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Front propagation steered by a high-wavenumber modulation: Theory and experiments.

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Spatially modulated forcing in dynamical systems creates coexisting patterns and complex front dynamics. This study investigates these phenomena in the high-wavenumber limit, verified by experiments.

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Area of Science:

  • Nonlinear Dynamics
  • Pattern Formation
  • Liquid Crystal Physics

Background:

  • Dynamical systems with homogeneous forcing exhibit multistability, leading to rich front dynamics between equilibria.
  • Spatially modulated forcing qualitatively preserves this phenomenology, but the organization of equilibria and front dynamics remains incompletely understood.

Purpose of the Study:

  • Investigate equilibria and front dynamics in the high-wavenumber limit under spatially modulated forcing.
  • Analyze pattern formation and coexistence with uniform states.
  • Characterize front dynamics theoretically and numerically.

Main Methods:

  • Utilized a model of liquid crystal light valve reorientation with spatially modulated optical forcing.
  • Applied the homogenization method for analysis.
  • Conducted theoretical and numerical characterization of front dynamics.

Main Results:

  • Spatially modulated forcing induces patterns that coexist with the uniform state, even in regions where the system is typically monostable.
  • Theoretical and numerical analyses elucidated the organization of equilibria and front dynamics.
  • Experimental results confirmed the predicted phenomena and bistability law.

Conclusions:

  • The study provides a comprehensive understanding of equilibria and front dynamics in high-wavenumber systems with modulated forcing.
  • Experimental validation confirms the theoretical framework and the law governing bistability.
  • Findings contribute to the understanding of pattern formation and multistability in driven systems.