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Diffraction of spherical waves by a toroidal obstacle: eikonal approach to excitable reaction-diffusion systems

Mulholland, A.J. and Gomatam, J. and McQuillan, P. (1996) Diffraction of spherical waves by a toroidal obstacle: eikonal approach to excitable reaction-diffusion systems. Proceedings A: Mathematical, Physical and Engineering Sciences, 452 (1955). pp. 2785-2799.

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Abstract

Diffraction of spherical waves by a toroidal obstacle is analysed using the eikonal approximation to the reaction-diffusion equations with excitable kinetics. We demonstrate the existence of two stationary spherical wave segments, one larger and the other smaller than a hemisphere, blocking the hole of the torus. A detailed stability analysis indicates that the former is unstable and the latter is stable. This analysis suggests that the trapping of a spherical wave front by a toroidal obstacle may be verified experimentally using a chemical medium like the Belouzov-Zhabotinsky reagent in the excitable regime.