Disruption and recovery of reaction–diffusion wavefronts colliding with obstacles

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

Physica A: Statistical Mechanics and its Applications, 2019, vol. 517, issue C, 307-320

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.

Keywords: Nonlinear wave; Numerical simulation; Obstacle; Power-law; Reaction–diffusion (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:517:y:2019:i:c:p:307-320

DOI: 10.1016/j.physa.2018.11.024

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