns

• Main Author: Paoletti, Guglielmo (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2014.
• Series: Springer Theses, Recognizing Outstanding Ph.D. Research,
• Subjects: Physics.; Computer simulation.; Probabilities.; Mathematical physics.; Statistical physics.; Dynamical systems.; Statistical Physics, Dynamical Systems and Complexity.; Numerical and Computational Physics.; Mathematical Physics.; Probability Theory and Stochastic Processes.; Simulation and Modeling.

The model investigated in this work, a particular cellular automaton with stochastic evolution, was introduced as the simplest case of self-organized-criticality, that is, a dynamical system which shows algebraic long-range correlations without any tuning of parameters.   The author derives exact re...

Table of Contents:

• Introduction
• The Abelian Sandpile Model
• Algebraic structure
• Identity characterization
• Pattern formation
• Conclusions
• SL(2, Z)
• Complex notation for vectors in R2
• Generalized quadratic B´ezier curve
• Tessellation.