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Communications in Mathematical Physics

, Volume 265, Issue 1, pp 165–188 | Cite as

Minimal Configurations for the Frenkel-Kontorova Model on a Quasicrystal

  • Jean-Marc GambaudoEmail author
  • Pierre Guiraud
  • Samuel Petite
Article

Abstract

In this paper, we consider the Frenkel-Kontorova model of a one dimensional chain of atoms submitted to a potential. This potential splits into an interaction potential and a potential induced by an underlying substrate which is a quasicrystal. Under standard hypotheses, we show that every minimal configuration has a rotation number, that the rotation number varies continuously with the minimal configuration, and that every non negative real number is the rotation number of a minimal configuration. This generalizes well known results obtained by S. Aubry and P.Y. le Daeron in the case of a crystalline substrate.

Keywords

Neural Network Statistical Physic Real Number Complex System Nonlinear Dynamics 
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.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Jean-Marc Gambaudo
    • 1
    Email author
  • Pierre Guiraud
    • 2
  • Samuel Petite
    • 3
  1. 1.Centro de Modelamiento Matemático, U.M.I. CNRS 2807Universidad de ChileSantiagoChile
  2. 2.Departamento de Ingeniería Matemática, Fac. Ciencias Físicas y MatemáticasUniversidad de ChileSantiagoChile
  3. 3.Institut de Mathématiques de Bourgogne, U.M.R. CNRS 5584Université de Bourgogne, U.F.R. des Sciences et TéchniquesDijon CedexFrance

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