NASU Pidstryhach Institute for Applied Problems in Mechanics and Mathematics

L'viv, Ukraine

NASU Pidstryhach Institute for Applied Problems in Mechanics and Mathematics

L'viv, Ukraine
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Shevchuk V.A.,NASU Pidstryhach Institute for Applied Problems in Mechanics and Mathematics
Journal of Thermal Stresses | Year: 2017

The transient thermal stress crack problem for a half-space with a multilayer coating under thermal surface loading containing an undercoat crack, perpendicular to the interface, is considered. The problem is solved using the principle of superposition and uncoupled quasi-static thermoelasticity. Transient temperature distribution and corresponding thermal stresses for the uncracked multilayer assembly are obtained in a closed analytical form using the model with generalized thermal boundary conditions of heat exchange of a half-space with ambient media via the coating. The crack problem is formulated as a perturbation mixed boundary value problem, in which the crack surface loading should be equal and opposite to the thermal stresses obtained for the uncracked medium, and is reduced to a singular integral equation and solved numerically. Numerical computations are performed for the analysis of influence of the coating upon thermal stresses and thermal stress intensity factor. © 2017 Taylor & Francis

Andriychuk M.I.,NASU Pidstryhach Institute for Applied Problems in Mechanics and Mathematics
2017 11th International Conference on Antenna Theory and Techniques, ICATT 2017 | Year: 2017

A nonlinear synthesis problem according to given amplitude radiation pattern for plane aperture is considered in two ways. An analytical formula for the optimal current is obtained in the first approach. This current generates the amplitude radiation pattern which is close to the given one with the prescribed accuracy. The second approach consists of variational statement of synthesis problem. The numerical results illustrate that each method has advantages in the certain range of frequencies. © 2017 IEEE.

Sachuk Y.V.,European University at Kiev | Maksymuk O.V.,NASU Pidstryhach Institute for Applied Problems in Mechanics and Mathematics
Journal of Mathematical Sciences (United States) | Year: 2017

We consider contact problems of determination of the stress-strain state in the elastic half plane under the action of punches of different shapes (parabolic, cylindrical, elliptic, and hyperbolic). We study specific features of the distribution of contact pressure and stresses in the elastic half plane by using the developed software modules with the use of specially embedded libraries for the evaluation of elliptic integrals of the third kind and the construction of 3D -images and level lines. © 2016, Springer Science+Business Media New York.

Antonova T.M.,Lvivska Politekhnika National University | Sus' O.M.,NASU Pidstryhach Institute for Applied Problems in Mechanics and Mathematics
Journal of Mathematical Sciences (United States) | Year: 2017

For two-dimensional continued fractions whose elements belong to some rectangular sets of a complex plane, we establish the truncation error bound of their figured approximants. It is shown that the two-dimensional continued fractions are uniformly convergent with respect to a sequence of these rectangular sets. © 2017 Springer Science+Business Media New York

Martynyak R.,NASU Pidstryhach Institute for Applied Problems in Mechanics and Mathematics | Chumak K.,NASU Pidstryhach Institute for Applied Problems in Mechanics and Mathematics
International Journal of Heat and Mass Transfer | Year: 2012

The thermoelastic contact of two isotropic solids separated by an interface gap is considered. The gap is formed due to an initial sloping smooth groove on the boundary of one of solids and filled with heat-conductive substance (gas or liquid). The heat is supposed to flow from the material with the higher thermal distortivity into the material with the smaller one. The gap filler influence on heat transfer between two solids is modeled by thermal resistance linearly dependent on the height of the gap. The conditions of perfect thermal contact and nonfrictional mechanical contact are assumed to be satisfied at the interface outside the gap. The contact problem is reduced to a set of two nonlinear singular integrodifferential equations, which is solved numerically. The effect of the imposed heat flow and heat conduction of the gap filler on the length and height of the gap, temperature jump at the interface, distribution of heat flows along and through the interface and distribution of contact stresses is analyzed. © 2011 Elsevier Ltd. All rights reserved.

Plyatsko R.,NASU Pidstryhach Institute for Applied Problems in Mechanics and Mathematics | Fenyk M.,NASU Pidstryhach Institute for Applied Problems in Mechanics and Mathematics
Physical Review D - Particles, Fields, Gravitation and Cosmology | Year: 2013

The Mathisson-Papapetrou equations in Kerr's background are considered. The region of existence of highly relativistic planar circular orbits of a spinning particle in this background and dependence of the particle's Lorentz γ factor on its spin and radial coordinate are investigated. It is shown that in contrast to the highly relativistic circular orbits of a spinless particle, the corresponding orbits of a spinning particle are allowed in a much wider space region. Some of these orbits show the significant attractive action of the spin-gravity coupling on a particle and others are caused by the significant repulsive action. Numerical estimates for electrons, protons, and neutrinos in the gravitational field of black holes are presented. © 2013 American Physical Society.

Plyatsko R.,NASU Pidstryhach Institute for Applied Problems in Mechanics and Mathematics | Fenyk M.,NASU Pidstryhach Institute for Applied Problems in Mechanics and Mathematics
Physical Review D - Particles, Fields, Gravitation and Cosmology | Year: 2012

The Mathisson-Papapetrou equations in Schwarzschild's background both at the Mathisson-Pirani and Tulczyjew-Dixon supplementary condition are considered. The region of existence of highly relativistic planar circular orbits of a spinning particle in this background and dependence of the particle's orbital velocity on its spin and radial coordinate are investigated. It is shown that in contrast to the highly relativistic circular orbits of a spinless particle, which exist only for r=1.5r g(1+δ), 0<δ≪1, the corresponding orbits of a spinning particle are allowed in a wider space region, and the dimension of this region essentially depends on the supplementary condition. At the Mathisson-Pirani condition new numerical results which describe some typical cases of noncircular highly relativistic orbits of a spinning particle starting from r>1.5r g are presented. © 2012 American Physical Society.

Plyatsko R.,NASU Pidstryhach Institute for Applied Problems in Mechanics and Mathematics | Fenyk M.,NASU Pidstryhach Institute for Applied Problems in Mechanics and Mathematics
Physical Review D - Particles, Fields, Gravitation and Cosmology | Year: 2015

Descriptions of highly relativistic fermions in a gravitational field in the classical (nonquantum) and quantum approaches are discussed. The results following from the Mathisson-Papapetrou equations for a fast spinning particle in Schwarzschild's and Kerr's background are considered. Numerical estimates for electron, proton and neutrino in the gravitational field of black holes are presented. The general relativistic Dirac equation is analyzed from the point of view it is using for the adequate description of highly relativistic fermions in a gravitational field, in the linear and nonlinear spin approximation. It is necessary to have some corrected Dirac equation for a highly relativistic fermion with strong spin-gravity coupling. © 2015 American Physical Society.

Malamud M.M.,NASU Pidstryhach Institute for Applied Problems in Mechanics and Mathematics
Russian Journal of Mathematical Physics | Year: 2010

Diverse closed (and selfadjoint) realizations of elliptic differential expressions, on smooth (bounded or unbounded) domains Ω in ℝn with compact boundary ∂Ω are considered. Trace-ideal properties of powers of resolvent differences for these closed realizations of A are proved by using the concept of boundary triples and operator-valued Weyl-Titchmarsh functions, and estimates for negative eigenvalues of certain selfadjoint extensions of the nonnegative minimal operator are derived. Our results extend classical theorems due to Vishik, Povzner, Birman, and Grubb. © 2010 Pleiades Publishing, Ltd.

Bulatsyk O.O.,NASU Pidstryhach Institute for Applied Problems in Mechanics and Mathematics
Proceedings of International Seminar/Workshop on Direct and Inverse Problems of Electromagnetic and Acoustic Wave Theory, DIPED | Year: 2013

The nonlinear integral equation of Hammerstein type arising in the antenna synthesis problem according to the given power pattern is investigated. This equation contains the nonlinearity of the third degree in the integrant. Its solutions are presented by a real positive function (amplitude pattern) and a polynomial with complex zeros (whose phase coincides with the phase pattern). The both amplitude pattern and zeros of the polynomials are found from a set of equations, one of which is the nonlinear integral equation, and the rest (as many as twice the polynomial degree) are the transcendental ones. Numerical results for a concrete problem are described. © 2013 Pidstryhach Institute for Applied Problems in Mechanics and Mathematics, NASU.

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