LEADER 04651nam 22007695 450 001 9910300389003321 005 20200630104551.0 010 $a3-319-01204-5 024 7 $a10.1007/978-3-319-01204-9 035 $a(CKB)2670000000428608 035 $a(EBL)1466695 035 $a(SSID)ssj0001010778 035 $a(PQKBManifestationID)11593327 035 $a(PQKBTitleCode)TC0001010778 035 $a(PQKBWorkID)11018177 035 $a(PQKB)10740826 035 $a(MiAaPQ)EBC1466695 035 $a(DE-He213)978-3-319-01204-9 035 $a(PPN)172423678 035 $a(EXLCZ)992670000000428608 100 $a20130916d2014 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aDeterministic Abelian Sandpile Models and Patterns /$fby Guglielmo Paoletti 205 $a1st ed. 2014. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2014. 215 $a1 online resource (171 p.) 225 1 $aSpringer Theses, Recognizing Outstanding Ph.D. Research,$x2190-5053 300 $aDescription based upon print version of record. 311 $a3-319-01203-7 327 $aIntroduction -- 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. 330 $aThe model investigated in this work, a particular cellular automaton with stochastic evolution, was introduced as the simplest case of self-organized-criticality, that is, a dynamical system which shows algebraic long-range correlations without any tuning of parameters.   The author derives exact results which are potentially also interesting outside the area of critical phenomena. Exact means also site-by-site and not only ensemble average or coarse graining. Very complex and amazingly beautiful periodic patterns are often generated by the dynamics involved, especially in deterministic protocols in which the sand is added at chosen sites. For example, the author studies the appearance of allometric structures, that is, patterns which grow in the same way in their whole body, and not only near their boundaries, as commonly occurs. The local conservation laws which govern the evolution of these patterns are also presented. This work has already attracted interest, not only in non-equilibrium statistical mechanics, but also in mathematics, both in probability and in combinatorics. There are also interesting connections with number theory. Lastly, it also poses new questions about an old subject. As such, it will be of interest to computer practitioners, demonstrating the simplicity with which charming patterns can be obtained, as well as to researchers working in many other areas. 410 0$aSpringer Theses, Recognizing Outstanding Ph.D. Research,$x2190-5053 606 $aStatistical physics 606 $aDynamical systems 606 $aPhysics 606 $aMathematical physics 606 $aProbabilities 606 $aComputer simulation 606 $aComplex Systems$3https://scigraph.springernature.com/ontologies/product-market-codes/P33000 606 $aNumerical and Computational Physics, Simulation$3https://scigraph.springernature.com/ontologies/product-market-codes/P19021 606 $aMathematical Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/M35000 606 $aProbability Theory and Stochastic Processes$3https://scigraph.springernature.com/ontologies/product-market-codes/M27004 606 $aSimulation and Modeling$3https://scigraph.springernature.com/ontologies/product-market-codes/I19000 606 $aStatistical Physics and Dynamical Systems$3https://scigraph.springernature.com/ontologies/product-market-codes/P19090 615 0$aStatistical physics. 615 0$aDynamical systems. 615 0$aPhysics. 615 0$aMathematical physics. 615 0$aProbabilities. 615 0$aComputer simulation. 615 14$aComplex Systems. 615 24$aNumerical and Computational Physics, Simulation. 615 24$aMathematical Physics. 615 24$aProbability Theory and Stochastic Processes. 615 24$aSimulation and Modeling. 615 24$aStatistical Physics and Dynamical Systems. 676 $a530 676 $a530.15 700 $aPaoletti$b Guglielmo$4aut$4http://id.loc.gov/vocabulary/relators/aut$0791353 906 $aBOOK 912 $a9910300389003321 996 $aDeterministic Abelian Sandpile Models and Patterns$91768733 997 $aUNINA