Order Parameter Equations for Front Transitions: Nonuniformly Curved Fronts

Abstract

Kinematic equations for the motion of slowly propagating, weakly curved fronts in bistable media are derived. The equations generalize earlier derivations where algebraic relations between the normal front velocity and its curvature are assumed. Such relations do not capture the dynamics near nonequilibrium Ising-Bloch (NIB) bifurcations, where transitions between counterpropagating Bloch fronts may spontaneously occur. The kinematic equations consist of coupled integro-differential equations for the front curvature and the front velocity, the order parameter associated with the NIB bifurcation. They capture the NIB bifurcation, the instabilities of Ising and Bloch fronts to transverse perturbations, the core structure of a spiral wave, and the dynamic process of spiral wave nucleation.

20 pages. Aric Hagberg: http://cnls.lanl.gov/~aric; Ehud Meron:http://www.bgu.ac.il/BIDR/research/staff/meron.html

References in corpus (11)

• 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
• 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
• Dynamic Front Transitions and Spiral-Vortex Nucleation
• The Dynamics of Curved Fronts: Beyond Geometry
• Order Parameter Equations for Front Transitions: Planar and Circular Fronts

Cited by in corpus (5)

• The existence of localized vegetation patterns in a systematically reduced model for dryland vegetation
• Time-delayed-feedback control of pattern formation in symmetrical bistable media
• Transformation between dense and sparse spirals in symmetrical bistable media
• Reduction approach to the dynamics of interacting front solutions in a bistable reaction-diffusion system and its application to heterogeneous media
• Complex pattern formation driven by the interaction of stable fronts in a competition-diffusion system