skip to content
Deterministic Abelian sandpile models and patterns Preview this item
ClosePreview this item
Checking...

Deterministic Abelian sandpile models and patterns

Author: Guglielmo Paoletti
Publisher: Cham : Springer, [2013?] ©2014
Dissertation: Ph. D. University of Pisa 2012
Series: Springer theses
Edition/Format:   Thesis/dissertation : Document : Thesis/dissertation : eBook   Computer File : EnglishView all editions and formats
Database:WorldCat
Summary:
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  Read more...
Rating:

(not yet rated) 0 with reviews - Be the first.

Subjects
More like this

 

Find a copy online

Links to this item

Find a copy in the library

&AllPage.SpinnerRetrieving; Finding libraries that hold this item...

Details

Genre/Form: Electronic books
Additional Physical Format: Print version:
Paoletti, Guglielmo.
Deterministic Abelian Sandpile Models and Patterns.
Dordrecht : Springer, ©2013
Material Type: Document, Thesis/dissertation, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Guglielmo Paoletti
ISBN: 9783319012049 3319012045
OCLC Number: 859600045
Description: 1 online resource (xii, 163 pages) : illustrations.
Contents: 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.
Series Title: Springer theses
Responsibility: Guglielmo Paoletti.
More information:

Abstract:

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.

Reviews

User-contributed reviews
Retrieving GoodReads reviews...
Retrieving DOGObooks reviews...

Tags

Be the first.
Confirm this request

You may have already requested this item. Please select Ok if you would like to proceed with this request anyway.

Linked Data


Primary Entity

<http://www.worldcat.org/oclc/859600045> # Deterministic Abelian sandpile models and patterns
    a schema:CreativeWork, schema:Book, pto:Web_document, bgn:Thesis, schema:MediaObject ;
   bgn:inSupportOf "" ;
   library:oclcnum "859600045" ;
   library:placeOfPublication <http://id.loc.gov/vocabulary/countries/sz> ;
   schema:about <http://experiment.worldcat.org/entity/work/data/1744867999#Topic/mathematical_physics> ; # Mathematical Physics
   schema:about <http://experiment.worldcat.org/entity/work/data/1744867999#Topic/probability_theory_and_stochastic_processes> ; # Probability Theory and Stochastic Processes
   schema:about <http://experiment.worldcat.org/entity/work/data/1744867999#Topic/statistical_physics_dynamical_systems_and_complexity> ; # Statistical Physics, Dynamical Systems and Complexity
   schema:about <http://experiment.worldcat.org/entity/work/data/1744867999#Topic/astronomie> ; # Astronomie
   schema:about <http://experiment.worldcat.org/entity/work/data/1744867999#Topic/numerical_and_computational_physics> ; # Numerical and Computational Physics
   schema:about <http://experiment.worldcat.org/entity/work/data/1744867999#Topic/physique> ; # Physique
   schema:about <http://experiment.worldcat.org/entity/work/data/1744867999#Topic/mathematics_calculus> ; # MATHEMATICS--Calculus
   schema:about <http://experiment.worldcat.org/entity/work/data/1744867999#Topic/mathematics_mathematical_analysis> ; # MATHEMATICS--Mathematical Analysis
   schema:about <http://dewey.info/class/515.984/e23/> ;
   schema:about <http://id.worldcat.org/fast/936125> ; # Functions, Abelian
   schema:about <http://experiment.worldcat.org/entity/work/data/1744867999#Topic/simulation_and_modeling> ; # Simulation and Modeling
   schema:author <http://viaf.org/viaf/307346625> ; # Guglielmo Paoletti
   schema:copyrightYear "2014" ;
   schema:datePublished "2013" ;
   schema:description "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."@en ;
   schema:description "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."@en ;
   schema:exampleOfWork <http://worldcat.org/entity/work/id/1744867999> ;
   schema:genre "Electronic books"@en ;
   schema:inLanguage "en" ;
   schema:isPartOf <http://worldcat.org/issn/2190-5053> ; # Springer theses,
   schema:isSimilarTo <http://worldcat.org/entity/work/data/1744867999#CreativeWork/deterministic_abelian_sandpile_models_and_patterns> ;
   schema:name "Deterministic Abelian sandpile models and patterns"@en ;
   schema:productID "859600045" ;
   schema:url <http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=641293> ;
   schema:url <http://public.eblib.com/choice/publicfullrecord.aspx?p=1466695> ;
   schema:url <http://dx.doi.org/10.1007/978-3-319-01204-9> ;
   schema:workExample <http://worldcat.org/isbn/9783319012049> ;
   schema:workExample <http://dx.doi.org/10.1007/978-3-319-01204-9> ;
   wdrs:describedby <http://www.worldcat.org/title/-/oclc/859600045> ;
    .


Related Entities

<http://experiment.worldcat.org/entity/work/data/1744867999#Topic/mathematical_physics> # Mathematical Physics
    a schema:Intangible ;
   schema:name "Mathematical Physics"@en ;
    .

<http://experiment.worldcat.org/entity/work/data/1744867999#Topic/mathematics_calculus> # MATHEMATICS--Calculus
    a schema:Intangible ;
   schema:name "MATHEMATICS--Calculus"@en ;
    .

<http://experiment.worldcat.org/entity/work/data/1744867999#Topic/mathematics_mathematical_analysis> # MATHEMATICS--Mathematical Analysis
    a schema:Intangible ;
   schema:name "MATHEMATICS--Mathematical Analysis"@en ;
    .

<http://experiment.worldcat.org/entity/work/data/1744867999#Topic/numerical_and_computational_physics> # Numerical and Computational Physics
    a schema:Intangible ;
   schema:name "Numerical and Computational Physics"@en ;
    .

<http://experiment.worldcat.org/entity/work/data/1744867999#Topic/probability_theory_and_stochastic_processes> # Probability Theory and Stochastic Processes
    a schema:Intangible ;
   schema:name "Probability Theory and Stochastic Processes"@en ;
    .

<http://experiment.worldcat.org/entity/work/data/1744867999#Topic/simulation_and_modeling> # Simulation and Modeling
    a schema:Intangible ;
   schema:name "Simulation and Modeling"@en ;
    .

<http://experiment.worldcat.org/entity/work/data/1744867999#Topic/statistical_physics_dynamical_systems_and_complexity> # Statistical Physics, Dynamical Systems and Complexity
    a schema:Intangible ;
   schema:name "Statistical Physics, Dynamical Systems and Complexity"@en ;
    .

<http://id.worldcat.org/fast/936125> # Functions, Abelian
    a schema:Intangible ;
   schema:name "Functions, Abelian"@en ;
    .

<http://viaf.org/viaf/307346625> # Guglielmo Paoletti
    a schema:Person ;
   schema:familyName "Paoletti" ;
   schema:givenName "Guglielmo" ;
   schema:name "Guglielmo Paoletti" ;
    .

<http://worldcat.org/entity/work/data/1744867999#CreativeWork/deterministic_abelian_sandpile_models_and_patterns>
    a schema:CreativeWork ;
   rdfs:label "Deterministic Abelian Sandpile Models and Patterns." ;
   schema:description "Print version:" ;
   schema:isSimilarTo <http://www.worldcat.org/oclc/859600045> ; # Deterministic Abelian sandpile models and patterns
    .

<http://worldcat.org/isbn/9783319012049>
    a schema:ProductModel ;
   schema:isbn "3319012045" ;
   schema:isbn "9783319012049" ;
    .

<http://worldcat.org/issn/2190-5053> # Springer theses,
    a bgn:PublicationSeries ;
   schema:hasPart <http://www.worldcat.org/oclc/859600045> ; # Deterministic Abelian sandpile models and patterns
   schema:issn "2190-5053" ;
   schema:name "Springer theses," ;
    .


Content-negotiable representations

Close Window

Please sign in to WorldCat 

Don't have an account? You can easily create a free account.