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Diffraction by a spherical cap

Published online by Cambridge University Press:  24 October 2008

D. P. Thomas
D. P. Thomas
Affiliation:
Department of Applied Mathematics, University of Liverpool
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Extract

1. It was first observed by Rayleigh(17) in 1897 that low-frequency approximations to the solutions of the steady-state wave equation could be obtained from the solutions of the corresponding static problems. Rayleigh determined only the first term in the expansion of the solution in powers of the product of the wave number and a typical dimension. Many recent investigations have been concerned with deriving a systematic method of calculating the higher-order terms in the above expansion. Most of the problems which have been solved in this manner have been concerned with scattering by a disk or by a strip: the first systematic approach to these problems was that of Bouwkamp ((3), p. 71).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 59 , Issue 1 , January 1963 , pp. 197 - 209
Copyright
Copyright © Cambridge Philosophical Society 1963

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References

REFERENCES

(1)Baker, B. B. and Copson, E. T.The mathematical theory of Huygens' principle, 2nd ed. (Oxford, 1950).Google Scholar
(2)Bazer, J. and Brown, A.I.R.E. Trans. Antennas and Propagation, AP–7, Special Supple-ment (1959), pp. 12–20.CrossRefGoogle Scholar
(3)Bouwkamp, C. J.Reports on Progress in Physics, 17 (1954), 35–100.CrossRefGoogle Scholar
(4)Carlson, J. F. and Heins, A. E.Quart. Appl. Math. 4 (1947), 313–329.CrossRefGoogle Scholar
(5)Collins, W. D.Proc. Cambridge Philos. Soc. 55 (1959), 377–379.CrossRefGoogle Scholar
(6)Collins, W. D.Proc. Cambridge Philos. Soc. 57 (1961), 367–384.CrossRefGoogle Scholar
(7)Collins, W. D.Quart. J. Mech. Appl. Math. 14 (1961), 101–117.CrossRefGoogle Scholar
(8)Heins, A. E. and Maccamy, R. C.Z. Angew. Math. Phys. 11 (1960), 249–264.CrossRefGoogle Scholar
(9)De Hoop, A. T.Appl. Sci. Res. B, 7 (1958–1959), 463–469.CrossRefGoogle Scholar
(10)Van De Hulst, H. C.Physica, 15 (1949), 740–746.CrossRefGoogle Scholar
(11)Jones, D. S.Phil. Mag. (7), 46 (1955), 957–962.CrossRefGoogle Scholar
(12)Jones, D. S.Comm. Pure Appl. Math. 9 (1956), 713–746.CrossRefGoogle Scholar
(13)Levine, H. and Schwinger, J.Phys. Rev. 75 (1949), 1423–1432.CrossRefGoogle Scholar
(14)Magnus, W.New York University E. M. Report, no. 80.Google Scholar
(15)Morse, P. M. and Feshbach, H.Methods of theoretical physics (McGraw-Hill; New York, 1953).Google Scholar
(16)Noble, B.Electromagnetic waves (ed. Langer, Rudolph E.), pp. 323–360. (University of Wisconsin Press; Madison, 1962).Google Scholar
(17)Rayleigh, Lord. Phil. Mag. (4), 43 (1897), 259–272.CrossRefGoogle Scholar
(18)Senior, T. B. A.Canadian J. Phys. 38 (1960), 1632–1641.CrossRefGoogle Scholar
(19)Senior, T. B. A.Studies in radar cross sections, 46 (1961) (Department of Electrical Engineering, University of Michigan).Google Scholar
(20)Williams, W. E.Z. Angew. Math. Phys. 13 (1962), 133–152.CrossRefGoogle Scholar
(21)Williams, W. E.Proc. Roy. Soc. London, Ser. A, 267 (1962), 77–87.Google Scholar