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Information × Registration Number 0211U000730, 0108U001782 , R & D reports Title Interaction of internal and shallow poorly nonlinear waving packages in a two-layer liquid popup.stage_title Head Avramenko Olga Valentinovna, Registration Date 21-02-2011 Organization Kirovograd state pedagogical university named by Volodymyr Vynnychenko popup.description2 1. The report contains 123 pages with 25 figures, 3 applications. The text of the report is presented in one book has a list of used literature sources (112 titles). 2. Key words: soliton, wave packet, the method of multiple scale expansions, envelope of the wave packet, evolution equation, resonance, stability, shape of the wave packet, linear problem, the wave number, frequency. 3. Text of abstract: Object: The wave processes in stratified environments. Subject of the investigation is propagation of wave packets in two- and three-layer hydro-mechanical system, oscillatory system of linear equations. The purpose of research: analysis of weakly nonlinear hydrodynamic processes in two- and three-layer systems, analysis and numerical study of various characteristics that describe the propagation of wave packets in stratified fluids. Objectives of the study: getting of the new analytical results, in particular, output of evolution equations for envelope the wave packet in hydro-mechanical systems "fluid layer – fluid layer", «fluid layer with a solid bottom – fluid layer with a free surface», «fluid layer with a solid bottom – fluid layer – fluid layer with a free surface»; nonlinear stability analysis based on geometrical and physical parameters of systems "fluid layer – fluid layer", «fluid layer with a solid bottom – fluid layer with a free surface»; investigation form of the wave packet for models "fluid layer – fluid layer", «fluid layer with a solid bottom – fluid layer with a free surface»; analysis and numerical investigation of second harmonic resonance and other properties, patterns and mechanical effects that are specific to the considering internal and surface waves; investigation of random wave fields for different stratified fluids. Methods of investigation. The method of multiple scale expansions for higher approximations of nonlinear problems of propagation of wave packets in two- and tree-layer fluid environment, the symbolic transformation method for solving linear problems and investigation numerical characteristics of wave packets, the asymptotic methods. Results: 1. The solutions of linear first approximation and dispersion relations problem propagation of wave packets in three-layer system «fluid layer with a solid bottom – fluid layer – fluid layer with a free surface» are obtained. 2. The third approximation of evolution equations and the solution in the third approximation of the problem of weakly nonlinear evolution of wave packets in systems "fluid layer – fluid layer", «fluid layer with a solid bottom – fluid layer with a free surface» are obtained. 3. Analysis of the shape of wave packets on the basis of the amplitudes of the second harmonic at such models the “layer-layer”, “the hard-bottom - a layer with free surface” carried out. Characteristic features of the second harmonic resonance of these systems were detected. 4. The Schrodinger equation for the propagation of wave packets with wave numbers close to critical is displaying. The correlation between wave number and a small parameter and the corresponding expansion of the wave number for a small parameter for systems "fluid layer – fluid layer", «fluid layer with a solid bottom – fluid layer with a free surface» are obtained. 5. The primary analysis of the problem of random waves in a uniform fluid and the corresponding mathematical models is conducted. 6. The expansion of random fields in integrals of Fourier-Stiltyes is conducted; expansion of functions in series by small coefficient of nonlinearity is found; the annex for the first small parameter is obtained; verification of the result by performing the limit transition to the result of previous researchers is implemented. The basic dynamic equation of the first small parameter is obtained; the transition from problem statement to the basic dynamic equation using the method of successive approximations is shown. 7. The theorem of oscillation of independent solutions of a differential equation is proved; the finite array is obtained on condition, that the linear differential equation of order 2 has solutions of the given functions. The analytical analysis and geometrically-kinematical interpretation sufficient stability conditions are presented; the locus of nonasymptotically stable system is shown. 8. The cases of finite speed of signal transmission, in particular, in automatic control systems remote objects and their long-haul were considered. Thus the relevant differential equations with delay terms introduced and determined stability margin, the characteristic polynomial obtained by the corresponding complex powers. 9. Geometrical model of quantum mechanics is in terms of Banach spaces, as well as some examples and properties ?-orthogonality. The question of the validity of the hypothesis: let the norm of X is strictly convex and X is the WFS, then X is a Hilbert space. The problem put forward: whether P (X) WFS, if X - WFS and P: X > X - the projection of unit norm. The question of measuring the distance between the densities of random variables was studied. The degree of implementation. Considerable number of theoretical research results that have been used and are used in two Candidates theses, are received. The obtained results have become a composite part of 4 training courses and special courses, are used to demonstrate the practical application of mathematics. Recommendations for the introduction and implementation of the conclusions of the results SRW. One candidate dissertations, five qualification works, eight course work is protected according to research. Eighteenth articles in professional journals and 8 articles in national collections were published. The research results can be used by: the scientists of the National Academy of Sciences of Ukraine: the Institute of Hydromechanics, the Sea Hydrophysical Institute, the Institute of Mechanics, the Institute of Mathematics; the universities: in the system of professional training of students of specialty "Mechanics”, “Applied Mathematics”, “Informatics”, at special courses, in writing of research works, in the formation of the variable part educational plans. The practical importance of results. Realization of researches in general is of theoretical value, however, with consideration of modern needs modeling of wave processes arising in practical activities. Investigation of second-harmonic amplitude and, based on the structure of wave packets leading to the conclusion that in the case of high waves packet has a sharp crest, and blunted sole, for shallow waves a blunt ridge, and sharpened soles. Problem of wave packets on the interface of two liquid environments can simulate highly stratified field by the depth termocline in the Pacific Ocean. The study of surface tension can be applied in development of radically the new technology, using two fluid environments, which is not mixed Product Description popup.authors Євладенко Володимир Миколайович Авраменко Ольга Валентинівна Білецька Юлія Григорівна Гуртовий Юрій Валерійович Каленнікова Тетяна Олександрівна Нарадовий Володимир Володимирович Плічко Анатолій Миколайович Ріжняк Галина Ренатівна Селезов Ігорь Тимофійович Філер Залмен Юхимович Шевченко Наталя Григорівна Янчукова Наталя Вікторівна popup.nrat_date 2020-04-02 Close