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Physics of Particles and Nuclei Letters

, Volume 6, Issue 7, pp 554–558 | Cite as

Discrete symmetry analysis of lattice systems

  • V. V. Kornyak
Article

Abstract

Discrete dynamical systems and mesoscopic lattice models are considered from the point of view of their symmetry groups. Some peculiarities in behavior of discrete systems induced by symmetries are pointed out. We reveal also the group origin of moving soliton-like structures similar to “spaceships” in cellular automata.

PACS number

04.60.Nc 01.30.Cc 03.67.-a 

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References

  1. 1.
    V. V. Kornyak, On Compatibility of Discrete Relations, Computer Algebra in Scientific Computing 2005, LNCS V.3718, Ed. by V. G. Ganzha, E. W. Mayr, and E. V. Vorozhtsov (Springer-Verlag, Berlin, Heidelberg, 2005), pp. 272–284; http://arXiv.org/abs/math-ph/0504048.CrossRefGoogle Scholar
  2. 2.
    V. V. Kornyak, “Discrete Relations On Abstract Simplicial Complexes,” Program. Comp. Software 32, 84–89 (2006).MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    B. D. McKay, “Practical Graph Isomporphism,” Congressus Numerantium 30, 45–87 (1981); http://cs.anu.edu.au/bdm/nauty/PGI.MathSciNetGoogle Scholar
  4. 4.
  5. 5.
    V. V. Kornyak, Cellular Automata with Symmetric Local Rules, Computer Algebra in Scientific Computing 2006. LNCS V.4194; Ed. by V. G. Ganzha, E. W. Mayr, and E. V. Vorozhtsov (Springer-Verlag, Berlin, Heidelberg, 2005), pp. 24–25.Google Scholar
  6. 6.
    M. Gardner, “On Cellular Automata Self-Reproduction, the Garden of Eden and the Game of “Life”, Sci. Am. 224, 112–117 (1971).CrossRefGoogle Scholar
  7. 7.
    G. t’Hooft, “Quantum Gravity as a Dissipative Deterministic System,” SPIN-1999/07, gr-qc/9903084; Class. Quant. Grav. 16, 3263 (1999); in Fundamental Interactions: From Symmetries to Black Holes, Proc. of the Conf. held on the occasion of the Eméritat of François Englert, 24–27 March 1999, Ed. by J.-M. Frére et al. (Univ. Libre de Bruxelles, Belgium, 1999,), pp. 221–240.MATHCrossRefMathSciNetADSGoogle Scholar
  8. 8.
    G. t’Hooft, “The Mathematical Basis for Deterministic Quantum Mechanics,” ITP-UU-06/14, SPIN-06/12, quant-ph/0604008 (2006), pp. 1–17.Google Scholar
  9. 9.
    D. H. E. Gross, Microcanonical Thermodynamics: Phase Transitions in “Small” Systems (World Sci., Singapore, 2001), p. 269.Google Scholar
  10. 10.
    D. H. E. Gross, “A New Thermodynamics from Nuclei To Stars,” Entropy 6, 158–179 (2004).MATHCrossRefADSGoogle Scholar
  11. 11.
    D. H. E. Gross and E. V. Votyakov, “Phase Transitions in “Small” Systems,” Eur. Phys. J. B 15, 115–126 (2000).ADSGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2009

Authors and Affiliations

  1. 1.LIT JINRMoscowRussia

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