East European Journal of Physics

5-17

Authors: Mykola P. Odeychuk, Victor I. Tkachenko, Leonid A. Bulavin, Boris V. Borts, Stella I. Skoromnaya

A model is proposed for describing the shape change of isotropic and anisotropic graphite under the influence of high temperatures and high neutron radiation fluences. The model is based on a new approach, which uses the following provisions: description of the near-pore neighborhood in graphite as a solid solution using the theory of phase transformations of the first kind; consideration of a new phase as a spheroidal pore of small eccentricity, flattened along the direction of greatest stress; taking into account the clustering of carbon atoms at fluences of more than . The graphite non-isotropy is characterized by different pore sizes, different diffusion coefficients, the lengths of the paths of graphite atoms along and across volume of the sample, which in turn depend on the temperature of the sample. It is proposed that the initial element on the basis of which a new phase will be formed is the spheroidal pore of small eccentricity, flattened along the direction of the highest tension. A kinetic equation that describes the diffusion of pores under the influence of high temperatures and intense neutron fluxes is obtained. Initially, the pores are in a field of predetermined stresses oriented along and across the sample. The contribution of diffusion processes is due to the term proportional to the pore distribution function in the sample, and the effect of the neutron flux is described by an additional term in the kinetic equation. The obtained kinetic equation for anisotropic graphite can be transformed for isotropic graphite. For isotropic and anisotropic graphite, model solutions have been obtained that characterize the change in its volume with time under the influence of a neutron flux and high temperature. It is shown that the magnitude of the change in the relative volume of reactor graphite for isotropic graphite exceeds a similar value for anisotropic graphite. Theoretical confirmation of the laws governing the swelling of anisotropic graphites under the influence of large neutron fluences and in the high-temperature field, previously obtained by other authors, is obtained: longitudinal compression of anisotropic graphite samples corresponds to a change in the linear dimensions of isotropic graphites; the transverse compression of anisotropic graphite samples is less than the change in the longitudinal linear dimensions of isotropic graphites.

34-40

Authors: Ivan V. Gushchin, Volodymyr M. Kuklin, Eugen V. Poklonskiy

The paper presents the results of the study of the models of convective instability near its threshold of thin layers of liquid and gas bounded by poorly conducting walls. These models single out one spatial scale of interaction, leaving the possibility for the evolution of the system to choose the symmetry character. This is due to the fact that the conditions for the realization of the modes of convective instability near the threshold are chosen. All spatial perturbations of the same spatial scale, but of different orientations, interact with each other. It turned out that the presence of minima of the interaction potential of the Proctor-Sivashinsky equation modes, the absolute value of the wave number vectors of which is unchanged, determines the choice of symmetry and, accordingly, the characteristics of the spatial structure. In the case of a more realistic model of convection described by the Proctor-Sivashinsky equation, it was possible to observe both the first-order phase transition and the second-order phase transition and detect the form of the state function, which is responsible for the topology of the resulting convective structures: metastable rolls and stable square cells. In this paper, it is shown that the nature of the structural-phase transition in a liquid when taking into account the dependence of viscosity on temperature in the Proctor-Sivashinsky model is similar to the case of the absence of such a dependence. The transition time turns out to be the same, despite the fact that a different structure is formed - hexagonal convective cells. As in the Swift-Hohenberg model, a hard mode for the formation of hexagonal cells in a gas medium is possible only for a sufficiently noticeable dependence of its viscosity on temperature. The phase transition times are inversely proportional to the difference in the values of this function for two consecutive states. A similar description of phase transitions did not use phenomenological approaches and various speculative considerations, which allows for a closer look at the nature of transients.

47-57

Authors: Khanna M. Kapil, Murei K. Gilbert

Raman Effect is the measurement of the intensity and wavelength of the inelastically scattered radiation that falls on a molecule. The electric field of the incident radiation polarizes the molecule on which it falls and this leads to the creation of an oscillating dipole. The incident polarized laser light is inelastically scattered by the molecular sample. The scattered light contains modified wavelengths called the Stokes and anti-Stokes lines or wavelengths. The oscillating electric dipole, created by the incident radiation, creates an oscillating electric field around it. Since the oscillating electric field of the incident radiation creates an oscillating electric dipole that create an oscillating electric field around it, it was surmised that this oscillating electric field can affect the frequency of vibration or oscillation of the oscillating electric dipole that produces it. This novel effect will change the frequency (frequencies) of the scattered radiation resulting in Stokes and anti-Stokes lines with modified frequencies. This theoretical research and its importance can be understood like this. For instance, if there are two cells or molecules, side by side, in which one is a healthy cell and the other is cancerous, or two different types of molecules are sitting side by side, this types of scattering should be able to distinguish one from the other since the Stokes and anti-Stokes lines from the two molecules will not be identical. Thus, the incident radiation of angular frequency

70-76

Authors: Viktory A. Lototskaya, Leonid F. Yakovenko, Evgeniy N. Aleksenko, Nikolay I. Velichko, Yuriy S. Doronin, Anna A. Tkachenko, Ivan P. Zaritskiy, Vyacheslav V. Abraimov, Wen Zhu Shao

The mechanical properties (limit of forced elasticity, fracture stress, total deformation to failure and its components) of a 75 m-thick polyimide film of kapton H type under uniaxial tension conditions at 293 K after exposure to the outer space factors were studied. The electromagnetic radiation of the transatmospheric Sun in the wavelength range of 250-2500 nm (EMRS) for 100 hours and vacuum ultraviolet (VUV) and ultra soft x-ray (USX) radiation in the range of 1.24-170 nm – for 100 and 500 hours were simulated under laboratory conditions. The effect of separate exposure in each of the wavelength ranges was investigated. It was found that after irradiation in the both wavelength ranges the films remained in a forced-elastic state. The tension diagrams, like in the initial state, have two stages. The contributions of the elastic, irreversible and highly elastic (delayed and reversible at test temperature) components to the total deformation to failure were determined. It was found that the limit of forced elasticity increased after irradiation both with EMRS, and with VUV and USX radiation. In this case an increase in the limit of the forced elasticity under the influence of EMRS was caused by heating of the film in the course of irradiation, and under the influence of VUV and USX radiation – by radiation effects. The fracture stress and total deformation to failure change weakly and only under the influence of VUV and USX radiation. With changing the duration of exposure to VUV and USX radiation (100 or 500 hours), the fracture stress and the total deformation to failure change non-monotonously. The negative consequence of exposure to VUV and USX radiation is the contribution values redistribution of the individual components of the total deformation to failure. VUV and USX radiation within 500 hours leads to a halving of the contribution of elastic deformation, which is reversible at deformation temperature.

82-90

Authors: Еvgen A. Barannik, Viktor I. Pupchenko, Anatoliy I. Marusenko, Olexiy V. Knyazyev, Igor M. Tsybin, Aleksandr E. Berkovich

In this work the spatial resolution and measurement accuracy of the ultrasound diagnostic system at acoustic remote palpation (ARP) using high-intensity focusing ultrasound (HIFU) are studied theoretically and experimentally. A physical model is proposed, which describes the specific features of ARP taking into account the remote nature of ultrasound Doppler probing of the soft tissues local movements, which are caused by the radiation pressure of HIFU pulse. Taking into account the accepted simplifying assumptions it is shown that the model conclusions are in a good agreement with the results of the experiments on measuring the value of displacements under the influence of HIFU. In particular, the nontrivial dependence of the value of displacements, measured by the Doppler method, on the probing depth and focusing degree of the incident and scattered wave beams, is proved. An experimental study was performed on the transverse resolution at ARP in the case of probing of the medium with Young's modulus irregularity, as well as on the influence of noise and interference on the measurement accuracy and resolution. It is concluded, that the transverse resolution at ARP is determined by the parameters of the local area of the movement, and can be significantly higher than the transverse intrinsic resolution of the ultrasound system at B-mode of diagnostics. The obtained results indicate that ARP is a promising method for monitoring the process of the soft tissues thermal ablation, when HIFU is used.

95-100

Authors: Алла Таньшина

"If I were offered to declare the names of only two physicists who were most famous in Ukrainian science, I would call the theorist L.D. Landau and experimenter L.V. Shubnikov" Academician of NAS of Ukraine OI Akhiezer

4-9

Authors: Igor M. Pankratov, Volodymyr Yu. Bochko

The secondary runaway electrons generation is the process in which already existing high energy runaway electrons knock out thermal plasma electrons directly into the runaway region by close Coulomb collisions. Such knocked-on electrons are immediately accelerated to ultrarelativistic velocities, since in the runaway region the toroidal electric field force overcomes the collisional friction force with thermal plasma particles. The avalanche of runaway electrons with mega-electron-volt energy emerges, hit of which with the construction elements of large-scale tokamaks and future international tokamak ITER can lead to catastrophic consequences. Due to its importance, this phenomenon is being actively studied both theoretically and experimentally in leading thermonuclear fusion centers. It is known that during secondary generation, the value of the transversal component of knocked-on electrons momentum with respect to the confining magnetic field may be significantly higher than the longitudinal one: p⊥ >> p∥. Thus, conditions for knocked-on electron trapping in a non-uniform tokamak magnetic field occur (banana orbits). Such electrons can no longer be accelerated by the inducted toroidal electric field to high energies, avalanche formation is partially suppressed. The question is how long this population of knocked-on and trapped electrons exists. In the presented paper, it is shown the additional possibility of formation and existence of such long-lived banana orbits of suprathermal electrons under conditions of plasma MHD activity when MHD instability spikes induced the strong burst of the toroidal electric field that results in the abrupt growth in these knocked-on and trapped electrons. This phenomenon is considered for the recent low-density EAST (Institute of Plasma Physics, Chinese Academy of Sciences, Hefei, China) tokamak quasistationary runaway discharges. Long-lived trapped electrons (p⊥ >> p∥) also have an influence on the intensity of ECE emission. The considered phenomenon is important for correct interpretation of the runaway experiments on present-day tokamaks.

21-28

Authors: Volodymyr Yu. Shablenko

A set of fixed points in N-point gravitational lenses is studied in the paper. We use complex form of lens mapping to study fixed points. There are some merits of using a complex form over coordinate. In coordinate form gravitational lens is described by a system of two equations and in complex form is described by one equation. We transform complex equation of N-point gravitational lens into polynomial equation. It is convenient to study polynomial equation. Lens mapping presented as a linear combination of two mappings: complex analytical and identity. Analytical mapping is specified by deflection function. Fixed points are roots of deflection function. We show, that all fixed points of lens mapping appertain to the minimal convex polygon. Vertices of the polygon are points into which dimensionless point masses are. Method of construction of fixed points in N-point gravitational lens is shown. There are no fixed points in 1-point gravitational lens. We study properties of fixed points and their relation to the center of mass of the system. We obtained dependence of distribution of fixed points on center of mass. We analyzed different possibilities of distribution in N-point gravitational lens. Some cases, when fixed points merge with the center of mass are shown. We show a linear dependence of fixed point on center of mass in 2-point gravitational lens and we have built a model of this dependence. We obtained dependence of fixed point to center of mass in 3-point lens in case when masses form a triangle or line. In case of triangle, there are examples when fixed points merges. We study conditions, when there are no one-valued dependence of distribution of fixed points in case of 3-points gravitational lens and more complicated lens.

38-45

Authors: Victor M. Grytsyna, Dmitry G. Malykhin, Tetiana S. Yurkova, Kostiantyn V. Kovtun, Tetiana P. Chernyayeva, Gennadiy P. Kovtun, Iryna G. Tantsura, Victor M. Voyevodin

Using X-ray structural analysis, features of changes in characteristics of crystallographic texture during cold working of Zr-2.5%Nb alloy plates by longitudinal and cross rolling has been investigated. To make original plates, longitudinal fragments and rings of 15.01.5 mm² tube annealed at 580 °C were used. The plates were rolled at room temperature to the degrees in the range from 6 to 56% with 5…7% per pass and the rate of 5...10s-1. Using the method of inverse pole figures with measuring by the Bragg-Brentano optical scheme, densities of reflections along normal to plane of the plates (pole densities) was determined. Based on this, distributions of orientations of c-axes of hcp lattice of the material have been analyzed. Local features of the distributions, which were attributed to signs of twinning effects in texture changes in the alloy, are revealed. At subsequent analysis, an effect of strain non-uniformity associ-ated with prehistory of the plates was taken into account. It is established that the second stage of (moderate) changes in Kearns textural coefficient of the plates with the deformation degrees differs from the initial stage of accelerated changes by activation of compression twins. By the method of tilt scanning (of rocking curves) around the Bragg-Brentano position at registration of (0004) reflection intensi-ties, changes in orientation distributions of c-axes in longitudinal and cross section of the plates for both parties were investigated. It is noted that the main textural changes in process of deformation of the plates occur in the cross-sectional plane of the original tube and are most expressed on the cross-rolling plates. The doublet in the distributions of c axes, characteristic for rolling texture of hcp metals of titanium subgroup, was noted just at the second stage of the texture changes in the material. Its directionality is mainly associated with the plane of cross-section of the original tube. A connection is revealed between features of the pole density distributions and expression degree of the textural doublet on the rocking curves. According to the results obtained and analysis of other publications, twinning na-ture of the textural doublet was confirmed and a schematic sequence of its formation was proposed with participation of compression twins of {11 2} 23 system and tensile twins of {10 2} 011 and {11 1} 26 systems.

54-62

Authors: Gennadiy M. Onyshchenko, Volodymyr D. Ryzhikov, Ivan I. Yakymenko, Valery D. Khodusov, Sergei V. Naydenov, Alexandr D. Opolonin, Sergei V. Makhota

The contributions of gamma rays from the inelastic scattering reaction and the resonant reaction in the process of slowing down fast neutrons inside the oxide detector volume are investigated. For this the countable efficiency of the ZnWO4, CdWO4, Bi4Ge3O12 oxide scintillators in terms of pulses/neutron during the registration of the fast neutrons from a 239Pu-Be source was measured. It is assumed that the response of detectors during neutron moderation in oxide scintillators with an effective thickness of about 40—50 mm is formed by instantaneous gamma rays from inelastic, resonant inelastic scattering reactions, as well as delayed gamma rays from the capture reaction of resonance neutrons. The parameters of the nuclei, which determine the detector response — the density of the nuclear levels of the compound nuclei being formed, the widths of the resonance regions, the lifetimes of the excited nucleus state were considered. It was found that the registration of a cascade of gamma rays from the discharge of excited levels leads to a significant increase in the countable efficiency of the detector and, as a consequence, an increase in the sensitivity of the detector to fast neutrons. The measured response in terms of pulses/neutron for the ZWO detector — 64, for CWO — 36, for BGO — 2.5. The response of the detectors was recorded by the broadband tract with a time feedback of  0.7 ns. The measured values of the efficiency are explained by the fact that, in our case, the reaction of inelastic scattering is the starting process, which starts the process of discharging nuclear long-lived ( 1–1000 ns) states excited in both inelastic scattering and in resonance capture reaction. The registration of the gamma-quanta from discharge leads to an increase the countable efficiency of the detector. The observed increase of the countable efficiency of the secondary gamma quanta is realized when neutrons are moderated inside the oxide detectors with a thickness of 40—50 mm or more. The measurement error of the registration efficiency was about 7%.

71-80

Authors: Thomas O. Daniel, Uno Ye. Uno, Kasim U. Isah, Umaru Ahmadu

The study aimed at the investigation and application of SnS thin film semiconductor as a channel layer semiconductor in the assembly of an electric double layer field effect transistor which is important for the achievement and development of novel device concepts, applications and tuning of physical properties of materials since the reported EDLFET and the modulation of electronic states have so far been realised on oxides, nitrides, carbon nanotubes and organic semiconductor but has been rarely reported for the chalcogenides. Honey was used as a gel like electrolytic gate dielectric to generate an enhanced electric field response over SnS semiconductor channel layer and due to its ability to produces high on-current and low voltage operation while forming an ionic gel-like solution similar to ionic gels which consist of ionic liguids. SnS gated honey Electric double layer field effect transistor was assembled using tin sulphide (SnS) thin film as semiconductor channel layer and honey as gate dielectric. The measured gate capacitance of honey using LCR meter was measured as 2.15 μF/ cm2 while the dielectric constant is 20.50. The semiconductor layer was deposited using Aerosol assisted chemical vapour deposition and annealed in open air at 250℃ on an etched region about the middle of a 4×4 mm FTO glass substrate with the source and drain electrode region defined by the etching and masking at the two ends of the substrate. Iridium was used as the gate electrode while a copper wire was masked to the source and drain region to create electrode contact. The Profilometry, X-ray diffraction, Scanning electron microscope, Energy dispersive X-ray spectroscopy, Hall Effect measurement and digital multimeters were used to characterise the device. The SnS thin film was found to be polycrystalline consisting of Sn and S elements with define grains, an optical band of 1.42 eV and of 0.4 μm thickness. The transistor operated with a p type channel conductivity in a depletion mode with a field effect mobility of 16.67 cm2/Vs, cut-off voltage of 1.6 V, Drain saturation current of1.35μA, a transconductance of -809.61 nA/V and a sub threshold slope of -1.6 Vdec-1 which is comparable to standard specifications in Electronics Data sheets. Positive gate bias results in a shift in the cut off voltage due to charge trapping in the channel/dielectric interface.

5-10

Authors: Nataliia S. Goloskubova, Yuri V. Mikhlin

Nonlinear traveling waves of the Klein-Gordon equation with cubic nonlinearity are considered. These waves are described by the nonlinear ordinary differential equation of the second order having the energy integral. Linearized equation for variation obtained for such waves is transformed to the ordinary one using separation of variables. Then so-called algebraization by Ince is used. Namely, a new independent variable associated with the solution under consideration is introduced to the equation in variations. Integral of energy for the stationary waves is used in this transformation. An advantage of this approach is that an analysis of the stability problem does no need to use the specific form of the solution under consideration. As a result of the algebraization, the equation in variations with variable in time coefficients is transformed to equation with singular points. Indices of the singularities are found. Necessary conditions of the waves stability are obtained. Solutions of the variational equation, corresponding to boundaries of the stability/instability regions in the system parameter space, are constructed in power series by the new independent variable. Infinite recurrent systems of linear homogeneous algebraic equations to determine coefficients of the series can be written. Non-trivial solutions of these systems can be obtained if their determinants are equal to zero. These determinants are calculated up to the fifth order inclusively, then relations connecting the system parameters and corresponding to boundaries of the stability/ instability regions in the system parameter place are obtained. Namely, the relation between parameters of anharmonicity and energy of the waves are constructed. Analytical results are illustrated by numerical simulation by using the Runge-Kutta procedure for some chosen parameters of the system. A correspondence of the numerical and analytical results is observed.

19-26

Authors: Olga Zhytniakivska, Uliana Tarabara, Kateryna Vus, Valeriya Trusova, Galyna Gorbenko, N. Gadjev, Todor Deligeorgiev

The applicability of the novel cationic phosphonium dye TDV1 to monitor the complexation between DNA and pathologically aggregated proteins, amyloid fibrils, was tested using the optical spectroscopy and molecular docking techniques. TDV1 has been found to be highly emissive in buffer solution and is characterized by one well-defined fluorescence peak attributed to the dye monomers. The association of the dye with the double stranded DNA was followed by the enhancement of monomer fluorescence coupled with a bathochromic shift of the emission maximum. The addition of fibrillar lysozyme (LzF) to TDV1-DNA mixture led to the further enhancement of fluorescence intensity of the monomeric dye form coupled with a hypsochromic shift of the emission maximum and an appearance of a second long-wavelength peak. An assumption has been made that the fluorescence enhancement augmenting with increasing the protein concentration in the TDV1/DNA system is produced by the interaction of the free TDV1 monomers with lysozyme fibrils as well as by the LzF-induced conformational alterations of DNA. The long-wavelength peak emerging in the presence of LzF is presumably a consequence of the J-aggregate formation upon the TDV1 association with lysozyme fibrils. The molecular docking studies showed that TDV1 monomers are incorporated into the fibril grooves associating with 7 β-strands in such a way that the dye long axis is parallel to the fibril axis. The most energetically favorable position of TDV1 is the S60-W62/G54-L56 groove in the lysozyme fibril core. In contrast, the TDV1 dimers seem to associate with the more hydrophilic side of the model β-sheet. Cumulatively, the results from the absorption and fluorescence measurements, together with the molecular docking analysis are consistent with the minor groove mode of the TDV1 binding to dsDNA. The electrostatic interactions seem to play a predominant role in the TDV1 complexation with the double stranded DNA, while the hydrophobic interactions and steric hindrances are supposed to be influential in the association of TDV1 with fibrillar lysozyme.

33-38

Authors: Mykhailo M. Solovan, Taras T. Kovaliuk, Pavlo D. Maryanchuk

The paper presents the results of studies of the effect of silicon surface treatment on the electrical and photoelectric properties of nanostructured MoOx/n-Si heterojunctions. The nanostructured heterojunctions MoOx/n-Si, were prepared by deposition of thin films of molybdenum oxide (n-type conductivity) by reactive magnetron sputtering in the universal vacuum system Leybold Heraeus L560 on the nanostructured silicon substrates (n-type conductivity), which were made by chemical etching with the assistance of silver nanoparticles. Dark and light volt-ampere (I – V) characteristics of the heterojunctions under study were measured, the value of the potential barrier height, the values of the serial Rs and the shunt Rsh resistance at room temperature were determined. It was established that the silicon surface treatment does not affect the potential barrier height, but significantly affects the values of serial Rs and shunt Rsh resistance. The electrical and photoelectric properties of the obtained structures were investigated, the dominant mechanisms of current transfer through the heterostructures under forward bias are well described in the framework of emission-recombination and tunneling models with the presence of interface states. The main mechanism for the charge carrier transport through heterojunctions with the reverse bias is the Frenkel–Pool emission. Investigation of photoelectric properties of heterojunctions MoOx/n-Si was carried out at illumination by white light with intensity Popt = 80 mW/сm2. It was established that the heterostructure No.5 MoOx/n-Si with grown nanowires and etched silver nanoparticles has a maximum open-circuit voltage Voc = 0.17 V, short-circuit current density Isc = 10 mA/cm2. The possibilities of using the obtained heterostructures as photodiodes were analyzed.

46-51

Authors: Natalia Yu. Filonenko, Alexander I. Babachenko, Ganna A. Kononenko

In the paper we obtained the expression of cementite free energy and determined the solubility of manganese and silicon in Fe3C cementite depending on the temperature. Investigation was carried out for alloys with carbon content of 0.55-0.60 % (wt.), silicon content of 0.95-1.0 % (wt.), manganese content of 0.8-0.9% (wt.), the rest was iron. The smelting of Fe-Mn-Si-C system alloys was carried out in the alundum crucible furnace in argon atmosphere. The cooling rate of alloys after casting was 10 K/s. Microstructure analysis along with X-ray diffraction analysis was used to determine the structural state of the alloys. In addition, the physical characteristics of the alloys studied in this paper were determined, such as alloy chemical dependence of ultimate strength, extension and contraction ratio, impact toughness and hardness. The results obtained in this paper showed that the iron-based alloy with the content of carbon of 0.57 % (wt.), silicon of 0.97 % (wt.) and manganese of 0.85 % (wt.)) had the superior microstructure and physical properties. The microstructure of alloys studied in the paper is represented by pearlite, which makes up to 95 % of the volume. In the alloys we revealed the highly dispersed inclusions of Fe2.7Mn0.3C, Fe0.25Mn1.4C0.6 and Fe9SiC0.4 carbides, whose volume ratio was up to 1.5 %, the rest was ferrite. As it is known, the structural constituent of pearlite is cementite. The cementite has a significant effect on the physical properties of alloys. Application of quasi-chemical method enables to calculate the free energy of silicon and manganese doped with cementite and to determine the temperature dependence of silicon and manganese content in cementite. It is ascertained that there is a slight increase of carbon content in cementite (up to 28.79 % (atoms). Manganese can replace up to 12 % of iron atoms, and silicon can replace up to 4.5 % of iron atoms, depending on temperature. The calculated data obtained in this paper are in good agreement with those found experimentally by other authors.

58-63

Authors: Viktoriia V. Lisovska, Tetiana V. Malykhina, Valentina O. Shpagina, Ruslan M. Timchenko

The proposed work demonstrates the results of creating and investigating the mathematical model of the source of fast neutrons. Computer modeling of the energy spectrum of fast neutrons was carried out for 239PuBe neutron source. The model of the source of fast neutrons has been developed. Neutrons in this model have an energy spectrum from 100 keV to 11 MeV with 100 keV step. Simulation is performed by the Monte-Carlo method. The model carrier is a computer program developed in the C++ programming language in the Linux operating system environment, using the Geant4 toolkit. All necessary classes describing low-energy models were used for the simulation of the passage of neutrons through materials of detectors. Those take into account the elastic scattering, inelastic scattering, radiative capture and fission. We consider these processes because models of processes implemented in our software will be also used for other problems of neutrons transport, for example, for passing neutrons through various substances, and for conducting virtual laboratory works. The PhysicsList class of our program contains classes G4NeutronHPElastic, G4NeutronHPElasticData, G4NeutronHPInelastic, G4NeutronHPInelasticData, G4NeutronHPCapture, G4NeutronHPCaptureData, etc. based on the NeutronHP model for neutron interactions at low energy, as well as the neutron data library G4NDL4.5. Diagrams containing energy spectra of a source of fast neutrons modeled in two ways are presented in the paper. The analysis of the obtained energy spectra is carried out. Virtual nuclear physics experiments are carried out with the aim of testing the elaborated neutron-matter interaction model. The processes occurring in scintillator substances during the passage of fast neutrons through them, have been studied. 109 neutrons were used as primary particles emitted isotropically, and we used our simulation results of 239PuBe neutron source to describe the initial energy spectrum. The created model of 239PuBe neutron source can be used for the investigation of scintillation detectors Bi4Ge3O12, CdWO4, Gd2SiO5 and others, as well as studying their characteristics. Processes in heavy oxide scintillators substance during the registration of fast neutrons can be studied using the developed model. It is shown that for registration of the flow of neutrons from 239PuBe neutron source, using Bi4Ge3O12 or CdWO4 scintillators is more preferable. Results of the virtual nuclear physical experiments satisfy the published experimental data.

69-74

Authors: Vasyl I. Maslov, Denys S. Bondar, Iryna P. Levchuk, Sofiia A. Nikonova, Ivan M. Onishchenko

Plasma-based accelerators sustain accelerating gradients which are several orders greater than obtained in conventional accelerators. Focusing of electron and positron beams by wakefield, excited in plasma, in electron-positron collider is very important. The focusing mechanism in the plasma, in which all electron bunches of a sequence are focused identically, has been proposed by authors earlier. The mechanism of focusing of a sequence of relativistic positron bunches in plasma, in which all positron bunches of sequence are focused identically and uniformly, has been investigated in this paper by numerical simulation by 2.5D code LCODE. Mechanism of this identical and uniform focusing involves the use of wave-length λ, which coinciding with double longitudinal dimension of bunches λ=2b, the first bunch current is in two times smaller than the current of the following bunches of sequence and the distance between bunches equals to one and a half of wavelength 1.5λ. We numerically simulate the self-consistent radial dynamics of lengthy positron bunches in homogeneous plasma. In simulation we use the hydrodynamic description of plasma. In other words the plasma is considered to be cold electron liquid, and positron bunches are aggregate of macroparticles. Positron bunches are considered to be homogeneous cylinders in the longitudinal direction. Positrons in bunches are distributed in radial direction according to Gaussian distribution. It is shown that in this case only first bunch is in the finite longitudinal electrical wakefield Ez0. Other bunches are in zero longitudinal electrical wakefield Ez=0. Between bunches of this sequence longitudinal electrical wakefield and radial force are not zero Ez0, Fr0. The focusing radial force in regions, occupied by bunches, is constant along each bunch Fr=const. Between bunches the radial force is inhomogeneous Frconst. All positron bunches of sequence are focused identically and uniformly.

113-116

Authors: Alla Tanshina

Development Strategy of the Institute of Theoretical Physics Akhiezer (hereinafter - ITF) has also passed the test of time: the institute has managed to keep up-to-date scientific directions and the continuity of the leading scientific schools of the UFTI - KIPT. Of course, there were problems. But a serious international ITF rating helped him to resist in the difficult post-Soviet era, and in modern times. The focus of today's ITF is the development of current and advanced frontiers of modern physical science. But most importantly, all the research departments of the ITF have in their staff talented (and very initiative) young scientists, despite the fact that the past years have not very much favored the influx of young people into science. Moreover, their creative achievements were marked by scientific awards of both domestic and international level. The truth that is professed in the ITF: the main thing is not only to accumulate knowledge and experience, but also to pass them on to a worthy change. The fact that the relations in the team are humanly built friendly and democratically helps very well. And it is already obvious: the ITF has withstood the competition in the post-Soviet space and has accumulated a solid scientific potential. Today, the scientific ideology of the ITF is its traditions.

4-33

Authors: Michael Kopp, Anatoly Tur, Volodymyr Yanovsky

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 the vertical temperature gradient and the constant magnetic field. The Rayleigh-Benard problem for stationary convection in 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 subject to the profile of the inhomogeneous rotation (Rossby number ) is obtained. It is shown that the negative values of the Rossby number have a destabilizing effect, since the critical Rayleigh number becomes smaller, than in the case of the uniform rotation , or of the rotation with positive Rossby numbers . To describe the nonlinear convective phenomena the local Cartesian coordinate system was used, where the inhomogeneous rotation of the fluid layer was represented as the rotation with a constant angular velocity and azimuthal shear 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 a nonlinear Ginzburg-Landau equation was obtaned. This equation describes the evolution of 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.

40-45

Authors: Taras Horbatiuk, Volodymyr Kotlyar, Mykola Maslov, Anton Safronov

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 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 GeV/c. The CSs calculated at the leading order (LO) with Pythia 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 N2LO 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 N2LO, 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.

55-64

Authors: Yuriy Grigoriev, Andriy Zelinskiy, Tetiana Malykhina, Valentina Shpagina

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.

75-85

Authors: Oleksandr Koropov, Roman Skorokhod

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.