DOI: 10.1017/s0305004100046570. On the Rayleigh assumption in scattering by a periodic surface. II

On the Rayleigh assumption in scattering by a periodic surface. II

10.1017/s0305004100046570

Crossref journal-article

Cambridge University Press (CUP)

Mathematical Proceedings of the Cambridge Philosophical Society (56)

Abstract

AbstractThe Rayleigh assumption, which concerns the domain of validity of a representation for the field scattered by a periodic surface under time-harmonic plane-wave excitation, is re-examined. The analysis employs a technique developed to locate singularities of solutions to the Helmholtz equation. When applied to the surface profile v = b cos κu (-∞ < u < ∞) considered originally by Lord Rayleigh, it is found that the Rayleigh assumption is valid if 0 ≤ κb < 0·448 and is not valid if κb > 0·448; this is more precise than an earlier result. It is shown how these findings may be reconciled with the work of others who have suggested, or concluded, that the Rayleigh assumption is never valid.

Bibliography

Millar, R. F. (1971). On the Rayleigh assumption in scattering by a periodic surface. II. Mathematical Proceedings of the Cambridge Philosophical Society, 69(1), 217â225.

Authors 1

R. F. Millar (first)

References 16 Referenced 107

{'key': 'S0305004100046570_ref012', 'first-page': '1441', 'article-title': "Sur la diffraction d'une onde plane par un réseau infiniment conducteur", 'volume': '264', 'author': 'Petit', 'year': '1967', 'journal-title': 'C.R. Acad. Sci. Paris Sér. B'} / C.R. Acad. Sci. Paris Sér. B / Sur la diffraction d'une onde plane par un réseau infiniment conducteur by Petit (1967)
{'key': 'S0305004100046570_ref009', 'first-page': '1352', 'article-title': "Sur la méthode des spectres d'ondes planes dans les problèmes de diffraction", 'volume': '266', 'author': 'Pavageau', 'year': '1968', 'journal-title': 'C.R. Acad. Sci. Paris. Sér. B'} / C.R. Acad. Sci. Paris. Sér. B / Sur la méthode des spectres d'ondes planes dans les problèmes de diffraction by Pavageau (1968)
10.1137/0501031
10.1016/0003-4916(65)90269-1
{'key': 'S0305004100046570_ref006', 'first-page': '167', 'article-title': 'Singularities of two-dimensional exterior solutions of the Helmholtz equation', 'volume': '69', 'author': 'Millar', 'year': '1970', 'journal-title': 'Proc. Cambridge Philos. Soc.'} / Proc. Cambridge Philos. Soc. / Singularities of two-dimensional exterior solutions of the Helmholtz equation by Millar (1970)
{'key': 'S0305004100046570_ref013', 'volume-title': 'The theory of sound', 'volume': 'II', 'author': 'Rayleigh', 'year': '1945'} / The theory of sound by Rayleigh (1945)
10.1364/JOSA.43.000408
10.1137/0501030
10.1007/BF01215039
10.1090/S0002-9939-1956-0078912-4
10.1121/1.1919253
10.1139/p63-209
{'key': 'S0305004100046570_ref011', 'first-page': '468', 'article-title': "Sur la diffraction d'une onde plane par un réseau infiniment conducteur", 'volume': '262', 'author': 'Petit', 'year': '1966', 'journal-title': 'C.R. Acad. Sci. Paris Sér. B'} / C.R. Acad. Sci. Paris Sér. B / Sur la diffraction d'une onde plane par un réseau infiniment conducteur by Petit (1966)
{'key': 'S0305004100046570_ref010', 'first-page': '2077', 'article-title': 'Étude théorique de la diffraction par un réseau', 'volume': '259', 'author': 'Petit', 'year': '1964', 'journal-title': 'C.R. Acad. Sci. Paris'} / C.R. Acad. Sci. Paris / Étude théorique de la diffraction par un réseau by Petit (1964)
10.1017/S0305004100003613
10.1098/rspa.1907.0051

Dates

Type	When
Created	16 years, 9 months ago (Nov. 7, 2008, 5:28 a.m.)
Deposited	6 years, 2 months ago (May 31, 2019, 12:28 p.m.)
Indexed	3 months ago (May 26, 2025, 9:45 a.m.)
Issued	54 years, 7 months ago (Jan. 1, 1971)
Published	54 years, 7 months ago (Jan. 1, 1971)
Published Online	16 years, 10 months ago (Oct. 24, 2008)
Published Print	54 years, 7 months ago (Jan. 1, 1971)

Funders 0

None

BibTeX

@article{Millar_1971, title={On the Rayleigh assumption in scattering by a periodic surface. II}, volume={69}, ISSN={1469-8064}, url={http://dx.doi.org/10.1017/s0305004100046570}, DOI={10.1017/s0305004100046570}, number={1}, journal={Mathematical Proceedings of the Cambridge Philosophical Society}, publisher={Cambridge University Press (CUP)}, author={Millar, R. F.}, year={1971}, month=jan, pages={217–225} }

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