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A model for a driven Frenkel–Kontorova chain

Author

Listed:
  • Wolfgang Quapp

    (Mathematisches Institut, Universität Leipzig, PF 100920)

  • Josep Maria Bofill

    (Departament de Química Inorgànica i Orgànica, Secció de Química Orgànica, and Institut de Química Teòrica i Computacional, (IQTCUB), Universitat de Barcelona)

Abstract

We study a Frenkel–Kontorova (FK) model of a finite chain with free-end boundary conditions. The model has two competing potentials. Newton trajectories are an ideal tool to understand the circumstances under a driving of an FK chain by external forces. To reach the insights we calculate some stationary structures for a chain with 23 particles. We search the lowest energy saddle points for a complete minimum energy path of the chain for a movement over the full period of the on-site potential, a sliding. If an additional tilting is set, then one is interested in barrier breakdown points (BBPs) on the potential energy surface for a critical tilting force named the static frictional force. In symmetric cases, such BBPs are often valley-ridge inflection points of the potential energy surface. We explain the theory and demonstrate it with an example. We propose a model for a DC drive, as well as an AC drive, of the chain using special directional vectors of the external force. Graphical abstract

Suggested Citation

  • Wolfgang Quapp & Josep Maria Bofill, 2019. "A model for a driven Frenkel–Kontorova chain," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 92(5), pages 1-15, May.
    • Handle: RePEc:spr:eurphb:v:92:y:2019:i:5:d:10.1140_epjb_e2019-90703-0
    DOI: 10.1140/epjb/e2019-90703-0
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