Order parameter equations for front transitions: Nonuniformly curved fronts

Aric Hagberg, Ehud Meron

Research output: Contribution to journalArticlepeer-review

22 Scopus citations


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.

Original languageEnglish
Pages (from-to)460-473
Number of pages14
JournalPhysica D: Nonlinear Phenomena
Issue number1-4
StatePublished - 1 Jan 1998


  • Interface motion
  • Reaction-diffusion
  • Spiral waves

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Applied Mathematics


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