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.
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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).
B. F. Gordiets, A. I. Osipov, and L. A. Shelepin, Kinetical Processes in Gases and Molecular Lasers [in Russian], Nauka, Moscow (1980).
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).
F. Esposito and M. Capitelli, Chem. Phys. Lett., 302, 49 (1999).
F. Esposito and M. Capitelli, Chem. Phys. Lett., 303, 636 (1999).
F. Esposito and M. Capitelli, Chem. Phys. Lett., 364, 180 (2002).
J. Hadamard, “Sur les problemes aux derivees partielles et leur signification physique,” Bull. Univ. Princeton, 13, 49 (1902).
J. Hadamard, Le probleme de Caucy et les equations aux derivees partielles lineaires hyperboliques, Hermann, Paris (1932).
A. N. Tikhonov, Dokl. Akad. Nauk SSSR, 39, 195 (1943).
A. N. Tikhonov, Dokl. Akad. Nauk SSSR, 151, 501 (1963).
A. N. Tikhonov, Dokl. Akad. Nauk SSSR, 153, 49 (1963).
A. M. Gubanov, E. K. Eroshenkov, O. A. Malkin, and L. S. Polak, Kinetika i Kataliz, 13, 33 (1972).
A. S. Biryukov, V. K. Konyukhov, A. I. Lukovnikov, and R. I. Serikov, Zh. Éksp. Teor. Fiz., 66, 1248 (1974).
Y. A. Kulagin, R. I. Serikov, I. V. Simanovskii, and L. A. Shelepin, J. Russ. Laser Res., 20, 560 (1999).
A. N. Tikhonov and V. Ya. Arsenin, Solutions of Ill-Posed Problems, Halsted Press, New York (1977).
A. N. Tikhonov, A. V. Goncharskii, V. V. Stepanov, and A. G. Yagola, Regularizing Algorithms and A Priori Information [in Russian], Nauka, Moscow (1983).
A. V. Goncharskii, A. S. Leonov, and A. G. Yagola, Zh. Vych. Mat. i Mat. Fiz., 12, 1592 (1972).
V. K. Ivanov, Izv. Vuzov. Matematika, No. 2, 96 (1958).
V. K. Ivanov, Dokl. Akad. Nauk SSSR, 142, 997 (1962).
V. K. Ivanov, Dokl. Akad. Nauk SSSR, 145, 270 (1962).
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).
A. V. Goncharskii and V. V. Stepanov, Dokl. Akad. Nauk SSSR, 245, 1296 (1979).
A. V. Goncharskii and V. V. Stepanov, Vestn. MGU, Ser. 15, No. 3, 12 (1980).
A. V. Goncharskii and A. G. Yagola, Dokl. Akad. Nauk SSSR, 184, 771 (1969).
F. P. Vasil’ev, Methods of Solution of Extremum Problems [in Russian], Nauka, Moscow (1981).
B. N. Pshenichnyi and Yu. M. Danilin, Numerical Methods in Extremum Problems [in Russian], Nauka, Moscow (1975).
J. O. Hirschfelder, C. F. Curtiss, and R. B. Bird, Molecular Theory of Gases and Liquids, Wiley, New York (1954).
L. Jerig, K. Thielen, and P. Roth, AIAA J., 29, 1136 (1990).
L. B. Ibragimova, G. D. Smekhov, and O. P. Shatalov, Mekh. Zhidk. i Gazov, No. 1, 181 (1999).
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.
M. S. Massey, Rept. Progr. Phys., 12, 248 (1949).
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).
S. V. Kulikov, A. L. Smirnov, and O. N. Ternovaya, Zh. Khim. Fiz., No. 12, 53 (2000).
S. O. Macheret and I. V. Adamovich, J. Chem. Phys., 113, 7351 (2000).
C. Itzykson and J. B. Zuber, Introduction to Quantum Field Theory, McGraw-Hill, New York, (1980).
W. A. Day, The Thermodynamics of Simple Materials with Fading Memory, Springer-Verlag, New York (1972).
N. Petrov and I. Brankov, Modern Problems of Thermodynamics [in Russian], Mir, Moscow (1986).
S. L. Sobolev, Usp. Fiz. Nauk, 161, 5 (1991).
V. I. Korobko, The Golden Proportion and Problems of Harmony of the Systems [in Russian], Publishers of the Association of Building Institutes, Moscow (1997).
E. M. Soroko, Structural Harmony of the Systems [in Russian], Nauka i Tekhnika, Minsk (1984).
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).
R. M. Yulmetuev, S. A. Demin, N. A. Emelyanova, et al., Physica A, 331, 300 (2004).
R. M. Yulmetuev, P. Haggi, and F. M. Gafarov, Phys. Rev. E, 62, 6178 (2000).
R. M. Yulmetuev, P. Haggi, and F. M. Gafarov, Phys. Rev. E, 64, 432 (2001).
A. N. Tikhonov and V. B. Glasko, Zh. Vych. Mat. i Mat. Fiz., 5, 463 (1965).
A. B. Vasil’eva and A. N. Tikhonov, Integral Equations [in Russian], Moscow State University Press, Moscow (1989).
A. V. Zinchenko, N. N. Paramonova, V. I. Privalov, and A. I. Reshetnikov, Meteorolog. i Gidrolog., No. 5, 35 (2001).
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.
V. F. Raputa and A. I. Krylova, Meteorol. Gidrol., No. 3, 49 (1995).
D. E. Haas-Laursen, D. E. Hartley, and R. G. Prinn, J. Geophys. Res., 101, 22823 (1996).
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).
A. I. Osipov and S. L. Shelepin, Vestn. Mosk. Univ. Ser. 3. Fiz. Astron., No. 5, 37 (2003).
A. I. Osipov and S. L. Shelepin, Vestn. Mosk. Univ. Ser. 3. Fiz. Astron., No. 6, 64 (2004).
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Osipov, A.I., Shelepin, L.A. & Shelepin, S.L. Inverse problem method in laser physics. J Russ Laser Res 26, 116–136 (2005). https://doi.org/10.1007/s10946-005-0011-7
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DOI: https://doi.org/10.1007/s10946-005-0011-7