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 journal › Article

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

Mulholland, A.J. ; Gomatam, J. ; McQuillan, P. / Diffraction of spherical waves by a toroidal obstacle: eikonal approach to excitable reaction-diffusion systems. In: Proceedings A: Mathematical, Physical and Engineering Sciences. 1996 ; Vol. 452, No. 1955. pp. 2785-2799.
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Mulholland, AJ, 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, vol. 452, no. 1955, pp. 2785-2799.

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 journal › Article

TY - JOUR

T1 - Diffraction of spherical waves by a toroidal obstacle: eikonal approach to excitable reaction-diffusion systems

AU - Mulholland, A.J.

AU - Gomatam, J.

AU - McQuillan, P.

PY - 1996

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N2 - 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.

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.

UR - http://www.jstor.org/stable/52870

M3 - Article

VL - 452

SP - 2785

EP - 2799

JO - Proceedings A: Mathematical, Physical and Engineering Sciences

T2 - Proceedings A: Mathematical, Physical and Engineering Sciences

JF - Proceedings A: Mathematical, Physical and Engineering Sciences

SN - 1364-5021

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

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