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Disruption and recovery of reaction–diffusion wavefronts interacting with concave, fractal, and soft obstacles

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  • Yu, Yang F.
  • Fuller, Chase A.
  • McGuire, Margaret K.
  • Glaser, Rebecca
  • Smith, Nathaniel J.
  • Manz, Niklas
  • Lindner, John F.

Abstract

In a recent publication (Smith et al., 2019), we documented the distinct recovery of reaction–diffusion wavefronts disrupted by hard convex obstacles. Here, we extend that work to include concave, spiral, fractal, random, and soft obstacles. Curvature dependent wavefront velocities ultimately restore the wavefronts, with perturbations that decay as power-law functions of time. But concave, spiral, and fractal obstacles can sustain wavefronts locally for long times. Soft obstacles with variable diffusivity, either intrinsically or due to light sensitivity, can enforce one-way propagation and, appropriately configured, can locally and indefinitely sustain incident wavefronts, creating clocks or repeaters, beating hearts for these excitable systems.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:phsmap:v:565:y:2021:i:c:s0378437120308347
    DOI: 10.1016/j.physa.2020.125536
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    References listed on IDEAS

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    1. Tang, Jun & Luo, Jin-Ming & Ma, Jun & Yi, Ming & Yang, Xian-Qing, 2013. "Spiral waves in systems with fractal heterogeneity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(22), pages 5764-5771.
    2. Richard A. Gray & Arkady M. Pertsov & José Jalife, 1998. "Erratum: Spatial and temporal organization during cardiac fibrillation," Nature, Nature, vol. 393(6681), pages 191-191, May.
    3. 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.
    4. 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.
    5. 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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