Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-25T02:43:52.805Z Has data issue: false hasContentIssue false
  • English
  • Français

The asymptotic analysis of canonical problems in high-frequency scattering theory

II. The circular and parabolic cylinders

Published online by Cambridge University Press:  24 October 2008

W. G. C. Boyd
W. G. C. Boyd
Affiliation:
Department of Mathematics, University of Dundee, Dundee DD1 4HN
Get access Rights & Permissions [Opens in a new window]

Abstract

This is the second part of a two-part paper in which a systematic method is advanced for treating separation of variables problems asymptotically as the frequency becomes large. The method assumes an integral representation in which the contour of integration is the real axis. The contour is then deformed in the neighbourhood of the real axis to derive rigorous asymptotic expansions of the field. In this paper the method is applied to scattering in homogeneous media by the circular and parabolic cylinders.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 74 , Issue 2 , September 1973 , pp. 313 - 332
Copyright
Copyright © Cambridge Philosophical Society 1973

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)Abramowitz, M. and Stegun, I. A.Handbook of mathematical functions (Dover; New York, 1965).Google Scholar
(2)Bowman, J. J., Senior, T. B. A. and Uslenghi, P. L. E.Electromagnetic and acoustic scattering by simple shapes (North-Holland; Amsterdam, 1969)Google Scholar
(3)Boyd, W. G. C.High-frequency scattering in a certain stratified medium. Proc. Roy. Soc. Edinburgh Sect. A (To be published.)Google Scholar
(4)Boyd, W. G. C.The asymptotic analysis of canonical problems in high-frequency scattering theory. I. Stratified media above a plane boundary. Proc. Cambridge Philos. Soc. 74 (1973), 287–310.Google Scholar
(5)Cherry, T. M.Expansion in terms of parabolic cylinder functions. Proc. Edinburgh Math. Soc. 8 (1947), 50–65.CrossRefGoogle Scholar
(6)Jones, D. S.The theory of electromagnetism (Pergamon; Oxford, 1964).Google Scholar
(7)Keller, J. B.Diffraction by a convex cylinder. I.R.E. Trans. Antennas Propag. 4 (1956), 312–321.CrossRefGoogle Scholar
(8)Lownon, T. A.Integral representation of the Hankel function in terms of parabolic cylinder functions. Quart. J. Mech. Appl. Math. 23 (1970), 315–327.Google Scholar
(9)Ludwig, D.Diffraction by a circular cavity. J. Mathematical Phys. 11 (1970), 1617–1630.Google Scholar
(10)Nussenzveig, H. M.High-frequency scattering by an impenetrable sphere. Ann. Physics 34 (1965), 23–95.Google Scholar
(11)Nussenlveig, H. M.High-frequency scattering by a transparent sphere. I. Direct reflection and transmission. J. Mathematical Phys. 10 (1969), 82–124.CrossRefGoogle Scholar
(12)Roebuck, I.On cylindrical waves in stratified media: high-frequency refraction and diffraction at a plane interface. Proc. Cambridge Philos. Soc. 67 (1970), 133–161.Google Scholar
(13)Ursell, F.Creeping modes in a shadow. Proc. Cambridge Philos. Soc. 64 (1968), 171–191.Google Scholar
(14)Watson, G. N.Theory of Bessel functions (Cambridge University Press; 2nd edition, 1944).Google Scholar
(15)Whittaker, E. T. and Watson, G. N.A course of modern analysis (Cambridge University Press; 4th edition, 1927).Google Scholar