Construction transfer matrices for nonhomogeneous differentiation operators

Authors

  • Леонид Борисович Лерман Іnstitut chemistries of surface are the name of O.O. Chuyka of NAN of Ukraine, General Naumov, 17, Kyiv, Ukraine, 03164, Ukraine
  • Лилия Владимировна Породько Іnstitute chemistries of surface are the name of O.O. Chuyka of NAN of Ukraine, General Naumov, 17, Kyiv, Ukraine, 03164, Ukraine

DOI:

https://doi.org/10.15587/2313-8416.2014.27535

Keywords:

differential equations, transfer matrices, Poisson equation, variables separation, laminated sphere

Abstract

The construction algorithm of transfer matrices for nonhomogeneous differentiation operators on example of Poisson equation in spherical coordinates is presented. Design formulas to estimation of unknown fields in separate slabs of laminated sphere are obtained. This method allows you to transfer the compatibility conditions with layer upon layer, eliminating unnecessary arbitrary constants without additional solutions of algebraic systems of sufficiently high order.

Author Biographies

Леонид Борисович Лерман, Іnstitut chemistries of surface are the name of O.O. Chuyka of NAN of Ukraine, General Naumov, 17, Kyiv, Ukraine, 03164

PhD of Іnstitut chemistries of surface are the name of O.O. Chuyka of NAN of Ukraine

Department of "Theory of Nanostructured Systems"

Лилия Владимировна Породько, Іnstitute chemistries of surface are the name of O.O. Chuyka of NAN of Ukraine, General Naumov, 17, Kyiv, Ukraine, 03164

Graduate student

Department of "Theory of Nanostructured Systems"

References

Born, M., Wolf, E. (1999). Principles of Optics: 7th Edition. Cambridge University Press, 987.

He, B., Rui, X., Zhang, H. (2012). Transfer Matrix Method for Natural Vibration Analysis of Tree System. Mathematical Problems in Engineering, 1–19. doi:10.1155/2012/393204

Moroz, A. (2005). A recursive transfer-matrix solution for a dipole radiating inside and outside a stratified sphere. Annals of Physics, 315 (2), 352–418. doi:10.1016/j.aop.2004.07.002>

Wu, Z. S., Wang, Y. P. (1991). Electromagnetic scattering for multilayered sphere: Recursive algorithms. Radio Science, 26 (6), 1393–1401. doi:10.1029/91rs01192

Gurwich, I., Kleiman, M., Shiloah, N., Cohen, A. (2000). Scattering of Electromagnetic Radiation by Multilayered Spheroidal Particles: Recursive Procedure. Appl. Opt., 39 (3), 470–477. doi:10.1364/ao.39.000470

Grechko, L. G., Lerman, L. B., Shkoda, N. G. (2004). Scattering of electromagnetic waves on multilayered sphere. Bulletin of Kyiv University. Series: Physics & Mathematics, 3, 376–384.

Grechko, L. G., Lerman, L. B., Shkoda, N. G. (2004). Multi-layered ellipsoid in electric field. Bulletin of Kyiv University. Series: Physics & Mathematics, 1, 386–394.

Lerman, L. B. (1994). Oscillation of flat layered shells with local elastic supports. Int. Appl. Mech, 30 (2), 129−134.

Grechko, L. G., Lerman, L. B., Bilokrinizna, L. M. (2006). Surfaces modes in ellipsoidal multi-layered small particles. Bulletin of Kyiv University. Series: Physics & Mathematics, 4, 416–425.

Porodko, L. V., Lerman, L. B. (2013). Electrodynamic energy in layered spherical nanoparticles. Technology audit and production reserves, 1 (14), 41–44.

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Published

2014-10-14

Issue

Vol. 3 No. 2 (3) (2014)

Section

Physics and mathematics

License

Copyright (c) 2014 Леонид Борисович Лерман, Лилия Владимировна Породько

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