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

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.