Deterministic Abelian Sandpile Models and Patterns

Nonfiction, Science & Nature, Science, Physics, Mathematical Physics, General Physics
Cover of the book Deterministic Abelian Sandpile Models and Patterns by Guglielmo Paoletti, Springer International Publishing
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Guglielmo Paoletti ISBN: 9783319012049
Publisher: Springer International Publishing Publication: September 16, 2013
Imprint: Springer Language: English
Author: Guglielmo Paoletti
ISBN: 9783319012049
Publisher: Springer International Publishing
Publication: September 16, 2013
Imprint: Springer
Language: English

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 results which are potentially also interesting outside the area of critical phenomena. Exact means also site-by-site 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 non-equilibrium 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.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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 results which are potentially also interesting outside the area of critical phenomena. Exact means also site-by-site 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 non-equilibrium 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.

More books from Springer International Publishing

Cover of the book Coordination, Organizations, Institutions, and Norms in Agent Systems X by Guglielmo Paoletti
Cover of the book The Natural World and Science Education in the United States by Guglielmo Paoletti
Cover of the book Cardiac CT Imaging by Guglielmo Paoletti
Cover of the book Premodern Rulers and Postmodern Viewers by Guglielmo Paoletti
Cover of the book Stabilization of Switched Nonlinear Systems with Unstable Modes by Guglielmo Paoletti
Cover of the book The Future of Thermal Comfort in an Energy- Constrained World by Guglielmo Paoletti
Cover of the book In Defense of Processed Food by Guglielmo Paoletti
Cover of the book Modern Trends in Cartography by Guglielmo Paoletti
Cover of the book Assessment in Music Education: from Policy to Practice by Guglielmo Paoletti
Cover of the book Mergers and Acquisitions by Guglielmo Paoletti
Cover of the book Wired/Wireless Internet Communications by Guglielmo Paoletti
Cover of the book The Litani River, Lebanon: An Assessment and Current Challenges by Guglielmo Paoletti
Cover of the book The Crafty Animator by Guglielmo Paoletti
Cover of the book Productivity and Inequality by Guglielmo Paoletti
Cover of the book Multimodal Pragmatics and Translation by Guglielmo Paoletti
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy