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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Novosyadlyj B.,Ivan Franko National University of Lviv | Sergijenko O.,Ivan Franko National University of Lviv | Durrer R.,University of Geneva | Pelykh V.,NASU Pidstryhach Institute for Applied Problems in Mechanics and Mathematics
Physical Review D - Particles, Fields, Gravitation and Cosmology | Year: 2012

The dynamics of expansion and large-scale structure formation of the Universe are analyzed for models with dark energy in the form of a phantom scalar field which initially mimics a Λ-term and evolves slowly to the Big Rip singularity. The discussed model of dark energy has three parameters-the density and the equation of state parameter at the current epoch, Ω de and w 0, and the asymptotic value of the equation of state parameter at a→, ca2. Their best-fit values are determined jointly with all other cosmological parameters by the Markov chain Monte Carlo method using observational data on cosmic microwave background anisotropies and polarization, supernovae type Ia luminosity distances, baryon acoustic oscillations measurements, and more. Similar computations are carried out for ΛCDM and a quintessence scalar field model of dark energy. It is shown that the current data slightly prefer the phantom model, but the differences in the maximum likelihoods are not statistically significant. It is also shown that the phantom dark energy with monotonically increasing density in the future will cause the decay of large-scale linear matter density perturbations due to the gravitational domination of dark energy perturbations long before the Big Rip singularity. © 2012 American Physical Society.


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.


Chumak K.,NASU Pidstryhach Institute for Applied Problems in Mechanics and Mathematics
International Journal of Solids and Structures | Year: 2016

This paper presents a study on adhesive contact between a periodically grooved surface and a flat surface. The effect of interfacial adhesion is included through the use of the Maugis-Dugdale adhesive contact model. The contact problem is reduced to a singular integral equation with Hilbert kernel for a height of the interface gaps and a system of two transcendental equations for widths of the gaps and the adhesion zones. Solutions are obtained for three different equilibrium states of the contact pair involving loading and unloading. The effects of the dimensions of the initial grooves and the adhesive stress on dimensions of the interface gaps, pull-off stress and adhesion hysteresis are investigated. © 2015 Elsevier Ltd.


Malanchuk N.I.,NASU Pidstryhach Institute for Applied Problems in Mechanics and Mathematics
Materials Science | Year: 2011

We study the problem of contact interaction of two elastic isotropic bodies under the conditions of plane deformation with regard for slip caused by the local inhomogeneity of the friction coefficient under consecutive loading by normal and shear forces. By the method of complex potentials, this contact problem is reduced to a singular integral equation for the relative shift of the boundaries of the bodies in the region of slip whose solution is found in the analytic form. The influence of external loads on the relative shift of the boundaries of the bodies in this region, their length, and contact stresses is analyzed. © 2011 Springer Science+Business Media, Inc.


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.


Man'ko S.S.,NASU Pidstryhach Institute for Applied Problems in Mechanics and Mathematics
Journal of Mathematical Physics | Year: 2012

We study Schrödinger operators on star metric graphs with potentials of the form αε-2Q(ε-1x). In dimension 1 such potentials, with additional assumptions on Q, approximate in the sense of distributions as ε → 0 the first derivative of the Dirac delta-function. We establish the convergence of the Schrödinger operators in the uniform resolvent topology and show that the limit operator depends on α and Q in a very nontrivial way. © 2012 American Institute of Physics.


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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