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

Anthony Mulholland, J. Gomatam, P. McQuillan

Research output: Contribution to journalArticle (Academic Journal)peer-review

3 Citations (Scopus)

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.
Original languageEnglish
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Publication statusPublished - 1996

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