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Journal of Russian Laser Research

, Volume 26, Issue 2, pp 116–136 | Cite as

Inverse problem method in laser physics

  • A. I. Osipov
  • L. A. Shelepin
  • S. L. Shelepin
Article
  • 36 Downloads

Abstract

Applications of the method of ill-posed inverse problems in laser physics are considered. Means of calculating the level cross sections of physical-chemical reactions with subsequent calculation of the reaction rate constants are developed. Mathematical and numerical aspects for the realization of ill-posed inverse problem are considered in detail using the concrete example of level cross sections of dissociation.

Keywords

active laser medium ill-posed inverse problem level cross section rate constant 

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References

  1. 1.
    G. G. Chernyi and S. A. Losev (Eds.), Physical-Chemical Processes in Gas Dynamics [in Russian], Vol. 1, The Dynamics of the Physical-Chemical Processes in Gas and Plasma, Moscow State University Press, Moscow (1995).Google Scholar
  2. 2.
    B. F. Gordiets, A. I. Osipov, and L. A. Shelepin, Kinetical Processes in Gases and Molecular Lasers [in Russian], Nauka, Moscow (1980).Google Scholar
  3. 3.
    G. G. Chernyi and S. A. Losev (Eds.), Physical-Chemical Processes in Gas Dynamics [in Russian], Vol. 2, Physical-Chemical Kinetics and Thermodynamics, Moscow State University Press, Moscow (1995).Google Scholar
  4. 4.
    F. Esposito and M. Capitelli, Chem. Phys. Lett., 302, 49 (1999).CrossRefGoogle Scholar
  5. 5.
    F. Esposito and M. Capitelli, Chem. Phys. Lett., 303, 636 (1999).CrossRefGoogle Scholar
  6. 6.
    F. Esposito and M. Capitelli, Chem. Phys. Lett., 364, 180 (2002).CrossRefGoogle Scholar
  7. 7.
    J. Hadamard, “Sur les problemes aux derivees partielles et leur signification physique,” Bull. Univ. Princeton, 13, 49 (1902).Google Scholar
  8. 8.
    J. Hadamard, Le probleme de Caucy et les equations aux derivees partielles lineaires hyperboliques, Hermann, Paris (1932).Google Scholar
  9. 9.
    A. N. Tikhonov, Dokl. Akad. Nauk SSSR, 39, 195 (1943).Google Scholar
  10. 10.
    A. N. Tikhonov, Dokl. Akad. Nauk SSSR, 151, 501 (1963).Google Scholar
  11. 11.
    A. N. Tikhonov, Dokl. Akad. Nauk SSSR, 153, 49 (1963).Google Scholar
  12. 12.
    A. M. Gubanov, E. K. Eroshenkov, O. A. Malkin, and L. S. Polak, Kinetika i Kataliz, 13, 33 (1972).Google Scholar
  13. 13.
    A. S. Biryukov, V. K. Konyukhov, A. I. Lukovnikov, and R. I. Serikov, Zh. Éksp. Teor. Fiz., 66, 1248 (1974).Google Scholar
  14. 14.
    Y. A. Kulagin, R. I. Serikov, I. V. Simanovskii, and L. A. Shelepin, J. Russ. Laser Res., 20, 560 (1999).Google Scholar
  15. 15.
    A. N. Tikhonov and V. Ya. Arsenin, Solutions of Ill-Posed Problems, Halsted Press, New York (1977).Google Scholar
  16. 16.
    A. N. Tikhonov, A. V. Goncharskii, V. V. Stepanov, and A. G. Yagola, Regularizing Algorithms and A Priori Information [in Russian], Nauka, Moscow (1983).Google Scholar
  17. 17.
    A. V. Goncharskii, A. S. Leonov, and A. G. Yagola, Zh. Vych. Mat. i Mat. Fiz., 12, 1592 (1972).Google Scholar
  18. 18.
    V. K. Ivanov, Izv. Vuzov. Matematika, No. 2, 96 (1958).Google Scholar
  19. 19.
    V. K. Ivanov, Dokl. Akad. Nauk SSSR, 142, 997 (1962).Google Scholar
  20. 20.
    V. K. Ivanov, Dokl. Akad. Nauk SSSR, 145, 270 (1962).Google Scholar
  21. 21.
    A. N. Tikhonov, A. V. Goncharskii, V. V. Stepanov, and A. G. Yagola, Numerical Methods of Solution of Ill-Posed Problems [in Russian], Nauka, Moscow (1990).Google Scholar
  22. 22.
    A. V. Goncharskii and V. V. Stepanov, Dokl. Akad. Nauk SSSR, 245, 1296 (1979).Google Scholar
  23. 23.
    A. V. Goncharskii and V. V. Stepanov, Vestn. MGU, Ser. 15, No. 3, 12 (1980).Google Scholar
  24. 24.
    A. V. Goncharskii and A. G. Yagola, Dokl. Akad. Nauk SSSR, 184, 771 (1969).Google Scholar
  25. 25.
    F. P. Vasil’ev, Methods of Solution of Extremum Problems [in Russian], Nauka, Moscow (1981).Google Scholar
  26. 26.
    B. N. Pshenichnyi and Yu. M. Danilin, Numerical Methods in Extremum Problems [in Russian], Nauka, Moscow (1975).Google Scholar
  27. 27.
    J. O. Hirschfelder, C. F. Curtiss, and R. B. Bird, Molecular Theory of Gases and Liquids, Wiley, New York (1954).Google Scholar
  28. 28.
    L. Jerig, K. Thielen, and P. Roth, AIAA J., 29, 1136 (1990).Google Scholar
  29. 29.
    L. B. Ibragimova, G. D. Smekhov, and O. P. Shatalov, Mekh. Zhidk. i Gazov, No. 1, 181 (1999).Google Scholar
  30. 30.
    O. E. Krivonosova, S. A. Losev, V. P. Nalivaiko, et al., “Advisable Data on the Rate Constants of Chemical Reactions between the Molecules Consisting of N and O Atoms”, in: B. M. Smirnov (Ed.), Chemistry of Plasma: Collection of Papers. [in Russian], Issue 14, Energoatomizdat, Moscow (1987), p. 3.Google Scholar
  31. 31.
    M. S. Massey, Rept. Progr. Phys., 12, 248 (1949).CrossRefGoogle Scholar
  32. 32.
    A. N. Kolmogorov and S. V. Fomin, Elements of the Theory of Functions and Functional Analysis, Vol. 1, Graylock Press, Rochester, New York (1957) and Vol. 2, Graylock Press, Albany, New York (1961).Google Scholar
  33. 33.
    S. V. Kulikov, A. L. Smirnov, and O. N. Ternovaya, Zh. Khim. Fiz., No. 12, 53 (2000).Google Scholar
  34. 34.
    S. O. Macheret and I. V. Adamovich, J. Chem. Phys., 113, 7351 (2000).CrossRefGoogle Scholar
  35. 35.
    C. Itzykson and J. B. Zuber, Introduction to Quantum Field Theory, McGraw-Hill, New York, (1980).Google Scholar
  36. 36.
    W. A. Day, The Thermodynamics of Simple Materials with Fading Memory, Springer-Verlag, New York (1972).Google Scholar
  37. 37.
    N. Petrov and I. Brankov, Modern Problems of Thermodynamics [in Russian], Mir, Moscow (1986).Google Scholar
  38. 38.
    S. L. Sobolev, Usp. Fiz. Nauk, 161, 5 (1991).Google Scholar
  39. 39.
    V. I. Korobko, The Golden Proportion and Problems of Harmony of the Systems [in Russian], Publishers of the Association of Building Institutes, Moscow (1997).Google Scholar
  40. 40.
    E. M. Soroko, Structural Harmony of the Systems [in Russian], Nauka i Tekhnika, Minsk (1984).Google Scholar
  41. 41.
    V. I. Korobko, The Golden Proportion Principle in the Vegetable World. The Strategy of Life under the Conditions of the Planetary Econical Crisis [in Russian], Vol. 2, Gumanistika, St. Petersburg (2002).Google Scholar
  42. 42.
    R. M. Yulmetuev, S. A. Demin, N. A. Emelyanova, et al., Physica A, 331, 300 (2004).Google Scholar
  43. 43.
    R. M. Yulmetuev, P. Haggi, and F. M. Gafarov, Phys. Rev. E, 62, 6178 (2000).CrossRefGoogle Scholar
  44. 44.
    R. M. Yulmetuev, P. Haggi, and F. M. Gafarov, Phys. Rev. E, 64, 432 (2001).Google Scholar
  45. 45.
    A. N. Tikhonov and V. B. Glasko, Zh. Vych. Mat. i Mat. Fiz., 5, 463 (1965).Google Scholar
  46. 46.
    A. B. Vasil’eva and A. N. Tikhonov, Integral Equations [in Russian], Moscow State University Press, Moscow (1989).Google Scholar
  47. 47.
    A. V. Zinchenko, N. N. Paramonova, V. I. Privalov, and A. I. Reshetnikov, Meteorolog. i Gidrolog., No. 5, 35 (2001).Google Scholar
  48. 48.
    V. A. Borzilov, N. V. Klepikova, et.al., Complex of Mathematical Models of Atmospheric Propagation and Deposition of Radionuclides. Radiation Aspects of the Chenobyl’ Accident [in Russian], Gidrometeoizdat, St. Petersburg (1993), P. 82–86.Google Scholar
  49. 49.
    V. F. Raputa and A. I. Krylova, Meteorol. Gidrol., No. 3, 49 (1995).Google Scholar
  50. 50.
    D. E. Haas-Laursen, D. E. Hartley, and R. G. Prinn, J. Geophys. Res., 101, 22823 (1996).CrossRefGoogle Scholar
  51. 51.
    Yu. A. Kulagin, R. I. Serikov, I. V. Simanovskii and L. A. Shelepin, Application of the Method of Direct and Inverse Problems for the Calculation of Particle Size Distribution Function [in Russian], Preprint No. 46 of the P. N. Lebedev Physical Institute, Moscow (1999).Google Scholar
  52. 52.
    A. I. Osipov and S. L. Shelepin, Vestn. Mosk. Univ. Ser. 3. Fiz. Astron., No. 5, 37 (2003).Google Scholar
  53. 53.
    A. I. Osipov and S. L. Shelepin, Vestn. Mosk. Univ. Ser. 3. Fiz. Astron., No. 6, 64 (2004).Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • A. I. Osipov
    • 1
  • L. A. Shelepin
    • 1
  • S. L. Shelepin
    • 1
  1. 1.P. N. Lebedev Physical InstituteRussian Academy of SciencesMoscowRussia

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