Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



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: 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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DOI: https://doi.org/10.1090/qam/284080
Article copyright: © Copyright 1971 American Mathematical Society

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