Wave processes-fundamental basis for modern high technologies

Viktor Sergeevich Krutikov

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DOI: 10.4236/ns.2010.24038                

Abstract

Problems of moving boundaries, moving per-meable boundaries, questions of control over wave processes are fundamental physical prob-lems (acc. to V.L.Ginzburg) that exist for a long time from the moment of the wave equation emergence, for over three hundred years. This paper for the first time states a brief, but clear and quite integral disclosure of the author's approaches, and also a physical essence of analytical methods of functions evaluation of wave processes control - the basic processes of the Nature and the natural sciences, character-istic for all objects of the surrounding world without exception and able to occur only in the regions with moving and moving permeable boundaries. Absolutely immovable boundaries do not exist in the nature. Certain examples which are fundamental in theoretical physics of spherical, cylindrical and flat waves, including the waves induced by dilation of the final length cylinder, demonstrate physical, mathematical and engineering lucidity and simplicity (the so-lution comes to a quadratic equation), and, there-fore, the practical value of definition of control function for the predetermined (based on engi-neering requirements) functions of effect. This paper is designated for a wide range of scientific readers, with aim to render to the reader first of all the physical sense of the studied phenome-non, to show the novelty that it has introduced in the development of the corresponding direc-tion, to show that the way of the research (it is more important than the result) has not arisen “out of nothing”, and the gained results are only “a stone which cost him a whole life” (H.Poin-car).

Keywords

Waves; Mobility; Permeability; Boundary; Control; Inverse Problems

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	Ginsburg, V.L. (1985) O fizike i astrofizike. Physics and Astrophysics, 400, 100.
[2]	Poincar, H. (1983) O nauke. Science, 270, 218.
[3]	Tikhonov, A.N. and Samarskiy, А.А. (1972) Uravneniya matematicheskoy fiziki Equations of Mathematical Physics, 735.
[4]	Lavrent’yev, M.M. (1964) On one inverse problem for a wave equation. Doklady Akademii Nauk SSSR, 157(3), 520-521.
[5]	Lavrent’yev, M.А., Shabat, B.V. (1973) Problems of hydrodynamics and their mathematical models. Nauka, 416.
[6]	Krutikov, V.S. (1985) Odnomernye zadachi mekhaniki sploshnoi sredy s podvizhnymi granitsami (One-dimensional problems in continuum mechanics with moving bound- aries). Kiev, Izdatel'stvo Naukova Dumka, 125, 128.
[7]	Krutikov, V.S. (1996) Validity Limits of solutions to the wave equation for regions with moving permeable boundaries in impulse fluid dynamics and acoustics. Acoustical Physics, 42(4), 471-477.
[8]	Taylor, G. (1946) The airwave surrounding an expanding sphere. Proceedings of the Royal Society A, Mathematical and Physical Sciences, London, 186(1006), 273-292.
[9]	Krutikov, V.S. (1999) Waves surrounding an expanding permeable cylinder in a compressible medium. Doklady Physics, 44(10), 674-677.
[10]	Krutikov, V.S. (1993) Wave phenomena with finite dis-placements of permeable boundaries. Doklady Akademii Nauk, 333(4), 512-514.
[11]	Isakovich, M.A. (1973). Obschaya akustika. Fundamen-tal Acoustics, 495.
[12]	Krutikov, V.S. (1992) Interaction of weak shock waves with a spherical shell involving motion of the boundaries. Mekhanika Tverdogo Tela, 2, 178-186.
[13]	Krutikov, V.S. (1991) A Solution to the Inverse problem for the wave equation with nonlinear conditions in re-gions with moving boundaries. Prikladnaia Matematika i Mekhanika, 55(6), 1058-1062.
[14]	Krutikov, V.S. (1999) A new approach to solution to in-verse problems for a wave equation in domains with moving boundaries. Doklady Mathematics, 59(1), 10-13.
[15]	Krutikov, V.S. (1999) Waves surrounding an expanding permeable cylinder in a compressible medium. Doklady Physics, 44(10), 674-677.
[16]	Krutikov, V.S. (2003) An exact analytical solution to the inverse problem for a plasma cylinder expanding in a compressible medium. Technical Physics Letters, 29(12), 1014-1017.
[17]	Gulyi, G.A. (1990) Scientific fundamentals of pulse- discharge technologies. Naukova Dumka, Kiev, 208.
[18]	Shvets, I.S. (2002) 40th Anniversary of the institute of pulse processes and technologies at NAS of Ukraine. Science and production. Theory, Experiment, Practice of Electrodischarge Technologies, 4, 3-6.
[19]	Ginsburg, V.L. (2000) Physics: Past, present, and future. Priroda, 3.
[20]	Philippov, A.T. (1990) Mnogolikiy soliton. Nauka, 297.
[21]	Wigner, E. (1968) On Incomprehensible efficiency of mathematics in natural sciences. Uspekhi Phizicheskikh Nauk, 94(3), 540.
[22]	Prigozhin, I. and Stengers I. (1986) Order out of Chaos. Bantam Dell Publishing Group, Moskow, 364.
[23]	Reed, M. and Simon, B. (1977-1982) Methods of con-temporary mathematical physics. Springer, Moscow, 1-4.
[24]	Krutikov, V.S. (1995) Development of the method and solutions of pulse problems of continuum mechanics with moving boundaries. Dissertation by the Doctor of Physico-mathematical Sciences, Institute of Geophysics NAS of Ukraine, Kiev, 343.
[25]	Poya, D. (1970) Mathematical invention. Nauka, 45.
[26]	Krutikov, V.S. (2006) On an inverse problem for the wave equation in regions with mobile boundaries and an iteration method for the determination of control func-tions. Doklady Physics, 51(1), 1-5.