Dynamic Front Transitions and Spiral-Vortex Nucleation

Abstract

This is a study of front dynamics in reaction diffusion systems near Nonequilibrium Ising-Bloch bifurcations. We find that the relation between front velocity and perturbative factors, such as external fields and curvature, is typically multivalued. This unusual form allows small perturbations to induce dynamic transitions between counter-propagating fronts and nucleate spiral vortices. We use these findings to propose explanations for a few numerical and experimental observations including spiral breakup driven by advective fields, and spot splitting.

References in corpus (5)

• Complex Patterns in a Simple System
• Pattern Formation in Dissipative Nonvariational Systems: The Effects of Front Bifurcations
• From Labyrinthine Patterns to Spiral Turbulence
• Complex Patterns in Reaction-Diffusion Systems: A Tale of Two Front Instabilities
• Domain Walls in Non-Equilibrium Systems and the Emergence of Persistent Patterns

Cited by in corpus (12)

• Complex Patterns in Reaction-Diffusion Systems: A Tale of Two Front Instabilities
• Interface Proliferation and the Growth of Labyrinths in a Reaction-Diffusion System
• Controlling domain patterns far from equilibrium
• Breathing Spots in a Reaction-Diffusion System
• General theory of instabilities for patterns with sharp interfaces in reaction-diffusion systems
• The Dynamics of Curved Fronts: Beyond Geometry
• Order Parameter Equations for Front Transitions: Nonuniformly Curved Fronts
• Order Parameter Equations for Front Transitions: Planar and Circular Fronts
• Links, Knots and Knotted Labyrinths in Bistable Systems
• Propagation Failure in Excitable Media
• Interaction of Ising-Bloch fronts with Dirichlet Boundaries
• Complex pattern formation driven by the interaction of stable fronts in a competition-diffusion system