77 research outputs found
Order Parameter Equations for Front Transitions: Nonuniformly Curved Fronts
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.Comment: 20 pages. Aric Hagberg: http://cnls.lanl.gov/~aric; Ehud
Meron:http://www.bgu.ac.il/BIDR/research/staff/meron.htm
Kinematic Equations for Front Motion and Spiral-Wave Nucleation
We present a new set of kinematic equations for front motion in bistable
media. The equations extend earlier kinematic approaches by coupling the front
curvature with the order parameter associated with a parity breaking front
bifurcation. In addition to naturally describing the core region of rotating
spiral waves the equations can be be used to study the nucleation of
spiral-wave pairs along uniformly propagating fronts. The analysis of
spiral-wave nucleation reduces to the simpler problem of droplet, or domain,
nucleation in one space dimension.Comment: 8 pages. Aric Hagberg: http://cnls.lanl.gov/~aric; Ehud Meron:
http://www.bgu.ac.il/BIDR/research/staff/meron.htm
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