Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-25T13:24:37.006Z Has data issue: false hasContentIssue false
  • English
  • Français

The low frequency scalar diffraction by an elliptic disc

Published online by Cambridge University Press:  24 October 2008

B. D. Sleeman
B. D. Sleeman
Affiliation:
Department of Mathematics, University of Dundee, Dundee
Get access Rights & Permissions [Opens in a new window]

Summary

The problem of scalar Dirichlet diffraction of a plane wave by an elliptic disc is discussed. A scheme is given whereby the low frequency expansion of the scattered field may be readily obtained. Series expansions are obtained for the far-field amplitude up to and including the second order in the wave number. The first two terms of the scattering cross-section are also derived.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 63 , Issue 4 , October 1967 , pp. 1273 - 1280
Copyright
Copyright © Cambridge Philosophical Society 1967

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Arscott, F. M. and Khabaza, I. M.Tables of Lamé polynomials (Pergamon Press, 1962).Google Scholar
(2)Arscott, F. M.Periodic differential equations (Pergamon Press, 1964).Google Scholar
(3)Kellog, O. D.Foundations of potential theory (Springer, 1929).Google Scholar
(4)Kleinman, R. E.Arch. Rational Mech. Anal. 18 (1965), 205–229.CrossRefGoogle Scholar
(5)Kleinman, R. E.University of Michigan Report No. 7133–4-T. (1965).Google Scholar
(6)Morse, P. M. and Feshbach, H.Methods of theoretical physics, vol. 2 (McGraw Hill, 1953).Google Scholar
(7)Sleeman, B. D.J. Inst. Math. Appl. 3 (1967).Google Scholar
(8)Sleeman, B. D.J. Inst. Math. Appl. 3 (1967) 4–15.CrossRefGoogle Scholar