000 03461nam a22005055i 4500
001 978-3-319-01204-9
003 DE-He213
005 20140220082508.0
007 cr nn 008mamaa
008 130916s2014 gw | s |||| 0|eng d
020 _a9783319012049
_9978-3-319-01204-9
024 7 _a10.1007/978-3-319-01204-9
_2doi
050 4 _aQC174.7-175.36
072 7 _aPHS
_2bicssc
072 7 _aPHDT
_2bicssc
072 7 _aSCI055000
_2bisacsh
082 0 4 _a621
_223
100 1 _aPaoletti, Guglielmo.
_eauthor.
245 1 0 _aDeterministic Abelian Sandpile Models and Patterns
_h[electronic resource] /
_cby Guglielmo Paoletti.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Springer,
_c2014.
300 _aXII, 163 p. 64 illus., 33 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aSpringer Theses, Recognizing Outstanding Ph.D. Research,
_x2190-5053
505 0 _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.
520 _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.
650 0 _aPhysics.
650 0 _aComputer simulation.
650 0 _aDistribution (Probability theory).
650 1 4 _aPhysics.
650 2 4 _aStatistical Physics, Dynamical Systems and Complexity.
650 2 4 _aNumerical and Computational Physics.
650 2 4 _aMathematical Physics.
650 2 4 _aProbability Theory and Stochastic Processes.
650 2 4 _aSimulation and Modeling.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783319012032
830 0 _aSpringer Theses, Recognizing Outstanding Ph.D. Research,
_x2190-5053
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-319-01204-9
912 _aZDB-2-PHA
999 _c92608
_d92608