Power radiation by a scattered plane wave.
Item
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Title
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Power radiation by a scattered plane wave.
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Identifier
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AAI9997072
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identifier
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9997072
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Creator
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Balsim, Igor.
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Contributor
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Adviser: Richard Sacksteder
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Date
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2001
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Language
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English
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Publisher
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City University of New York.
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Subject
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Mathematics
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Abstract
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In this thesis we show how to estimate asymptotically, as k the wave number goes to infinity, the power of a plane wave of unit amplitude which is scattered by a cylinder with its axis perpendicular to the direction of propagation. The result Ekk2 ≅ 4p obtained in chapter VII shows that the power in the scattered wave is for high frequencies (or large wave numbers) asymptotically proportional to the square of the frequency. We also want to estimate asymptotically the normalization factor D(k). The estimate Dkk2 ≅ 12 shows that the dissipation function (normalization factor D(k) is also proportional to the square of the frequency and therefore E(k) is asymptotically proportional to D(k). Since, in general, both the power and the dissipation are proportional to the square of the amplitude, the latter result holds for plane waves of any amplitude.;The key tool used in obtaining our results was the method of steepest descent. The above problem leads rise to solving a Helmholtz equation in the exterior of the unit disc in two dimensions with boundary conditions given by the derivative of a plane wave. The solution can be expressed as an infinite sum of Hankel functions. The power can be expressed as a sum of ratios of the derivative of Bessel functions and Hankel functions. In order to get the desired asymptotic estimates we needed to get uniform estimates of the derivative of Hankel functions using the method of steepest descent.
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Type
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dissertation
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Source
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PQT Legacy CUNY.xlsx
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degree
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Ph.D.
