Order parameter equations for front transitions: Planar and circular fronts

Journal Article · Tue Apr 01 04:00:00 EST 1997 · Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

DOI:https://doi.org/10.1103/PhysRevE.55.4450· OSTI ID:491641

Hagberg, A ^[1]; Meron, E ^[2]; Rubinstein, I; Zaltzman, B ^[3]

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1. Center for Nonlinear Studies and T-7, Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States)
2. The Jacob Blaustein Institute for Desert Research and the Physics Department, Ben-Gurion University, Sede Boker Campus 84990 (Israel)
3. The Jacob Blaustein Institute for Desert Research and the Mathematics Department, Ben-Gurion University, Sede Boker Campus 84990 (Israel)

Near a parity breaking front bifurcation, small perturbations may reverse the propagation direction of fronts. Often this results in nonsteady asymptotic motion, such as breathing and domain breakup. Exploiting the time scale differences of an activator-inhibitor model and the proximity to the front bifurcation, we derive equations of motion for planar and circular fronts. The equations involve a translational degree of freedom and an order parameter describing transitions between left and right propagating fronts. Perturbations, such as a space dependent advective field or uniform curvature (axisymmetric spots), couple these two degrees of freedom. In both cases this leads to a transition from stationary to oscillating fronts as the parity breaking bifurcation is approached. For axisymmetric spots, two additional dynamic behaviors are found: rebound and collapse. {copyright} {ital 1997} {ital The American Physical Society}

• OSTI ID: 491641
• Journal Information: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, Journal Name: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics Journal Issue: 4 Vol. 55; ISSN 1063-651X; ISSN PLEEE8
• Country of Publication: United States
• Language: English

Related Subjects

40 CHEMISTRY
66 PHYSICS
CHEMICAL REACTIONS
CONFIGURATION
DIFFUSION
EQUATIONS OF MOTION
ORDER PARAMETERS
OSCILLATIONS
P INVARIANCE
REACTION KINETICS
SYMMETRY BREAKING