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Minimal model dynamics for twelvefold quasipatterns.

Damià Gomila1, Daniel Walgraef1

  • 1IFISC (CSIC-UIB), Instituto de Física Interdisciplinar y Sistemas Complejos, E-07122 Palma de Mallorca, Spain.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
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A new dynamical model explains twelvefold quasipattern formation in optical systems without external forcing. It highlights the crucial role of harmonics in stabilizing these complex patterns.

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Area of Science:

  • Nonlinear dynamics
  • Optical physics
  • Pattern formation

Background:

  • Twelvefold quasipatterns are observed in various systems, including optical ones.
  • Existing models often require external forcing for quasipattern generation.

Purpose of the Study:

  • To propose a dynamical model of the Swift-Hohenberg type for quasipattern formation.
  • To describe the generation of twelvefold quasipatterns without external forcing.
  • To incorporate angular dependence in nonlinear couplings.

Main Methods:

  • Development of a Swift-Hohenberg type dynamical model.
  • Inclusion of quadratic nonlinearities and angular-dependent nonlinear couplings.
  • Numerical analysis and amplitude equation framework.

Main Results:

  • The model successfully describes twelvefold quasipattern formation.
  • Harmonics built on critical modes are essential for quasipattern stabilization.
  • The model does not require external forcing for pattern generation.

Conclusions:

  • The proposed model provides a general mechanism for quasipattern formation.
  • Harmonics play a critical role in stabilizing quasipatterns.
  • The model is applicable to other systems with similar generic properties.