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Related Experiment Videos

Example of a chaotic crystal: the labyrinth.

M Le Berre1, E Ressayre, A Tallet

  • 1Laboratoire de Photophysique Moléculaire, Bâtiment 210, Université de Paris-Sud, 91405 Orsay Cedex, France.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 21, 2002
PubMed
Summary

Labyrinthine structures, disordered patterns in systems, share short-range order with turbulent crystals. Their stability relative to parallel rolls depends on system type and initial conditions.

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Area of Science:

  • Complex systems
  • Pattern formation
  • Fluid dynamics

Background:

  • Labyrinthine structures are common final states in pattern-forming systems.
  • These disordered patterns exhibit short-range positional order, similar to Newell-Pomeau turbulent crystals.
  • They can be viewed as a limiting case of disordered rolls with coherence length near the wavelength.

Purpose of the Study:

  • To investigate the relationship between labyrinthine structures and parallel rolls in two-dimensional model equations.
  • To compare the stability of labyrinthine structures versus parallel rolls under different modeling approaches.
  • To explore the conditions leading to the formation of labyrinths from parallel rolls.

Main Methods:

  • Analysis of various two-dimensional model equations.

Related Experiment Videos

  • Comparison of steady-state parameters for labyrinths and parallel rolls.
  • Numerical experiments to observe bifurcations between structures.
  • Energy comparison between variational models.

    • Main Results:

    • Labyrinths and parallel rolls emerge as steady states for the same parameters, dependent on initial conditions.
    • In variational models, rolls are consistently more stable than labyrinths, with very close energy values.
    • A numerical experiment demonstrated a clear bifurcation from parallel rolls to labyrinths in a nonvariational model, with labyrinths being the more stable state.

    Conclusions:

    • The occurrence of labyrinths versus parallel rolls is dictated by initial conditions in many pattern-forming systems.
    • Stability analysis reveals nuanced differences between variational and nonvariational models regarding these structures.
    • Nonvariational models can exhibit bifurcations where labyrinths become the preferred, more stable pattern.