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Drift laws for spiral waves on curved anisotropic surfaces

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Abstract
Rotating spiral waves organize spatial patterns in chemical, physical, and biological excitable systems. Factors affecting their dynamics, such as spatiotemporal drift, are of great interest for particular applications. Here, we propose a quantitative description for spiral wave dynamics on curved surfaces which shows that for a wide class of systems, including the Belousov-Zhabotinsky reaction and anisotropic cardiac tissue, the Ricci curvature scalar of the surface is the main determinant of spiral wave drift. The theory provides explicit equations for spiral wave drift direction, drift velocity, and the period of rotation. Depending on the parameters, the drift can be directed to the regions of either maximal or minimal Ricci scalar curvature, which was verified by direct numerical simulations.
Keywords
EXCITABLE MEDIA, 3-DIMENSIONAL SCROLL WAVES, HUMAN ATRIA, ROTATIONAL ANISOTROPY, PROPAGATION, MODEL, REENTRY, FILAMENTS, MUSCLE, TACHYCARDIA

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Citation

Please use this url to cite or link to this publication:

Chicago
Dierckx, Hans, Evelien Brisard, Henri Verschelde, and Alexander Panfilov. 2013. “Drift Laws for Spiral Waves on Curved Anisotropic Surfaces.” Physical Review E 88 (1).
APA
Dierckx, H., Brisard, E., Verschelde, H., & Panfilov, A. (2013). Drift laws for spiral waves on curved anisotropic surfaces. PHYSICAL REVIEW E, 88(1).
Vancouver
1.
Dierckx H, Brisard E, Verschelde H, Panfilov A. Drift laws for spiral waves on curved anisotropic surfaces. PHYSICAL REVIEW E. 2013;88(1).
MLA
Dierckx, Hans et al. “Drift Laws for Spiral Waves on Curved Anisotropic Surfaces.” PHYSICAL REVIEW E 88.1 (2013): n. pag. Print.
@article{4357654,
  abstract     = {Rotating spiral waves organize spatial patterns in chemical, physical, and biological excitable systems. Factors affecting their dynamics, such as spatiotemporal drift, are of great interest for particular applications. Here, we propose a quantitative description for spiral wave dynamics on curved surfaces which shows that for a wide class of systems, including the Belousov-Zhabotinsky reaction and anisotropic cardiac tissue, the Ricci curvature scalar of the surface is the main determinant of spiral wave drift. The theory provides explicit equations for spiral wave drift direction, drift velocity, and the period of rotation. Depending on the parameters, the drift can be directed to the regions of either maximal or minimal Ricci scalar curvature, which was verified by direct numerical simulations.},
  articleno    = {012908},
  author       = {Dierckx, Hans and Brisard, Evelien and Verschelde, Henri and Panfilov, Alexander},
  issn         = {1539-3755},
  journal      = {PHYSICAL REVIEW E},
  keywords     = {EXCITABLE MEDIA,3-DIMENSIONAL SCROLL WAVES,HUMAN ATRIA,ROTATIONAL ANISOTROPY,PROPAGATION,MODEL,REENTRY,FILAMENTS,MUSCLE,TACHYCARDIA},
  language     = {eng},
  number       = {1},
  pages        = {9},
  title        = {Drift laws for spiral waves on curved anisotropic surfaces},
  url          = {http://dx.doi.org/10.1103/PhysRevE.88.012908},
  volume       = {88},
  year         = {2013},
}

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