Order Parameter Equations for Front Transitions: Nonuniformly Curved Fronts

Details Order Parameter Equations for Front Transitions: Nonuniformly Curved Fronts Order Parameter Equations for Front Transitions: Nonuniformly Curved Fronts

1997-07-29

arxiv.org/abs/patt-sol/9707007v1

Nonlinear Sciences

Pattern Formation and Solitons

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

Scientific paper

10.1016/S0167-2789(98)00143-2

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.

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