BULLETIN TARAS SHEVCHENKO NATIONAL UNIVERSITY OF KYIV. Mathematics. Mechanics, 2019
The article is devoted to the problem of propagation of weakly nonlinear wave-packets along conta... more The article is devoted to the problem of propagation of weakly nonlinear wave-packets along contact surfaces in a three-layer hydrodynamic system "half space – layer – layer with rigid lid". The condition of solvability of the problem in the third-order approximation is obtained, the evolution equation is derived in the form of a nonlinear Schrodinger equation and the modulation stability condition for its solutions is obtained. The stability diagram and its analysis are presented for the solution which takes place in the case of the balance between dispersion and non-linearity.
We analyze the roots of the dispersion equation for the problem of wave propagation in a two-laye... more We analyze the roots of the dispersion equation for the problem of wave propagation in a two-layer liquid of finite depth with free surface for different values of the ratio of densities. It is shown that the roots obtained in the limiting cases are in good agreement with the previously known results. We prove the existence of two linearly independent solutions of the problem in the first approximation and study the shapes of the free and contact surfaces.
Journal of Automation and Information Sciences, 2015
ABSTRACT The problem of surface gravity waves generation under the motion of the ellipsoid submer... more ABSTRACT The problem of surface gravity waves generation under the motion of the ellipsoid submerged in a liquid half-space is considered. The problem for a sphere was considered as a special case. Using the mirror transformations for deviation of a free surface there were obtained the exact analytical solutions. The analysis found the existence of motion characteristic regimes under which the form of a free surface can essentially differ. On the basis of numerical simulation there was also investigated the problem for the elliptical wing with the conic nose part deflected with respect to a current. It was shown that the wave drag increased with a noise deflection.
Journal of Mechanics in Medicine and Biology, 2001
The effect of a vessel joint of different properties on the heart pulse propagation and anastomos... more The effect of a vessel joint of different properties on the heart pulse propagation and anastomosis junction is investigated. The system under consideration is modelled by an elastic piecewise-constant vessel consisting of two perfectly jointed vessels of different thicknesses and radii. A mathematical model is developed, to perform numerical calculations and to obtain some qualitative and quantitative estimations. The effect of different thicknesses and radii of jointed blood vessels on the concentrations of pressure, radial vessel wall displacement, bending moments and shear forces are analyzed in detail.
BULLETIN TARAS SHEVCHENKO NATIONAL UNIVERSITY OF KYIV. Mathematics. Mechanics, 2019
The article is devoted to the problem of propagation of weakly nonlinear wave-packets along conta... more The article is devoted to the problem of propagation of weakly nonlinear wave-packets along contact surfaces in a three-layer hydrodynamic system "half space – layer – layer with rigid lid". The condition of solvability of the problem in the third-order approximation is obtained, the evolution equation is derived in the form of a nonlinear Schrodinger equation and the modulation stability condition for its solutions is obtained. The stability diagram and its analysis are presented for the solution which takes place in the case of the balance between dispersion and non-linearity.
We analyze the roots of the dispersion equation for the problem of wave propagation in a two-laye... more We analyze the roots of the dispersion equation for the problem of wave propagation in a two-layer liquid of finite depth with free surface for different values of the ratio of densities. It is shown that the roots obtained in the limiting cases are in good agreement with the previously known results. We prove the existence of two linearly independent solutions of the problem in the first approximation and study the shapes of the free and contact surfaces.
Journal of Automation and Information Sciences, 2015
ABSTRACT The problem of surface gravity waves generation under the motion of the ellipsoid submer... more ABSTRACT The problem of surface gravity waves generation under the motion of the ellipsoid submerged in a liquid half-space is considered. The problem for a sphere was considered as a special case. Using the mirror transformations for deviation of a free surface there were obtained the exact analytical solutions. The analysis found the existence of motion characteristic regimes under which the form of a free surface can essentially differ. On the basis of numerical simulation there was also investigated the problem for the elliptical wing with the conic nose part deflected with respect to a current. It was shown that the wave drag increased with a noise deflection.
Journal of Mechanics in Medicine and Biology, 2001
The effect of a vessel joint of different properties on the heart pulse propagation and anastomos... more The effect of a vessel joint of different properties on the heart pulse propagation and anastomosis junction is investigated. The system under consideration is modelled by an elastic piecewise-constant vessel consisting of two perfectly jointed vessels of different thicknesses and radii. A mathematical model is developed, to perform numerical calculations and to obtain some qualitative and quantitative estimations. The effect of different thicknesses and radii of jointed blood vessels on the concentrations of pressure, radial vessel wall displacement, bending moments and shear forces are analyzed in detail.
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Papers by Olga Avramenko