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This study investigates pattern dynamics after directional quenches, revealing how stripe selection influences modulation equations. The research characterizes defect behavior, including grain boundaries and phase-slips, using a derived Burgers

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Area of Science:

  • Nonlinear Dynamics
  • Pattern Formation
  • Statistical Physics

Background:

  • Directional quenches are used to control pattern formation in various media.
  • Striped patterns emerge in the wake of these quenches, with selected wavenumber and orientation.
  • Understanding the dynamics of these patterns and defects is crucial for applications.

Purpose of the Study:

  • To analyze the modulational dynamics of striped patterns generated by directional quenches.
  • To derive a model describing transverse dynamics and defect behavior.
  • To connect quench properties to the parameters of the derived modulation equation.

Main Methods:

  • Multiple-scale analysis of the complex Ginzburg-Landau and Swift-Hohenberg equations.
  • Derivation of a one-dimensional viscous Burgers' equation for transverse dynamics.
  • Characterization of defect dynamics using the derived approximation.

Main Results:

  • A Burgers' equation accurately describes long-wavelength modulations and defect dynamics transverse to the quench.
  • The wavenumber selection property of the quench directly influences the nonlinear flux parameter.
  • The viscosity parameter of the Burgers' equation is linked to the stripe state's transverse diffusivity.
  • The derived model effectively characterizes transverse dynamics of defects like grain boundaries and phase-slips.

Conclusions:

  • The study provides a robust framework for understanding pattern evolution and defect dynamics post-quench.
  • The derived Burgers' equation offers a simplified yet accurate model for transverse dynamics.
  • This work elucidates the relationship between quench parameters and emergent pattern behavior.