Potential and Rayleigh-scattering theory for a spherical cap

Author:
John W. Miles

Journal:
Quart. Appl. Math. **29** (1971), 109-123

MSC:
Primary 78.31

DOI:
https://doi.org/10.1090/qam/284080

MathSciNet review:
284080

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Abstract | References | Similar Articles | Additional Information

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.

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Additional Information

DOI:
https://doi.org/10.1090/qam/284080

Article copyright:
© Copyright 1971
American Mathematical Society