
Title  Deterministic Abelian sandpile models and patterns 
Author(s)  Guglielmo Paoletti 
Description  1 online resource (xii, 163 pages) : illustrations 
Abstract Note  The model investigated in this work, a particular cellular automaton with stochastic evolution, was introduced as the simplest case of selforganizedcriticality, that is, a dynamical system which shows algebraic longrange correlations without any tuning of parameters. The author derives exact results which are potentially also interesting outside the area of critical phenomena. Exact means also sitebysite and not only ensemble average or coarse graining. Very complex and amazingly beautiful periodic patterns are often generated by the dynamics involved, especially in deterministic protocols in which the sand is added at chosen sites. For example, the author studies the appearance of allometric structures, that is, patterns which grow in the same way in their whole body, and not only near their boundaries, as commonly occurs. The local conservation laws which govern the evolution of these patterns are also presented. This work has already attracted interest, not only in nonequilibrium statistical mechanics, but also in mathematics, both in probability and in combinatorics. There are also interesting connections with number theory. Lastly, it also poses new questions about an old subject. As such, it will be of interest to computer practitioners, demonstrating the simplicity with which charming patterns can be obtained, as well as to researchers working in many other areas 
Contents Note  Introduction  The Abelian Sandpile Model  Algebraic structure  Identity characterization  Pattern formation  Conclusions  SL(2, Z)  Complex notation for vectors in R2  Generalized quadratic Bezier curve  Tessellation 
Notes  Includes bibliographical references 
Keyword(s)  1. EBOOK
2. EBOOK  SPRINGER
3. Functions, Abelian
4. MATHEMATICAL PHYSICS
5. MATHEMATICS / Calculus
6. MATHEMATICS / Mathematical Analysis
7. Numerical and Computational Physics
8. Probability Theory and Stochastic Processes
9. Simulation and Modeling
10. Statistical Physics, Dynamical Systems and Complexity

Item Type  eBook 
MultiMedia Links
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Circulation Data
Accession#  
Call#  Status  Issued To  Return Due On  Physical Location 
I02371 


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