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Accurate eikonal-curvature relation for wave fronts in locally anisotropic reaction-diffusion systems

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Abstract
The dependency of wave velocity in reaction-diffusion (RD) systems on the local front curvature determines not only the stability of wave propagation, but also the fundamental properties of other spatial configurations such as vortices. This Letter gives the first derivation of a covariant eikonal-curvature relation applicable to general RD systems with spatially varying anisotropic diffusion properties, such as cardiac tissue. The theoretical prediction that waves which seem planar can nevertheless possess a nonvanishing geometrical curvature induced by local anisotropy is confirmed by numerical simulations, which reveal deviations up to 20% from the nominal plane wave speed.
Keywords
MYOCARDIUM, FILAMENTS, INSTABILITY, PROPAGATION, SPIRAL WAVES, EXCITABLE MEDIA, DYNAMICS

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Citation

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Chicago
Dierckx, Hans, Olivier Bernus, and Henri Verschelde. 2011. “Accurate Eikonal-curvature Relation for Wave Fronts in Locally Anisotropic Reaction-diffusion Systems.” Physical Review Letters 107 (10).
APA
Dierckx, H., Bernus, O., & Verschelde, H. (2011). Accurate eikonal-curvature relation for wave fronts in locally anisotropic reaction-diffusion systems. PHYSICAL REVIEW LETTERS, 107(10).
Vancouver
1.
Dierckx H, Bernus O, Verschelde H. Accurate eikonal-curvature relation for wave fronts in locally anisotropic reaction-diffusion systems. PHYSICAL REVIEW LETTERS. 2011;107(10).
MLA
Dierckx, Hans, Olivier Bernus, and Henri Verschelde. “Accurate Eikonal-curvature Relation for Wave Fronts in Locally Anisotropic Reaction-diffusion Systems.” PHYSICAL REVIEW LETTERS 107.10 (2011): n. pag. Print.
@article{2119330,
  abstract     = {The dependency of wave velocity in reaction-diffusion (RD) systems on the local front curvature determines not only the stability of wave propagation, but also the fundamental properties of other spatial configurations such as vortices. This Letter gives the first derivation of a covariant eikonal-curvature relation applicable to general RD systems with spatially varying anisotropic diffusion properties, such as cardiac tissue. The theoretical prediction that waves which seem planar can nevertheless possess a nonvanishing geometrical curvature induced by local anisotropy is confirmed by numerical simulations, which reveal deviations up to 20% from the nominal plane wave speed.},
  articleno    = {108101},
  author       = {Dierckx, Hans and Bernus, Olivier and Verschelde, Henri},
  issn         = {0031-9007},
  journal      = {PHYSICAL REVIEW LETTERS},
  keywords     = {MYOCARDIUM,FILAMENTS,INSTABILITY,PROPAGATION,SPIRAL WAVES,EXCITABLE MEDIA,DYNAMICS},
  language     = {eng},
  number       = {10},
  pages        = {5},
  title        = {Accurate eikonal-curvature relation for wave fronts in locally anisotropic reaction-diffusion systems},
  url          = {http://dx.doi.org/10.1103/PhysRevLett.107.108101},
  volume       = {107},
  year         = {2011},
}

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