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

A.J. Mulholland, J. Gomatam, P. McQuillan

Research output: Contribution to journalArticle

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.
LanguageEnglish
Pages2785-2799
Number of pages14
JournalProceedings A: Mathematical, Physical and Engineering Sciences
Volume452
Issue number1955
Publication statusPublished - 1996

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Excitable Systems
spherical waves
Reaction-diffusion System
Diffraction
Hemisphere
Reaction-diffusion Equations
Trapping
diffraction
Wave Front
Stability Analysis
reaction-diffusion equations
Torus
Kinetics
Unstable
wave fronts
hemispheres
reagents
Approximation
trapping
Demonstrate

Cite this

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Diffraction of spherical waves by a toroidal obstacle: eikonal approach to excitable reaction-diffusion systems. / Mulholland, A.J.; Gomatam, J.; McQuillan, P.

In: Proceedings A: Mathematical, Physical and Engineering Sciences, Vol. 452, No. 1955, 1996, p. 2785-2799.

Research output: Contribution to journalArticle

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AU - Mulholland, A.J.

AU - Gomatam, J.

AU - McQuillan, P.

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AB - 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.

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M3 - Article

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T2 - Proceedings A: Mathematical, Physical and Engineering Sciences

JF - Proceedings A: Mathematical, Physical and Engineering Sciences

SN - 1364-5021

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