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Pattern Formation

Strings, Backgrounds and their Classification
  • Guglielmo PaolettiEmail author
Chapter
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Part of the Springer Theses book series (Springer Theses)

Abstract

It has been spent a huge amount of efforts in the study of Abelian Sandpile Model, as prototype of Self Organized Criticality.

Keywords

Abelian Sandpile Model Polygonal Frames Box Frame Recurrent Configurations Tile Background 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    D. Dhar, T. Sadhu, S. Chandra, Pattern formation in growing sandpiles. Europhys. Lett. 85, 48002 (2009)ADSCrossRefGoogle Scholar
  2. 2.
    T. Sadhu, D. Dhar, Pattern formation in growing sandpiles with multiple sources or sinks. J. Stat. Phys. 138, 815–837 (2010). doi: 10.1007/s10955-009-9901-3 MathSciNetADSCrossRefzbMATHGoogle Scholar
  3. 3.
    D. Dhar, T. Sadhu, Pattern Formation in Fast-Growing Sandpiles, ArXiv e-prints, (2011), arXiv:1109.2908v1Google Scholar
  4. 4.
    T. Sadhu, D. Dhar, The effect of noise on patterns formed by growing sandpiles. J. Stat. Mech.: Theor. Exp. 2011, P03001 (2011). arXiv:1012.4809Google Scholar
  5. 5.
    S. Caracciolo, G. Paoletti, A. Sportiello, Conservation laws for strings in the abelian sandpile model. Europhys. Lett. 90, 60003 (2010). arXiv:1002.3974v1Google Scholar
  6. 6.
    D. Dhar, Self-organized critical state of sandpile automaton models. Phys. Rev. Lett. 64, 1613–1616 (1990)MathSciNetADSCrossRefzbMATHGoogle Scholar
  7. 7.
    P. Bak, C. Tang, K. Wiesenfeld, Self-organized criticality: an explanation of the 1/f noise. Phys. Rev. Lett. 59, 381–384 (1987)MathSciNetADSCrossRefGoogle Scholar
  8. 8.
    M. Creutz, Abelian sandpiles. Comp. Phys. 5, 198–203 (1991)CrossRefGoogle Scholar
  9. 9.
    Y. Le-Borgne, D. Rossin, On the identity of the sandpile group, Discrete Mathematics. LaCIM 2000 Conf. Combinator. Comp. Sci. Appl. 256, 775–790 (2002)Google Scholar
  10. 10.
    S. Caracciolo, G. Paoletti, A. Sportiello, Explicit characterization of the identity configuration in an abelian sandpile model. J. Phys. A: Math. Theor. 41, 495003 (2008). arXiv:0809.3416v2Google Scholar
  11. 11.
    M. Creutz, Abelian sandpiles. Nucl. Phys. B (Proc. Suppl.), 20, 758–761 (1991)Google Scholar
  12. 12.
    S. Ostojic, Patterns formed by addition of grains to only one site of an abelian sandpile. Phys. A: Stat. Mech. Appl. 318, 187–199 (2003)CrossRefzbMATHGoogle Scholar
  13. 13.
    A. Fey-den Boer, F. Redig, Limiting shapes for deterministic centrally seeded growth models. J. Stat. Phys. 130, 579–597 (2008). doi: 10.1007/s10955-007-9450-6 MathSciNetADSCrossRefzbMATHGoogle Scholar
  14. 14.
    M. Widom, Bethe ansatz solution of the square-triangle random tiling model. Phys. Rev. Lett. 70, 2094–2097 (1993)ADSCrossRefGoogle Scholar
  15. 15.
    P.A. Kalugin, The square-triangle random-tiling model in the thermodynamic limit. J. Phys. A: Math. General 27, 3599 (1994)MathSciNetADSCrossRefzbMATHGoogle Scholar
  16. 16.
    A. Verberkmoes, B. Nienhuis, Triangular trimers on the triangular lattice: an exact solution. Phys. Rev. Lett. 83, 3986–3989 (1999)ADSCrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.LIP6 - (Université Paris 6) UPMCParis Cedex 05France

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