Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-23T11:10:26.071Z Has data issue: false hasContentIssue false
  • English
  • Français

Calculating the near field of a line of sources using Mellin transforms

Published online by Cambridge University Press:  17 February 2009

P. A. Martin
P. A. Martin
Affiliation:
Department of Mathematical and Computer SciencesColorado School of Mines Golden Colorado 80401-1887 [email protected].
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In slender-body theories, one cften has to find asymptotic approximations for certain integrals, representing distribution:; of sources along a line segment. Here, such approximations are obtained by a systematic method that uses Mellin transforms. Results are given near the line (using cylindrical polar coordinates) and near the ends of the line segment (using spherical polar coordinates).

Keywords

Mellii transformsasymptotic approximations; slender-body theory
Type
Articles
Information
The ANZIAM Journal , Volume 49 , Issue 1 , July 2007 , pp. 99 - 109
Copyright
Copyright © Australian Mathematical Society 2007

References

[1]Abramowitz, M. and Stegun, I. A.(eds.), Handbook of mathematical functions(Dover, New York, 1965)Google Scholar
[2] Bleistein, N. and R. A. Handelsman, Asymptotic expansions of integrals(Holt, Rinehart and Winston, New York, 1975).Google Scholar
[3] Chadwick, E., “A slender-body theory in Oseen flow”, Proc Roy Soc A 458(2002)2007– 2016.CrossRefGoogle Scholar
[4] Erdelyi, A., W. Magnus, F. Oberhettinger and F. G. Tricomi, Higher transcendental functions vol. I (McGraw-Hill, New York, 1953).Google Scholar
[5] Fikioris, G., “Integral evaluation using the Mellin transform and generalized hypergeometric functions: Tutorial and applications to antenna problems”, IEEE Trans Antennas & Propagation 54 (2006)3895– 3907.CrossRefGoogle Scholar
[6] Goldstein, S., Lectures on fluid mechanics (Interscience, London, 1960).Google Scholar
[7] Gradshteyn, I.S. and I. M. Ryzhik, Table of integrals, series, and products (Academic Press, London, 1980).Google Scholar
[8] Handelsman, R.A. and J. B. Keller, “Axially symmetric potential flow around a slender body”, J Fluid Mech.28(1967)131– 147.CrossRefGoogle Scholar
[9] Handelsman, R.A. and J. B. Keller, “The electrostatic field around a slender conducting body of revolution”, SIAM J Appl Math.15(1967)824– 841.CrossRefGoogle Scholar
[10] Martin, P.A., “End-point behaviour of solutions to hypersingular integral equations”, Proc Roy Soc. A432 (1991)301– 320.Google Scholar
[11] Martin, P.A., “Asymptotic approximations for functions defined by series, with some applications to the theory of guided waves”, IMA J Appl Math.54(1995)139– 157.CrossRefGoogle Scholar
[12] Moran, J.P., “Line source distributions and slender-body theory”, J FluidMech.17(1963)285– 304.CrossRefGoogle Scholar
[13] Paris, R.B. and D. Kaminski, Asymptotics and Mellin-Barnes integrals(Cambridge University Press, Cambridge, 2001).CrossRefGoogle Scholar
[14] Petrov, A.G., “Asymptotic expansions for axially symmetric cavities”, Euro J Appl Math.16 (2005)319– 334.CrossRefGoogle Scholar
[15] Sellier, A., “A general and formal slender-body theory in the non-lifting case”, Proc Roy Soc. A 453(1997)1733– 1751.CrossRefGoogle Scholar
[16] Tuck, E.O., “Some methods for flows past blunt slender bodies”, J FluidMech.18(1964)619– 635.CrossRefGoogle Scholar
[17] Tuck, E.O., “ Analytic aspects of slender body theory”, in Wave asymptotics (Manchester, 1990), (Cambridge University Press, Cambridge, 1992)184– 201.Google Scholar