Table of Contents Author Guidelines Submit a Manuscript
Advances in Mathematical Physics
Volume 2018, Article ID 7683929, 13 pages
https://doi.org/10.1155/2018/7683929
Research Article

Image Theory for Neumann Functions in the Prolate Spheroidal Geometry

1School of Mathematics and Physics, Yancheng Institute of Technology, Yancheng, Jiangsu 224051, China
2Department of Mathematics and Statistics, University of North Carolina at Charlotte, Charlotte, NC 28223, USA

Correspondence should be addressed to Shaozhong Deng; ude.ccnu@gnedoahs

Received 19 September 2017; Accepted 4 February 2018; Published 11 March 2018

Academic Editor: Pavel Kurasov

Copyright © 2018 Changfeng Xue et al. 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. W. R. Smythe, Static and Dynamic Electricity, Hemisphere, New York, NY, USA, 3rd edition, 1989.
  2. N. S. Koshlyakov, E. B. Gliner, and M. M. Smirnov, Differential Equations of Mathematical Physics, North-Holland, Amsterdam, 1964. View at MathSciNet
  3. I. V. Lindell, “Electrostatic image theory for the dielectric sphere,” Radio Science, vol. 27, no. 1, pp. 1–8, 1992. View at Publisher · View at Google Scholar · View at Scopus
  4. W. T. Norris, “Charge images in a dielectric sphere,” IEE Proceedings Science, Measurement and Technology, vol. 142, no. 2, pp. 142–150, 1995. View at Publisher · View at Google Scholar · View at Scopus
  5. S. Deng, W. Cai, and D. Jacobs, “A comparable study of image approximations to the reaction field,” Computer Physics Communications, vol. 177, no. 9, pp. 689–699, 2007. View at Publisher · View at Google Scholar · View at Scopus
  6. I. V. Lindell, G. Dassios, and K. I. Nikoskinen, “Electrostatic image theory for the conducting prolate spheroid,” Journal of Physics D: Applied Physics, vol. 34, no. 15, pp. 2302–2307, 2001. View at Publisher · View at Google Scholar · View at Scopus
  7. I. V. Lindell and K. I. Nikoskinen, “Electrostatic image theory for the dielectric prolate spheroid,” Journal of Electromagnetic Waves and Applications, vol. 15, no. 8, pp. 1075–1096, 2001. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  8. G. Dassios and J. C. Sten, “The image system and Green’s function for the ellipsoid,” in Imaging Microstructures: Mathematical and Computational Challenges, H. Ammari and H. Kang, Eds., vol. 494 of Contemp. Math., pp. 185–195, Amer. Math. Soc., Providence, RI, USA, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  9. G. Dassios, “Directional dependent Green's function and Kelvin images,” Archive of Applied Mechanics, vol. 82, no. 10-11, pp. 1325–1335, 2012. View at Publisher · View at Google Scholar · View at Scopus
  10. G. Dassios, Ellipsoidal Harmonics, Eencyclopedia of Mathematics and its Aapplications, Cambridge University Press, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  11. C. Xue and S. Deng, “Green’s function and image system for the Laplace operator in the prolate spheroidal geometry,” AIP Advances, vol. 7, no. 1, Article ID 015024, 2017. View at Publisher · View at Google Scholar · View at Scopus
  12. G. Dassios and J. C. Sten, “On the Neumann function and the method of images in spherical and ellipsoidal geometry,” Mathematical Methods in the Applied Sciences, vol. 35, no. 4, pp. 482–496, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  13. C. Xue and S. Deng, “Comment on "On the Neumann function and the method of images in spherical and ellipsoidal geometry",” Mathematical Methods in the Applied Sciences, vol. 40, no. 18, pp. 6832–6835, 2017. View at Publisher · View at Google Scholar · View at Scopus
  14. E. W. Hobson, The Theory of Spherical and Ellipsoidal Harmonics, Cambridge University Press, Cambridge, England, 1931. View at MathSciNet
  15. P. M. Morse and H. Feshbach, Methods of Theoretical Physics, McGraw-Hill, New York, NY, USA, 1953. View at MathSciNet
  16. J. Franklin, Green’s functions for neumann boundary conditions, 2012, https://arxiv.org/pdf/1201.6059.pdf.
  17. P. Weiss, “On hydrodynamical images. Arbitrary irrotational flow disturbed by a sphere,” Mathematical Proceedings of the Cambridge Philosophical Society, vol. 40, no. 3, pp. 259–261, 1944. View at Publisher · View at Google Scholar · View at Scopus
  18. P. Weiss, “Applications of Kelvin's transformation in electricity, magnetism and hydrodynamics,” Philosophical Magazine, vol. 38, pp. 200–214, 1947. View at Google Scholar · View at MathSciNet