Kinematics of rigidly rotating spiral waves |
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| Authors: | V.S. Zykov |
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| Affiliation: | 1. Department of Physics, Kasetsart University, 50 Phaholyothin Road, Jatujak, Bangkok 10900, Thailand;2. Faculty of Science and Technology, Valaya Alongkorn Rajabhat University Under the Royal Patronage, 1 Moo 20 Phaholyothin Road, Khlong Neung, Klong Luang, Phathum Thani 13180, Thailand;3. Department of Industrial Physics and Medical Instrumentation, King Mongkut’s University of Technology North Bangkok, 1518 Pibulsongkram Road, Bangkok 10800, Thailand;4. Lasers and Optics Research Group, King Mongkut’s University of Technology North Bangkok, 1518 Pibulsongkram Road, Bangkok 10800, Thailand;5. Institute of Experimental Physics, Otto-von-Guericke University Magdeburg, Universitätsplatz 2, D-39106 Magdeburg, Germany;1. Department of Physics, Lanzhou University of Technology, Lanzhou 73005, China;2. NAAM-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589,Saudi Arabia;3. School of Science, Chongqing University of Posts and Telecommunications, Chongqing 400065, China;4. Department of Physics, China University of Mining and Technology, Xuzhou 221116, China;1. Department of Industrial Physics and Medical Instrumentation, King Mongkut’s University of Technology North Bangkok, 1518 Pibulsongkram Road, Bangkok 10800, Thailand;2. Lasers and Optics Research Group, King Mongkut’s University of Technology North Bangkok, 1518 Pibulsongkram Road, Bangkok 10800, Thailand;3. Department of Physics, Kasetsart University, 50 Phaholyothin Road, Jatujak, Bangkok 10900, Thailand;4. Department of Chemistry, Chulalongkorn University, Bangkok 10330, Thailand;5. Institute of Experimental Physics, Otto-von-Guericke University Magdeburg, Universitätsplatz 2, D-39106 Magdeburg, Germany;1. Department of Physics, Koç University, 34450 Sar?yer, Istanbul, Turkey;2. Department of Mathematics, Koç University, 34450 Sar?yer, Istanbul, Turkey |
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| Abstract: | Spiral waves rigidly rotating in excitable media are studied by use of a free-boundary approach. This study reveals the selection principle which determines the shape and the rotation frequency of spiral waves in an unbounded medium with a given excitability. It is shown that a rigidly rotating spiral in a medium with a strongly reduced refractoriness is supported within a range of the medium excitability restricted by two universal limits. At the low excitability limit the spiral core radius diverges, while at the high excitability limit it vanishes. The simulations performed for the medium excitability higher than the high excitability limit reveal nonstationary rotating waves, which considerably differ from well-studied meandering spiral waves. It is shown how the proposed free-boundary approach can be extended to the case of an arbitrary refractoriness. The predictions of the free-boundary approach are in good agreement with the results from numerical simulations of the underlying reaction-diffusion model and with asymptotics derived earlier for highly and weakly excitable media. |
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