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Accurate eikonal-curvature relation for wave fronts in locally anisotropic reaction-diffusion systems
Hans Dierckx1, Olivier Bernus, Henri Verschelde
1Department of Physics and Astronomy, Ghent University, 9000 Gent, Belgium.
Physical Review Letters
|October 11, 2011
Summary
Wave speed in reaction-diffusion systems depends on front curvature. This study derives a new relation for anisotropic diffusion, revealing hidden geometrical curvature in planar waves and impacting vortex dynamics.
Area of Science:
- * Mathematical modeling and theoretical physics.
- * Computational biology and biophysics.
Background:
- * Wave propagation in reaction-diffusion (RD) systems is crucial for understanding phenomena like cardiac tissue dynamics.
- * Wave velocity is influenced by front curvature, affecting stability and spatial configurations (e.g., vortices).
- * Spatially varying anisotropic diffusion complicates wave behavior.
Purpose of the Study:
- * To derive a covariant eikonal-curvature relation for general RD systems with anisotropic diffusion.
- * To investigate the impact of local anisotropy on wave geometry and speed.
- * To provide a theoretical framework for understanding complex wave patterns.
Main Methods:
- * Theoretical derivation of a covariant eikonal-curvature relation.
- * Numerical simulations of wave propagation in anisotropic RD systems.
- * Analysis of deviations from nominal plane wave speed.
Main Results:
- * First derivation of a covariant eikonal-curvature relation for anisotropic RD systems.
- * Confirmation that planar waves can exhibit non-vanishing geometrical curvature due to local anisotropy.
- * Numerical simulations show up to 20% deviation from nominal plane wave speed.
Conclusions:
- * Local anisotropy induces geometrical curvature even in seemingly planar waves.
- * The derived relation accurately predicts wave behavior in complex anisotropic media.
- * Findings are critical for understanding wave stability and spatial patterns in biological tissues.
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