Potential and Rayleigh-scattering theory for a spherical cap

Author:

Miles John W.

Abstract

Harmonic functions are constructed for spherical-harmonic prescriptions of either a potential or its normal derivative on a spherical cap. The dipole-moment tensor and the Rayleigh-scattering properties of a spherical bowl, including the limiting case of a Helmholtz resonator, are determined. The results are uniformly valid with respect to the polar angle of the cap and resolve certain discrepancies in the existing literature.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics

Reference16 articles.

1. W. Thomson, Extraits de deux lettres adressées à M. Liouville, J. Math. Pures Appl. 12, 256–264 (1847)

2. N. M. Ferrers, On the distribution of electricity on a bowl, Quart. J. Math. 18, 97–109 (1882)

3. E. G. Gallop, The distribution of electricity on the circular disc and spherical bowl, Quart. J. Math 21, 229–256 (1886)

4. On the Potential of an Electrified Spherical Bowl, and on the Velocity Potential due to the Motion of an Infinite Liquid about such a Bowl;Basset, A. B.;Proc. Lond. Math. Soc.,1884

5. Lord Rayleigh, On the passage of waves through apertures in plane screens, and allied problems. Philos. Mag. 43, 259–272 (1897); Sci. Papers 4, 283–296

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1. Axisymmetric acoustic oscillations of a rigid spherical shell with two symmetric circular apertures;Journal of Sound and Vibration;2021-07

2. References;Canonical Problems in Scattering and Potential Theory Part II;2002-04-29

3. References;Monographs & Surveys in Pure & Applied Math;2001-05-30

4. Plane wave scattering from a cylindrical Helmholtz resonator: Dirichlet case;Optics Communications;1999-06

5. Scattering by a Spherical Cap;The Journal of the Acoustical Society of America;1971-09

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