Vortex glass and vortex liquid in oscillatory media.

Area of Science:

• Nonlinear dynamics
• Complex systems
• Pattern formation

Background:

• Two-dimensional oscillatory media often exhibit spiral or vortex solutions.
• These spiral solutions are typically assumed to be static or unchanging over time.
• The complex Ginzburg-Landau equation (CGLE) is a standard model for studying such phenomena.

Purpose of the Study:

• To investigate the dynamics of disordered, multispiral solutions in 2D oscillatory media.
• To determine if these multispiral states, under conditions where single-spiral solutions are stable, exhibit any evolution.
• To characterize the nature of any observed dynamics, particularly defect-mediated turbulence.

Main Methods:

• Utilized the complex Ginzburg-Landau equation (CGLE) to model the oscillatory media.
• Reduced the CGLE to a simpler model describing the evolution of vortex coordinates.
• Analyzed the behavior of multispiral solutions for specific parameter regimes.

Main Results:

• Demonstrated that disordered multispiral solutions, contrary to prior belief, evolve extremely slowly.
• Identified two distinct phases of this slow evolution, termed defect-mediated turbulence.
• Characterized these phases as a 'vortex liquid' (normal spiral diffusion) and a 'vortex glass' (slowly relaxing, intermittent behavior).

Conclusions:

• Multispiral states in 2D oscillatory media are not static but exhibit very slow dynamics.
• This slow evolution is driven by the collective motion of vortices (defects).
• The observed defect-mediated turbulence transitions between a diffusive vortex liquid and an intermittent vortex glass state.