DIFFRACTION OF SPHERICAL WAVES BY A TOROIDAL OBSTACLE - EIKONAL APPROACH TO EXCITABLE REACTION-DIFFUSION SYSTEMS

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