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.
|Number of pages||14|
|Journal||Proceedings A: Mathematical, Physical and Engineering Sciences|
|Publication status||Published - 1996|
Mulholland, A. J., Gomatam, J., & 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), 2785-2799.