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Related Experiment Videos

Defect formation in the Swift-Hohenberg equation.

Tobias Galla1, Esteban Moro

  • 1Theoretical Physics, University of Oxford, 1 Keble Road, United Kingdom. galla@thphys.ox.ac.uk

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|April 12, 2003
PubMed
Summary

The Kibble-Zurek theory accurately predicts defect formation in the Swift-Hohenberg model during rapid quenches. Local pattern variations and defect types influence the characteristic length scale and defect density.

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Area of Science:

  • Complex Systems
  • Nonlinear Dynamics
  • Fluid Dynamics

Background:

  • The Swift-Hohenberg model describes pattern formation in systems like Rayleigh-Bénard convection.
  • Understanding defect formation is crucial for characterizing pattern evolution.

Purpose of the Study:

  • To investigate defect dynamics during finite-time quenches in the 2D Swift-Hohenberg model.
  • To assess the applicability of the Kibble-Zurek theory to this system.
  • To identify key factors influencing defect density and selected length scales.

Main Methods:

  • Numerical simulations of the Swift-Hohenberg model.
  • Analytical investigations of defect formation dynamics.
  • Application of the Kibble-Zurek scaling theory.

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Main Results:

  • The Kibble-Zurek picture successfully describes the defect density generated during the quench.
  • Local variations in patterns and the coexistence of pointlike and extended defects are significant.
  • A characteristic length scale selected during the quench is identified and linked to defect density.

Conclusions:

  • The study validates the Kibble-Zurek theory for defect formation in the Swift-Hohenberg model.
  • Local domain properties and defect morphology are critical for understanding quench dynamics.
  • Findings provide insights into the coarsening process of patterns in this model.