East European Journal of Physics https://periodicals.karazin.ua/eejp <p>International peer-reviewed journal devoted to experimental and theoretical research on the nuclear physics, cosmic rays and particles, high-energy physics, solid state physics, plasma physics and controlled thermonuclear fusion, physics of charged particle beams, plasma electronics, radiation materials science, physics of thin films, condensed matter physics, functional materials and coatings, technical thermophysics and industrial power,&nbsp;medical physics and physical technologies in an interdisciplinary context.</p> <p><strong>East European Journal of Physics</strong> <strong>has been selected for coverage in Clarivate Analytics products and services.&nbsp;Beginning with 2017 it will be indexed and abstracted in: "Emerging Sources Citation Index"(ESCI).</strong></p> V.N. Karazin Kharkiv National University en-US East European Journal of Physics 2312-4334 <p>Authors who publish with this journal agree to the following terms:<br><br></p> <ol type="a"> <ul> <li class="show">Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a&nbsp;<a href="http://creativecommons.org/licenses/by/4.0/" target="_new">Creative Commons Attribution License</a>&nbsp;that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.</li> </ul> </ol> <ol type="a"> <ul> <li class="show">Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.</li> </ul> </ol> <ol type="a"> <ul> <li class="show">Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See&nbsp;<a href="http://opcit.eprints.org/oacitation-biblio.html" target="_new">The Effect of Open Access</a>).</li> </ul> </ol> Instabilities in a Non-Uniformly Rotating Medium with Stratification of the Temperature in an External Uniform Magnetic Field https://periodicals.karazin.ua/eejp/article/view/12395 <p>In this paper the stability of the non-uniformly rotating cylindrical plasma in the axial uniform magnetic field with the vertical temperature gradient is investigated. In the approximation of geometrical optics a dispersion equation for small axisymmetric perturbations is obtained with the effects of viscosity, ohmic and heat conductive dissipation taken into account. The stability criteria for azimuthal plasma flows are obtained in the presence of&nbsp; the vertical temperature gradient and&nbsp; the constant magnetic field. The Rayleigh-Benard problem for stationary convection in&nbsp; the non-uniformly rotating layer of the electrically conducting fluid in the axial uniform magnetic field is considered. In the linear theory of stationary convection the critical value of the Rayleigh number &nbsp;subject to the profile of &nbsp;the inhomogeneous rotation (Rossby number) is obtained. It is shown that the negative values of the Rossby number &nbsp;have a destabilizing effect, since the critical Rayleigh number &nbsp;becomes smaller, than in the case of the uniform rotation , or of the rotation with positive Rossby numbers . To describe the &nbsp;nonlinear convective phenomena the local Cartesian coordinate system was used, where the inhomogeneous rotation of the fluid layer&nbsp; was represented as the rotation with a constant angular velocity &nbsp;and azimuthal shear &nbsp;with linear dependence on the coordinate. As a result of applying the method of perturbation theory for the small parameter of supercriticality of the stationary Rayleigh number&nbsp; a nonlinear Ginzburg-Landau equation was obtaned. This equation describes the evolution of &nbsp;the finite amplitude of perturbations by utilizing the solution of the Ginzburg-Landau equation. It is shown that the weakly nonlinear convection based on the equations of the six-mode Lorentz model transforms into the identical Ginzburg-Landau equation. By utilizing the solution of the Ginzburg-Landau equation, we determined the dynamics of unsteady heat transfer for various profiles of the angular velocity of the rotation of electrically conductive fluid.</p> Michael Kopp Anatoly Tur Volodymyr Yanovsky ##submission.copyrightStatement## 2019-03-14 2019-03-14 1 4 33 10.26565/2312-4334-2019-1-01 Chiral Fermions Algorithms In Lattice QCD https://periodicals.karazin.ua/eejp/article/view/12396 <p>The theory that explains the strong interactions of the elementary particles, as part of the standard model, it is the so-called Quantum Chromodynamics (QCD) theory. In regimes of low energy this theory it is formulated and solved in a lattice with four dimensions using numerical simulations. This method it is called the lattice QCD theory. Quark propagator it the most important element that is calculated because it contains the physical information of lattice QCD. Computing quark propagator of chiral fermions in lattice means that we should invert the chiral Dirac operator, which has high complexity. In the standard inversion algorithms of the Krylov subspace methods, that are used in these kinds of simulations, the time of inversion is scaled with the inverse of the quark mass. In lattice QCD simulations with chiral fermions, this phenomenon it is knowing as the critical slowing-down problem. The purpose of this work is to show that the preconditioned GMRESR algorithm, developed in our previous work, solves this problem. The preconditioned GMRESR algorithm it is developed in U(1) group symmetry using QCDLAB 1.0 package, as good “environment” for testing new algorithms. In this paper we study the escalation of the time of inversion with the quark mass for this algorithm. It turned out that it is a fast inversion algorithm for lattice QCD simulations with chiral fermions, that “soothes” the critical slowing-down of standard algorithms. The results are compared with SHUMR algorithm that is optimal algorithm used in these kinds of simulations. The calculations are made for 100 statistically independent configurations on 64 x 64 lattice gauge U(1) field for three coupling constant and for some quark masses. The results showed that for the preconditioned GMRESR algorithm the coefficient k, related to the critical slowing down phenomena, it is approximately - 0.3 compared to the inverse proportional standard law (k = -1) that it is scaled SHUMR algorithm, even for dense lattices. These results make more stable and confirm the efficiency of our algorithm as an algorithm that avoid the critical slowing down phenomenon in lattice QCD simulations. In our future studies we have to develop the preconditioned GMRESR algorithm in four dimensions, in SU (3) lattice gauge theory.</p> Dafina Xhako Rudina Zeqirllari ##submission.copyrightStatement## 2019-03-14 2019-03-14 1 34 39 10.26565/2312-4334-2019-1-02 Production of cc¯ and bb¯ Quark Pairs in pp Collisions at Energies of Experiments at the Large Hadron Collider https://periodicals.karazin.ua/eejp/article/view/12397 <p>Production of charm and beauty quark–antiquark pairs in proton–proton collisions is simulated with the codes generated in the framework of MadGraph5_aMC@NLO. The tree–level partonic processes are taken into account in first three orders of the perturbative quantum chromodynamics. The considered hard processes have two, three, and four partons in the final states. These final states contain one or two heavy quark–antiquark pairs. The calculations are performed with parton distribution functions (PDF) obtained with neural network methods by NNPDF collaboration. Influence of the multiple partonic interactions (MPI), initial– and final–state showers on the cross sections (CSs) is studied consistently taking advantage of Pythia&nbsp;8 event generator. The CSs are computed in central and forward rapidity regions under conditions of the ALICE and LHCb experiments at the Large Hadron Collider at CERN. The studied transverse momentum interval of the heavy quarks spreads up to 30&nbsp;GeV/c.&nbsp;The CSs calculated at the leading order (LO) with Pythia&nbsp;8, in the tree approximation with MadGraph5, and within Fixed Order plus Next–to–Leading Logarithms (FONLL) approach agree with each other within bands of the uncertainties inherent to underlying theory and methods. Inclusion of next–to–leading order (NLO) and N<sup>2</sup>LO partonic processes into calculations in addition to LO ones results in growth of the CSs. This increase reduces to some extent discrepancies with the CSs measured by ALICE and LHCb. Variations of the CSs due to renormalization– and factorization–scale dependence are much larger than the increase of the CSs in NLO and N<sup>2</sup>LO, than the uncertainties springing in the NNPDF model, and then the accuracy achieved in the ALICE and LHCb cross section measurements. Effects of the MPI, the space– and time–like partonic showers on the heavy quark CSs are found to be not very essential.</p> Taras Horbatiuk Volodymyr Kotlyar Mykola Maslov Anton Safronov ##submission.copyrightStatement## 2019-03-14 2019-03-14 1 40 45 10.26565/2312-4334-2019-1-03 Spectra of Collective Excitations and Low-Frequency Asymptotics of Green’s Functions in Uniaxial and Biaxial Ferrimagnetics https://periodicals.karazin.ua/eejp/article/view/12398 <p>The paper studies the dynamic description of uniaxial and biaxial ferrimagnetics with spin s=1/2 in alternative external field. The nonlinear dynamic equations with sources are obtained, on basis on which low-frequency asymptotics of two-time Green functions in the uniaxial and biaxial cases of the ferrimagnet are obtained. Energy models are constructed that are specific functions of Casimir invariants of the algebra of Poisson brackets for magnetic degrees of freedom. On their basis, the question of the stable magnetic states has been solved for the considered systems. These equations were linearized, an explicit form of the collective excitations spectra was found, and their character was analyzed. The article studies the uniaxial case of a ferrimagnet, as well as biaxial cases of an antiferromagnet, easy-axis and easy-plane ferrimagnets. It is shown that for a uniaxial antiferromagnet the spectrum of magnetic excitations has a Goldstone character. For biaxial ferrimagnetic materials, it was found that the spectrum has either a quadratic character or a more complex dependence on the wave vector. It is shown that in the uniaxial case of an antiferromagnet the Green function of the type G<sub>sα,</sub><sub>sβ</sub>(k,0),&nbsp;G<sub>sα,</sub><sub>nβ</sub>(k,0) and G<sub>sα,</sub><sub>sβ</sub>(0,ω)&nbsp;have regular asymptotic behavior, and the Green function of type G<sub>nα,</sub><sub>nβ</sub>(k,0)≈1/k<sup>2</sup>&nbsp;and G<sub>sα,</sub><sub>nβ</sub>(0,ω)≈1/ω, G<sub>nα,</sub><sub>nβ</sub>(0,ω)≈1/ω<sup>2</sup>&nbsp; have a pole feature in the wave vector and frequency. Biaxial ferrimagnetic states have another type of the features of low-frequency asymptotics of the Green's functions. In the case of a ferrimagnet, the “easy-axis” of the asymptotic behavior of the Green functions G<sub>sα,</sub><sub>sβ</sub>(0,ω),&nbsp;G<sub>sα,</sub><sub>nβ</sub>(0,ω), G<sub>nα,</sub><sub>nβ</sub>(0,ω),&nbsp;G<sub>sα,</sub><sub>sβ</sub>(k,0),&nbsp;G<sub>sα,</sub><sub>nβ</sub>(k,0), G<sub>nα,</sub><sub>nβ</sub>(k,0) have a pole character. For the case of the “easy-plane” type ferrimagnet, the asymptotics of the Green functions G<sub>sα,</sub><sub>nβ</sub>(0,ω),&nbsp;G<sub>nα,</sub><sub>nβ</sub>(0,ω),&nbsp;G<sub>sα,</sub><sub>nβ</sub>(k,0),&nbsp;G<sub>nα,</sub><sub>nβ</sub>(k,0), have a pole character, and the Green function G<sub>sα,</sub><sub>sβ</sub>(k,ω) contains both the pole component and the regular part. A comparative analysis of the low-frequency asymptotics of Green functions shows that the nature of magnetic anisotropy significantly effects the structure of low-frequency asymptotics for uniaxial and biaxial cases of ferrimagnet. Separately, we note the non-Bogolyubov character of the Green function asymptotics for ferrimagnet with biaxial anisotropy G<sub>nα,</sub><sub>nβ</sub>(k,0)≈1/k<sup>4</sup><em>.</em></p> Anton Glushchenko Michail Kovalevsky Valentina Matskevych ##submission.copyrightStatement## 2019-03-14 2019-03-14 1 46 54 10.26565/2312-4334-2019-1-04 Dynamics of Electron in TEM Wave Field https://periodicals.karazin.ua/eejp/article/view/12400 <p>Big amount of works deals with solution of differential equations, associated with electron motion in electromagnetic field, using methods of classical electrodynamics. Solution of equation of an electron motion in TEM wave field is interesting task because this equation is mathematical model of big number of wave processes, which are used for researches of different physical processes. The proposed work dedicated to finding the solution for the equation of an electron motion in TEM wave field in laboratory system of coordinates using the theory of almost periodic functions. The work demonstrates that the projections of electron velocity on coordinate axis conform to the wave equation, and, consequently, could be expanded into generalized Fourier series at any value of the wave and electron parameters. In the present work, the formulas received before for electron velocity projection on coordinate axis, are transformed to a well-behaved form, and are broken down into non-perfect generalized Fourier series. Non-perfect Fourier series for projections of electron velocity on coordinate axis are found by means of plotting of complex series, which are called in the theory of almost periodic functions as ”closure of set”. For approximate computation of electron velocity it is possible to restrict oneself to finite number of series harmonics. Application of method of electron velocity components transformation into generalized Fourier series made it possible to find in electron velocity components series terms, which do not depend on time and are equal to average magnitudes of the respective values. Electron velocity components present functions of initial magnitudes of electron velocity components, of generalized phase magnitude and of the wave parameters. Initial magnitudes are not preset at random, but calculated from the equations, the type of which is specified in the work. Electron trajectory in coordinate space is calculated by integrating of the respective expressions for velocity projections on coordinate axis. For demonstration purpose the work deals with the example of electron dynamics in wave polarization plane with consideration of only permanent addends and first harmonics of Fourier series for electron velocity projections on coordinate axis. An approximate solution of the equations of electron dynamics in the plane of polarization of the wave is given. Solution for the equation of electron motion in TEM wave field in the laboratory coordinate system using the theory of almost periodic functions made it possible to solve the problem of dynamics of relativistic electron in the field of progressing TEM wave. It made it possible to demonstrate the availability of time-independent summands in the value of the speed of the electron, which moves in TEM wave. A very important circumstance is also the fact, that the theory makes it possible to investigate electron dynamics depending on the original wave intensity.</p> Yuriy Grigoriev Andrey Zelinskiy Tetiana Malykhina Valentina Shpagina ##submission.copyrightStatement## 2019-03-15 2019-03-15 1 55 64 10.26565/2312-4334-2019-1-05 Modulation Instability in Two Component Bose-Einstein Condensate with Dissipation https://periodicals.karazin.ua/eejp/article/view/12401 <p>In this paper, we consider the dynamic evolution of a binary mixture of a Bose-Einstein condensate taking into account the presence of dissipation inside the components. Using the introduction of the dissipative function, the modified Gross-Pitaevskii equations are obtained. &nbsp;These equations, in contrast to the usual Gross-Pitaevskii equations for two-component condensate, allow us to take into account the dissipation in the system. The influence of dissipative processes on the development of modulation instability in a spatially homogeneous two-component Bose-Einstein condensate is investigated. In contrast to the one-component Bose-Einstein condensate, in which modulation instability arises only when there are forces of attraction between atoms, in a two-component Bose-Einstein condensate nonlinear dynamics, leading to modulation instability is more complex. It essentially depends on the signs and values of the constant interaction of the components, which leads to a greater variety of possible scenarios for the development of modulation instability. The paper considers two cases. The first case is when repulsive forces act inside the components, and the second is when repulsive forces act in the first component, and in the second one - attractive forces. At the same time, the situation when there is a repulsion in the first component, and attraction between the particles in the second component differs significantly from the case of only positive interaction inside the components. The relations between the interaction constants that determine the development of the modulation instability turn out to be different. Given the relations between the interaction constants, taking into account dissipation processes, the occurrence of modulation instability in two-component Bose-Einstein condensates was studied, the maximum growth rate of oscillations was found, and the limits of the existence of modulation instability in the space of wave numbers were found. It is shown that the small effect of dissipation on the modulation instability in the Bose – Einstein condensate is explained not only by the smallness of the friction forces. For wave vectors corresponding to a mode with a maximum increment, the contribution of dissipation in the linear approximation with respect to the dissipative parameter is strictly zero. Thus, the condition for the development of the most rapidly growing mode of oscillations, which determines the beginning of the modulation instability, remains the same as in the nondissipative case.</p> Anatoly Ivashin Elena Marinenko ##submission.copyrightStatement## 2019-03-15 2019-03-15 1 65 74 10.26565/2312-4334-2019-1-06 Surface-Kinetics-Limited Ostwald Ripening of Spherical Precipitates at Grain Boundaries https://periodicals.karazin.ua/eejp/article/view/12402 <p>Ostwald ripening of sufficiently large (usually macroscopic) precipitates is the late stage of the diffusion decomposition of a supersaturated solid solution, occurring through the formation of fluctuations and subsequent growth of centers (nuclei) of a new phase. The paper describes a theoretical study of the Ostwald ripening of spherical precipitates of a newly formed phase at the grain boundary of finite thickness with the diffusion of impurity atoms from the grain interior to the grain boundary considered. The precipitate growth is assumed to be limited by the kinetics of impurity atom imbedding into the precipitate rather than by the impurity atom diffusion inside the grain boundary. The speed of diffusion growth of spherical precipitate located on the grain boundary is found. A system of equations which describes surface-kinetics-limited growth of Oswald ripening of spherical precipitates on the grain boundary is formulated. This system consists of the equation of growth rate of the precipitate, the kinetic equation for the precipitates size distribution function which is normalized by the precipitates density, and the equation of the balance of matter in the system (the law of conservation of matter). The law of conservation of matter takes into account the atoms of impurities which are in solid solutions of the grain boundary and the body of the grain as well as in the precipitates which is the specifics of our problem. The asymptotic time dependences are found for the average and critical precipitate radius, supersaturation of solid solution of impurity atoms in the grain boundary, precipitate size distribution function, precipitate density, and for the factor of grain boundary filling with precipitates (the area covered by the precipitates per unit area of the grain boundary) and the total number of impurity atoms in precipitates. The factor of grain boundary filling with precipitates is a characteristic of the two-dimensional Ostwald ripening problem. A discussion of the limits of validity of obtained results is given.</p> Oleksandr Koropov Roman Skorokhod ##submission.copyrightStatement## 2019-03-15 2019-03-15 1 75 85 10.26565/2312-4334-2019-1-07 O.I. Akhiezer Institute of Theoretical Physics https://periodicals.karazin.ua/eejp/article/view/12399 <p>Professor A.I. Akhiezer is an outstanding Soviet theoretical physicist who made an outstanding contribution to the development of science. He is one of the most active in the field of theoretical physics of Soviet scientists. He has done about a hundred papers on various problems of nuclear physics, quantum electrodynamics, and the theory of charged particle accelerators. A number of difficult and ingenious studies, which gave fundamental results, made a significant contribution to the development of these problems and made his name known and authoritative among scientists of the Soviet Union and abroad. Professor A.I. Akhiezer is one of the best Soviet theoretical physicists working in the field of atomic nucleus physics and quantum electrodynamics. He is the author of first-class works on the scattering of γ-quanta by nuclei, on the diffraction scattering of nuclear particles. He established the possibility of a new phenomenon — diffraction splitting of deuterons by nuclei. AI Akhiezer is the author of the pioneering work on the scattering of neutrons in crystals, which have become particularly important in connection with the question of the moderation of neutrons. Of great importance was his first work to determine the critical dimensions of the reactor, taking into account the slowing down of neutrons. Of particular note are the works of Professor A.I. Akhiezer and his school on the theory of linear accelerators of charged particles and the theory of plasma.</p> Alla Tanshyna ##submission.copyrightStatement## 2019-03-14 2019-03-14 1 86 91 10.26565/2312-4334-2019-1-08