• Українська
  • English

< | >

Current issue   Ukr. J. Phys. 2015, Vol. 60, N 7, p.601-613
https://doi.org/10.15407/ujpe60.07.0601   Paper

Starkov V.N., Brodyn M.S., Tomchuk P.M., Gayvoronsky V.Ya., Boyarchuk A.Yu.

Institute of Physics, Nat. Acad. of Sci. of Ukraine
(46, Prosp. Nauky, Kyiv 03680, Ukraine; e-mail: nikol12@voliacable.com)

Mathematical Interpretation of Experimental Research Results on Nonlinear Optical Material Properties

Section: Optics, Lasers, and Quantum Electronics
Language: English

Abstract: The problem of mathematical interpretation of experimental research results concerning the influence of incorporated TiO2 nanoparticles on the optical properties of the nonlinear optical material potassium dihydrogen phosphate has been formulated and solved, by using the computational physics methods. The mathematical model is reduced to a Fredholm integral equation of the first kind. A spline-iteration modification of the Landweber regularization method is suggested for solving the ill-posed problem. The results of computational experiments are compared with those of physical ones.

Key words:incorporated TiO2 nanoparticles, nonlinear optical material potassium dihydrogen phosphate, Fredholm integral equation, Landweber regularization method.

References:

  1. A.F. Verlan' and V.S. Sizikov, Integral Equations: Methods, Algorithms, Programs. Reference Textbook (Naukova Dumka, Kyiv, 1986) (in Russian).
  2. V.V. Ivanov, Methods of Computer Calculations. A Handbook (Naukova Dumka, Kyiv, 1986) (in Russian).
  3. V.Ya. Gayvoronsky, V.M. Starkov, M.A. Kopylovskyi, M.S. Brodyn, Ye.O. Vyshnyakov, O.Yu. Boyarchuk, and I.M. Prytula, Ukr. Fiz. Zh. 55, 875 (2010).
  4. V.N. Starkov, Constructive Methods of Computational Physics in Interpretation Problems (Naukova Dumka, Kyiv, 2002) (in Russian).
  5. V.N. Starkov and A.Yu. Boyarchuk, in Issues of Computation Optimization (V.M. Glushkov Institute of Cybernetics, Kyiv, 2009), Vol. 2, p. 339 (in Ukrainian).
  6. A.N. Kolmogorov and S.V. Fomin, Elements of the Theory of Functions and Functional Analysis (Dover, New York, 1999).
  7. A.N. Tikhonov and V.Ya. Arsenin, Solutions of Ill-Posed Problems (Wiley, New York, 1977).
  8. V.V. Vasin and A.L. Ageev, Incorrect Problems with A Priori Information (Nauka, Ekaterinburg, 1993) (in Russian).
  9. V.S. Sizikov, Inverse Application Problems and MatLab. A Handbook (Lan', Saint-Petersburg, 2011) (in Russian).
  10. A.K. Lowes, Inverse und Schlecht Gestellte Probleme (Teubner, Stuttgart, 1989).
  11. A. Bakushinsky and A. Goncharsky, Ill-Posed Problems: Theory and Applications (Kluwer, Dordrecht, 1994). CrossRef
  12. Encyclopedia of Mathematics, edited by I.M. Vinogradov (Moscow, Sovetskaya Entsyklopediya, 1977–1985) (in Russian), Vol. 5.
  13. G.M. Vainikko and A.Yu. Veretennikov, Iteration Procedures in Ill-Posed Problems (Nauka, Moscow, 1986) (in Russian).
  14. S.G. Solodkii, Dr. Sci. Phys. Mat. thesis (Institute of Mathematics, Kyiv, 2003).
  15. V.A. Morozov, Regular Methods for Solving Ill-Posed Problems (Moscow Univ., Moscow, 1974) (in Russian).
  16. A.V. Goncharskii, A.S. Leonov, and A.G. Yagola, Dokl. Akad. Nauk SSSR 203, 1238 (1972).
  17. A.V. Goncharskii, A.S. Leonov, and A.G. Yagola, Zh. Vychisl. Mat. Mat. Fiz. 13, 294 (1973).
  18. M. Defriese and C. De Mol, in Inverse Problems: An Interdisciplinary Study, edited by P.C. Sabatier (Academic Press, New York 1987), p. 261.