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Magnetically Induced Rotating Rayleigh-Taylor Instability
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Rotating waves in simple scalar excitable media: approximations and numerical solutions
B Ermentrout1, B I S van der Ventel2
1Department of Mathematics, University of Pittsburgh, Pittsburgh, USA. bard@pitt.edu.
Journal of Mathematical Biology
|March 30, 2016
Summary
This study investigates rotating waves in annular regions using semi-analytical methods and a phase model. The research focuses on calculating radial phase shifts, finding spiral twist varies non-monotonically with excitability near bifurcations.
Area of Science:
- Nonlinear dynamics
- Mathematical modeling
- Computational physics
Background:
- Rotating waves are crucial in various scientific fields.
- Understanding their behavior in confined geometries is complex.
- Phase models offer simplified yet insightful approaches.
Purpose of the Study:
- To analyze rotating waves in a 2D annular region.
- To develop and compare semi-analytical methods for predicting wave behavior.
- To determine the radial phase shift and its relation to spiral dynamics.
Main Methods:
- Utilized a one-variable phase model derived from saddle-node invariant circle (SNIC) bifurcation.
- Derived asymptotic expressions for the scalar dispersion relationship.
- Compared approximation methods against direct numerical simulations of the governing nonlinear partial differential equation.
Main Results:
- Developed approximation methods based on decomposing the solution into a base function and perturbation terms.
- Successfully derived expressions for the radial phase shift.
- Observed that the total twist of the spiral is not a monotonic function of excitability.
Conclusions:
- The radial phase shift is a key factor in understanding rotating wave dynamics.
- Maximum spiral twist occurs near the transition between excitable and oscillatory behaviors.
- Semi-analytical methods provide valuable approximations for complex nonlinear systems.
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