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Advances in Mathematical Physics
Volume 2015 (2015), Article ID 572458, 12 pages
http://dx.doi.org/10.1155/2015/572458
Research Article

Connection Formulae between Ellipsoidal and Spherical Harmonics with Applications to Fluid Dynamics and Electromagnetic Scattering

1Department of Chemical Engineering, University of Patras, 26504 Patras, Greece
2Institute of Chemical Engineering Sciences, Stadiou Street, P.O. Box 1414, Platani, 26504 Patras, Greece

Received 26 July 2014; Accepted 30 October 2014

Academic Editor: George Dassios

Copyright © 2015 Michael Doschoris and Panayiotis Vafeas. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. G. Dassios, Ellipsoidal Harmonics. Theory and Applications, Cambridge University Press, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  2. G. Dassios and K. Satrazemi, “Lamé functions and Ellipsoidal harmonics up to degree seven,” Submitted to International Journal of Special Functions and Applications.
  3. A. Ronveaux, Ed., Heun's Differential Equations, Oxford University Press, Oxford, UK, 1995.
  4. J. P. Bardhan and M. G. Knepley, “Computational science and re-discovery: open-source implementation of ellipsoidal harmonics for problems in potential theory,” Computational Science and Discovery, vol. 5, no. 1, Article ID 014006, 2012. View at Publisher · View at Google Scholar · View at Scopus
  5. P. Vafeas and G. Dassios, “Stokes flow in ellipsoidal geometry,” Journal of Mathematical Physics, vol. 47, no. 9, Article ID 093102, pp. 1–38, 2006. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  6. J. Happel, “Viscous flow in multiparticle systems: slow motion of fluids relative to beds of spherical particles,” AIChE Journal, vol. 4, pp. 197–201, 1958. View at Google Scholar
  7. X. S. Xu and M. Z. Wang, “General complete solutions of the equations of spatial and axisymmetric Stokes flow,” The Quarterly Journal of Mechanics and Applied Mathematics, vol. 44, no. 4, pp. 537–548, 1991. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  8. H. Neuber, “Ein neuer Ansatz zur Lösung räumlicher Probleme der Elastizitätstheorie,” Journal of Applied Mathematics and Mechanics, vol. 14, pp. 203–212, 1934. View at Google Scholar
  9. P. M. Naghdi and C. S. Hsu, “On the representation of displacements in linear elasticity in terms of three stress functions,” Journal of Mathematics and Mechanics, vol. 10, pp. 233–245, 1961. View at Google Scholar
  10. G. Dassios and P. Vafeas, “The 3D Happel model for complete isotropic Stokes flow,” International Journal of Mathematics and Mathematical Sciences, vol. 2004, no. 46, pp. 2429–2441, 2004. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  11. G. Perrusson, P. Vafeas, and D. Lesselier, “Low-frequency dipolar excitation of a perfect ellipsoidal conductor,” Quarterly of Applied Mathematics, vol. 68, no. 3, pp. 513–536, 2010. View at Google Scholar · View at MathSciNet · View at Scopus
  12. G. Dassios and R. Kleinman, Low Frequency Scattering, Oxford University Press, Oxford, UK, 2000. View at MathSciNet
  13. C. Athanasiadis, “The multi-layered ellipsoid with a soft core in the presence of a low-frequency acoustic wave,” Quarterly Journal of Mechanics and Applied Mathematics, vol. 47, no. 3, pp. 441–459, 1994. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  14. P. Vafeas, G. Perrusson, and D. Lesselier, “Low-frequency solution for a perfectly conducting sphere in a conductive medium with dipolar excitation,” Progress in Electromagnetics Research, vol. 49, pp. 87–111, 2004. View at Publisher · View at Google Scholar · View at Scopus