The scattering of a plane wave by a trap in the critical case |
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| Affiliation: | 1. University of Wisconsin-Madison, Geoscience Department, 1215 W Dayton, Madison, WI 53706, United States;2. University of Wisconsin-Extension, Wisconsin Geological and Natural History Survey, 3817 Mineral Point Rd, Madison, WI 53705, United States;1. Division of Medical Oncology, Department of Medicine, The Ottawa Hospital Cancer Centre, University of Ottawa, 501 Smyth Road, Ottawa, ON K1H 8L6, Canada;2. University of Ottawa, 451 Smyth Road, Ottawa, ON K1H 8M5, Canada;3. Clinical Epidemiology Program, Methods Centre, Ottawa Hospital Research Institute, 501 Smyth Road, Ottawa, ON K1H 8L6, Canada |
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| Abstract: | The scattering of a plane wave by a resonator with a narrow coupling channel is considered. The velocity potential of the scattered wave in this resonator has two series of poles with small imaginary parts, corresponding to the main trap and the coupling channel, the effect of which inside the trap differs by an order of magnitude. The critical case, when the limiting value for the poles from both series is the same, is investigated. It is shown that in this case two poles exist, which converge to this limiting value, and they both inherit resonance properties, characteristic for poles generated by the main trap. The principal terms of the asymptotic forms of the poles and the scattered wave are constructed. |
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