Diffraction of reaction-diffusion waves: the conformal-mapped eikonal equation |
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| Institution: | 1. IBM Research – Ireland, B3 F14 IBM Campus Damastown, Dublin 15, Ireland;2. University of Edinburgh School of Mathematics, James Clerk Maxwell Building, Peter Guthrie Tait Road, Edinburgh EH9 3FD, Scotland, UK;3. Lehigh University, Harold S. Mohler Laboratory, 200 West Packer Avenue, Bethlehem, PA 18015-1582, USA;1. School of Electronics Engineering, Xi''an University of Posts and Telecommunications, Xi''an 710121, China;2. State Key Laboratory of Transient Optics and Photonics, Xi''an Institute of Optics and Precision Mechanics, Chinese Academy of Sciences, Xi''an 710119, China;3. School of Mathematics and Physics, Weinan Normal University, Weinan 714099, China |
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| Abstract: | The interaction of reaction-diffusion (RD) waves with obstacles is considered. The conformal map transformation of the eikonal equation is used for investigating the behavior of waves in the presence of movable boundaries. It is shown that using the conformal map, the complicated boundary conditions become simple Neumann boundary conditions and can be easily dealt with numerically. The process is applied to diffraction of RD waves by two disks in two dimensions. The approach is extended to three-dimensions and the obstacles considered are 2 two-tori. A stable stationary solution, in the form of an unduloid, trapped between 2 two-tori, is obtained. It is shown that, if the obstacles are located a distance apart, the wave moves away from its stationary position giving rise to regular and irregular motions, depending on the choice of initial solutions. |
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