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Disruption and recovery of reaction–diffusion wavefronts colliding with obstacles

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  • Smith, Nathaniel J.
  • Glaser, Rebecca
  • Hui, Vincent W.H.
  • Lindner, John F.
  • Manz, Niklas

Abstract

We study the damage to and restoration of planar reaction–diffusion wavefronts colliding with convex obstacles in narrow two-dimensional channels using finite-difference numerical integration of the Tyson–Fife reduction of the Oregonator model of the Belousov–Zhabotinsky reaction. We characterize the obstacles’ effects on the wavefront shape by plotting wavefront delay versus time. Due to the curvature dependent wavefront velocities, the initial planar wavefront (or iso-concentration line) is restored after a relaxation period that can be characterized by a power-law. We find that recovery times are insensitive to obstacle concatenation or to the upstream obstacle shape but are sensitive to the downstream shape, with a vertical back side causing the longest disruption. Delays vary cyclically with obstacle orientations. The relaxation power-laws confirm that larger obstacles produce larger wavefront delays and longer recovery times, and for a given area larger obstacle width-to-length ratios produce longer delays. Possible applications include elucidating the effect of inhomogeneities on wavefront recovery in cardiac tissue.

Suggested Citation

  • Smith, Nathaniel J. & Glaser, Rebecca & Hui, Vincent W.H. & Lindner, John F. & Manz, Niklas, 2019. "Disruption and recovery of reaction–diffusion wavefronts colliding with obstacles," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 517(C), pages 307-320.
    • Handle: RePEc:eee:phsmap:v:517:y:2019:i:c:p:307-320
    DOI: 10.1016/j.physa.2018.11.024
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    References listed on IDEAS

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    1. Wang, Cheng & Tan, Jiale & Lou, Bendong, 2015. "Influence of obstacles on the propagation speeds of nonlinear waves driven by curvature," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 425(C), pages 41-49.
    2. Richard A. Gray & Arkady M. Pertsov & José Jalife, 1998. "Spatial and temporal organization during cardiac fibrillation," Nature, Nature, vol. 392(6671), pages 75-78, March.
    3. Rostami, Zahra & Rajagopal, Karthikeyan & Khalaf, Abdul Jalil M. & Jafari, Sajad & Perc, Matjaž & Slavinec, Mitja, 2018. "Wavefront-obstacle interactions and the initiation of reentry in excitable media," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 1162-1173.
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    Cited by:

    1. Kim, Sangkwon & Park, Jintae & Lee, Chaeyoung & Jeong, Darae & Choi, Yongho & Kwak, Soobin & Kim, Junseok, 2020. "Periodic travelling wave solutions for a reaction-diffusion system on landscape fitted domains," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    2. Yu, Yang F. & Fuller, Chase A. & McGuire, Margaret K. & Glaser, Rebecca & Smith, Nathaniel J. & Manz, Niklas & Lindner, John F., 2021. "Disruption and recovery of reaction–diffusion wavefronts interacting with concave, fractal, and soft obstacles," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 565(C).

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