The Resource Deterministic Abelian Sandpile Models and Patterns, by Guglielmo Paoletti, (electronic resource)
Deterministic Abelian Sandpile Models and Patterns, by Guglielmo Paoletti, (electronic resource)
 Summary
 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
 Language
 eng
 Extent
 XII, 163 p. 64 illus., 33 illus. in color.
 Contents

 Introduction
 The Abelian Sandpile Model
 Algebraic structure
 Identity characterization
 Pattern formation
 Conclusions
 SL(2, Z)
 Complex notation for vectors in R2
 Generalized quadratic Bézier curve
 Tessellation
 Isbn
 9783319012049
 Label
 Deterministic Abelian Sandpile Models and Patterns
 Title
 Deterministic Abelian Sandpile Models and Patterns
 Statement of responsibility
 by Guglielmo Paoletti
 Language
 eng
 Summary
 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
 Image bit depth
 0
 Literary form
 non fiction
 Series statement
 Springer Theses, Recognizing Outstanding Ph.D. Research,
 Label
 Deterministic Abelian Sandpile Models and Patterns, by Guglielmo Paoletti, (electronic resource)
 Antecedent source
 mixed
 Carrier category
 online resource
 Carrier category code
 cr
 Carrier MARC source
 rdacarrier
 Color
 not applicable
 Content category
 text
 Content type code
 txt
 Content type MARC source
 rdacontent
 Contents
 Introduction  The Abelian Sandpile Model  Algebraic structure  Identity characterization  Pattern formation  Conclusions  SL(2, Z)  Complex notation for vectors in R2  Generalized quadratic Bézier curve  Tessellation
 http://library.link/vocab/cover_art
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 Dimensions
 unknown
 http://library.link/vocab/discovery_link
 {'f': 'http://opac.lib.rpi.edu/record=b3552090'}
 Extent
 XII, 163 p. 64 illus., 33 illus. in color.
 File format
 multiple file formats
 Form of item
 electronic
 Isbn
 9783319012049
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code
 c
 Other physical details
 online resource.
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 Reformatting quality
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<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.lib.rpi.edu/portal/DeterministicAbelianSandpileModelsand/PyJpTdmSMe8/" typeof="WorkExample http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.lib.rpi.edu/portal/DeterministicAbelianSandpileModelsand/PyJpTdmSMe8/">Deterministic Abelian Sandpile Models and Patterns, by Guglielmo Paoletti, (electronic resource)</a></span>  <span property="offers" typeOf="Offer"><span property="offeredBy" typeof="Library ll:Library" resource="http://link.lib.rpi.edu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.lib.rpi.edu/">Rensselaer Libraries</a></span></span></span></span></div>