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Dynamic quasicrystalline patterns: wave-mode-turing-mode resonance with turing-mode self-interaction

Musslimani1, Pismen

  • 1Department of Mathematics, Technion-Israel Institute of Technology, Technion City, 32000 Haifa, Israel.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|November 23, 2000
PubMed
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Resonant Turing-mode interactions can stabilize quasicrystalline patterns. This stabilization occurs through quadratic wave-Turing interactions, even with weak Turing self-interactions present.

Area of Science:

  • Pattern formation
  • Nonlinear dynamics
  • Mathematical physics

Background:

  • Quasicrystalline patterns arise from complex interactions.
  • Turing-mode interactions influence pattern stability.
  • Wave and static composite modes are key components.

Purpose of the Study:

  • To investigate the impact of resonant Turing-mode interactions on quasicrystalline pattern evolution.
  • To determine conditions for pattern stabilization under these interactions.

Main Methods:

  • Perturbative analysis of pattern dynamics.
  • Study of resonant interactions between wave and static composite modes.
  • Examination of quadratic wave-mode-Turing-mode interactions.

Main Results:

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  • Stabilization of quasicrystalline patterns is achievable.
  • Quadratic wave-mode-Turing-mode interactions are crucial for stabilization.
  • Stabilization persists despite weak destabilizing Turing-mode self-interactions.

Conclusions:

  • Resonant Turing-mode interactions offer a mechanism for stabilizing quasicrystalline patterns.
  • The findings highlight the role of specific interaction types in pattern dynamics.