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Disclinations in square and hexagonal patterns.

A A Golovin1, A A Nepomnyashchy

  • 1Department of Engineering Sciences and Applied Mathematics, Northwestern University, Evanston, Illinois 60208-3100, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|June 6, 2003
PubMed
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Researchers observed stable fractional topological charge defects, known as disclinations, in various pattern-forming systems. These findings advance the understanding of pattern defects in physics and fluid dynamics.

Area of Science:

  • Physics
  • Fluid Dynamics
  • Nonlinear Dynamics

Background:

  • Pattern-forming systems are ubiquitous in nature and described by generic equations.
  • Topological defects, such as disclinations, can arise in these patterns.
  • Understanding the stability and structure of these defects is crucial for characterizing pattern dynamics.

Purpose of the Study:

  • To report the observation of defects with fractional topological charges (disclinations).
  • To investigate the stability of these disclinations in square and hexagonal patterns.
  • To analyze the structure of disclinations using generalized Cross-Newell equations.

Main Methods:

  • Numerical solutions of generic pattern-forming equations, including the Swift-Hohenberg and damped Kuramoto-Sivashinsky equations.

Related Experiment Videos

  • Modeling large-scale Rayleigh-Benard and Marangoni convection with nearly insulated boundaries.
  • Analysis of disclination structure via generalized Cross-Newell equations.

    • Main Results:

    • Observation of fractional topological charge disclinations in square and hexagonal patterns.
    • Demonstration that these disclinations can be stable when nucleated from specific initial conditions.
    • Characterization of the disclination structure through generalized Cross-Newell equations.

    Conclusions:

    • Fractional topological charge disclinations are observable in generic pattern-forming systems.
    • The stability of these disclinations is dependent on initial nucleation conditions.
    • Generalized Cross-Newell equations provide a framework for analyzing disclination structures.