Кафедра фізико-математичних наук

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The 2nd Scientific workshop for students "Computational Physics of DNA"
(2024) Perepelytsya, Sergiy; Tetiana, Bubon
The article is devoted to the 2nd Scientific workshop for students “Computational physics of DNA”.
Analytical approach for calculating the chemotaxis sensitivity function
(2017) Vasilev, Aleksey
We consider the chemotaxis problem for a one-dimensional system. To analyze the interaction of bacteria and an attractant, we use a modified Keller-Segel model, which accounts for the attractant absorption. To describe the system, we use the chemotaxis sensitivity function, which characterizes the nonuniformity of the bacteria distribution. In particular, we investigate how the chemotaxis sensitivity function depends on the concentration of an attractant at the boundary of the system. It is known that, in the system without absorption, the chemotaxis sensitivity function has a bell shape maximum. Here, we show that the attractant absorption and special boundary conditions for bacteria can cause the appearance of an additional maximum in the chemotaxis sensitivity function. The value of this maximum is determined by the intensity of absorption.
The charge 2 monopole via the ADHMN construction
(2021) Braden, Harry W.; Enolski, Victor
This paper describes the exact solution of the gauge and Higgs fields for charge two su(2) Euclidean monopoles. Despite BPS monopoles having been studied for over 35 years, and having uncovered extraordinarily beautiful structures, such analytic reconstruction has (with the exception of some partial results that will later be recalled) proved too hard. We often know more about the moduli space of these solutions than we do the actual fields. This is particularly true in the charge two setting: the Atiyah-Hitchin manifold, the moduli space of the centred charge two monopoles, is a well-studied and rich object and yet the analytic solution of the fields has proved elusive. Recently a general program for reconstructing the gauge theory data for su(2) Euclidean monopoles of general charge has been given, circumventing a number of previously intractable steps. This lowest charge case is a useful testing ground and will produce a number of new results. (The spherically symmetric case for charge one and coincident charge n monopoles is amenable to other approaches.) We will compare our results with some of the numerical studies that have been undertaken. Although constructing exact solutions – be they of gravity or gauge theory – is often viewed as a rather recondite area of research analytic solutions give at the very least some control over numerical results.
Comprehensive investigation of Er2O3 thin films grown with different ALD approaches
(2022) Khomenkova, Larysa; Merabet, H.; Chauvat, M.-P.; Frilay, C.; Portier, Xavier; Labbe, C.; Marie, P.; Cardin, J.; Boudin, S.; Rueff, J.-M.; Gourbilleau, F.
The effect of Er precursor nature (Er(CpMe)3 or Er(tmhd)3) and annealing treatment at 500–1100 ◦C on the structural and optical properties of Er2O3 films grown on Si substrates by thermal or O2-plasma-assisted atomic layer deposition was studied by means of spectroscopic ellipsometry, Fourier-transform infrared spectroscopy, Xray diffraction, transmission electron microscopy coupled with energy dispersive X-ray spectroscopy as well as photoluminescence method. An annealing at 500–800 ◦C resulted in the film crystallization mainly. Thermal treatment at high temperatures caused the formation of Er silicate phase due to the diffusion of Si atoms from the substrate in the films depth. This phase was found to be Er2SiO5 being crystallized at 1100 ◦C. Light emitting properties of the films are determined by Er2O3 native defects (like oxygen vacancies) and intra-4f shell transition in Er3+ ions. The latter dominated in the films annealed at 1000–1100 ◦C. The most intense Er3+ emission, observed in the films grown with O2-plasma-assisted approach, was explained by a lower contribution of oxygen vacancies as well as by pronounced crystallization of Er silicate phase. In this latter, the effect of concentration quenching of Er3+ luminescence was lower due to a larger distance between Er3+ neighbor ions.
Conformational flexibility of spermidine3+ interacting with DNA double helix
(2023) Perepelytsya, Sergiy; Vasiliu, Tudor; Laaksonen, Aatto; Engelbrecht, Leon De Villiers; Brancato, Giuseppe; Mocci, Francesca
Natural polyamines play a key role in many biological processes, particularly in the stabilization of DNA double helix structure in the cell nucleus. Among others, the conformational flexibility of polyamines, such as spermidine, is an essential property for the formation of complexes with DNA. Yet, the characterization of the conformational space of polyamines has not been fully elucidated. Using atomistic molecular dynamics (MD) simulations, we present a detailed study of the conformational space of spermidine3+ both in solution and in interaction with DNA. We have identified more than 2000 distinct conformations, which can be grouped into seven modes. Notably, the relative population of these modes is highly affected by the interaction of spermidine3+ with DNA, thus representing a fingerprint of complex formation. In particular, three of the seven dihedral angles of spermidine3+ are predominantly in trans conformation (with or without DNA), while the other four dihedral angles are observed to switch between trans, gauche+ and gauche-. The preference between the latter conformational states was analyzed in terms of the distinct energy contributions composing the potential energy. Overall, our results shed light on the conformational equilibrium and dynamics of spermidine3+, which in turn is important for understanding the nature of its interaction with DNA.
Corrigendum to "CO-PROX reactions on copper Y2O3-ZrO2 catalysts prepared by a single step co-precipitation technique" [Appl. Catal. B: Environ. 278 (1-12) (2020) 119258]
(2021) Marie, Olivier; Portier, Xavier; Korsunska, Nadiia; Khomenkova, Larysa
I, Dr Olivier MARIE, in the name of the whole authors regret that confusion arose regarding the sample synthesis. The 3 mol.% Y2O3-ZrO2 nano-powders doped with Cu that were used in present article were indeed synthesized at the Material Science Department of Donetsk Institute of Physics and Engineering named after O.O. Galkin of NAS of Ukraine (DonPhTI NAS of Ukraine). The quality Management System of Material Science Department of DonPhTI NAS of Ukraine complies with requirements of the international standard ISO 9001:2015. The department works in field of physical materials science, nanomaterials and nanotechnologies, including the development of the perspective technologies, structural modification of functional oxide materials and production of composite zirconia nanopowders and ceramic materials. The department is open for collaboration with all scientists who adhere to scientific ethics in their research. Dr, Oksana Gorban, from DonPhTI NAS of Ukraine would also like to provide correction regarding the sample synthesis procedure. The correct proportion of precursors is as follows: ‘Two distinct initial molar ratio were used ZrO(NO3)2:Y(NO3)3:Cu(NO3)2= 93:6:1 and 86:6:8 that were further dissolved in distilled water.’ Finally the acknowledgements were incomplete. The missing project number is reported hereafter. ‘This work was partly supported by the National Academy of Sciences of Ukraine(project III-4-16) as well as the Ministry of Education and Sciences of Ukraine(project 89452).’ The authors would like to apologise for any inconvenience caused.
Cu-Related Paramagnetic Centers in Cu- and (Cu,Y)-Doped ZrO2 Nanopowders
(2025) Nosenko, Valentyna; Vorona, Igor; Trachevskyi, Viacheslav; Zagorodniy, Yuriy; Okulov, Sergey; Isaieva, Oksana; Yukhymchuk, Volodymyr; Kulinich, Sergei; Borkovska, Lyudmyla; Khomenkova, Larysa
In this work, we studied Cu-doped and (Cu,Y)-codoped ZrO2 nanopowders produced through a coprecipitation approach to identify the nature of Cu-related bulk and surface paramagnetic centers. We conducted EPR, NMR, and Raman scattering studies on Cu- and (Cu,Y)-doped ZrO2 powders calcined at different temperatures. At low calcination temperatures (400 ◦C) and low Cu loading (0.1–1.0 mol.% of CuO), the EPR signal was found to be attributed to surface-related Cu-H2O complexes. For powders with higher Cu content (up to 8.0 mol.% of CuO), the superparamagnetic signal associated with the formation of copper clusters was observed. At higher calcination temperatures, the destruction of Cu-related surface complexes promotes the incorporation of Cu2+ ions into the bulk of ZrO2 nanocrystals at Zr positions. Co-doping ZrO2 with Cu and Y was observed to facilitate the incorporation of Cu2+ ions into cation sites at lower calcination temperatures when compared with Cu-doped ZrO2.
Derivative theta constants in singular half-periods
(2019) Bernatska, Julia
Abstract for Bogolyubov Kyiv Conference "Problems of Theoretical and Mathematical Physics", September 24-26, 2019, Kyiv, Ukraine.
Derivative Thomae formula for singular half-periods
(2019) Bernatska, Julia
Abstract for International scientific conference "Algebraic and Geometric Methods of Analysis", May 28 - June 3, 2019 Odesa, Ukraine.
Determination of groups all of whose proper subgroups have a commutator subgroup of order equal or less than p(p≥3) : corrigendum
(2008) Pylyavska, Olha
It is shown that the nonabelian p-groups all o f whose proper subgroups have a derived subgroup of order equal or less then p for p > 2 is either groups with commutator subgroup o f order p or groups, which are either 2-generated group from isoclinism families Ф3, Ф6. Ф8. Ф14 or 3-generated groups from isoclinism families Ф4, Ф11. The misprints and mistakes o f a previous paper are corrected.
Development and Characterization of Ceramic Inserts Used in Metallic Resonators of EPR Spectrometers to Increase Their Sensitivity
(2021) Lemishko, Serhii; Vorona, Igor; Golovina, Iryna; Yukhymchuk, Volodymyr; Okulov, Sergey; Nosenko, Valentyna; Solopan, Serhii; Belous, Anatolii
Cylindrical dielectric inserts for a standard EPR spectrometer with a metallic resonator have been developed on the basis of doped barium tetratitanate ceramics (BaTi4O9 + 8.5% ZnO) with the dielectric constant e = 36 and low dielectric losses (tan б ≈ 1.887 × 10−4) in a frequency interval of 9–10 GHz. It was found that the application of such dielectric inserts allows the EPR signal to be amplified owing to the redistribution of the microwave field in a standard rectangular TE102 resonator. The amplification is observed for both unsaturated samples and samples characterized by the saturation of the EPR signals. A gain factor of 9 was obtained for unsaturated test MnCl2 samples, and 1.5 for saturated test MgO : Mn ones.
Developmet of Ophthalmology in Ukraine and Latvia in the First Quarter of XX Centuty : parallels and intersections
(RTU Publishing House, 2008) Duplenko, Yurii; Kochubey, Nina
DNA condensation induced by Li+ counterions
(2024) Bubon, Tetiana; Piatnytskyi, Dmytro; Perepelytsya, Sergiy
Materials of the participants' report of Bogolyubov Kyiv Conference "Problems of Theoretical and Mathematical Physics", dedicated to the 115-th anniversary of the outstanding theoretician in physics and mathematics Mykola Bogolyubov
Dual-channel SPR biosensor for enhanced glioma relapse diagnostics: Blood cell aggregation as a biomarker for tumor malignancy
(2024) Samoylov, Anton; Khristosenko, Roman; Gridina, N.; Dorozinsky, Glib; Romanchuk, V.; Khomenkova, Larysa
Abstract. A biosensor based on the surface plasmon resonance (SPR) phenomenon has been developed for the express diagnosis of brain gliomas relapse by assessing blood cell aggregation indicators. The device features two optical channels, allowing for two studies to be performed simultaneously or enabling one channel to be used as a reference. This approach significantly increases biosensor sensitivity by reducing the impact of external factors. The optical excitation source is a p-polarized semiconductor laser with a 650 nm wavelength. The sensing elements were F1 optical glass plates with a refractive index of 1.61, with sputtered layers of chromium (5 nm) and gold (45…50 nm). As a result of the studies, a correlation was ascertained between the level of peripheral blood cell aggregation in patients and the degree of malignancy of gliomas. A statistically significant difference (p ≤ 0.05) was found between the groups of conditionally healthy individuals and those with grade II-IV gliomas. A decrease in the shift of the SPR curve during blood testing indicates an increase in cell aggregation levels and a decrease in their electric charge on membranes. This trend gradually intensifies with the increasing degree of glioma malig-nancy, reaching minimal values in patients with grade IV gliomas, indicating changes in the physicochemical properties of cell membranes and a reduction in their electric charge.
Effect of dopant loading and calcination conditions on structural and optical properties of ZrO2 nanopowders doped with copper and yttrium
(2024) Khomenkova, Larysa; Marchylo, Oleg; Polishchuk, Yulia; Ponomaryov, Semyon; Isaieva, Oksana; Vorona, Igor; Melnichuk, Liudmyla; Portier, Xavier; Melnichuk, Olexandr; Korsunska, Nadiia
Undoped, Cu and/or Y doped ZrO2 nanopowders were synthesized with Zr, Y, and Cu nitrates using a co-precipitation approach. Their structural and optical properties were examined regarding dopant content (0.1–8.0 mol.% of CuO and 3–15 mol.% of Y2O3) and calcination conditions (400 °C– 1000 °Cand, 1,2 or 5 h) through Raman scattering, XRD, TEM, EDS, AES, EPR,UV–vis and FTIR diffused reflectance methods. The results showed that both Cu and Y dopants promoted the appearance of additional oxygen vacancies in ZrO2 host, while the formation of tetragonal and cubic ZrO2 phases was primarily influenced by the Y content, regardless of Cu loading. The bandgap of most of the powders was observed within the 5.45–5.65 eV spectral range, while for those with high Y content it exceeded 5.8 eV. The (Cu,Y)-ZrO2 powders with 0.2 mol.% CuO and 3 mol.% Y2O3 calcined at 600 °Cfor 2 h demonstrated nanoscaled tetragonal grains (8–12 nm) and a significant surface area covered with dispersed CuxOspecies. For higher calcination temperatures, the formation of CuZr 2+ EPR centers, accompanied by tetragonal-to-monoclinic phase transformation, was found. For fitting of experimental FTIR reflection spectra, theoretical models with one, five, and seven oscillators were constructed for cubic, tetragonal, and monoclinic ZrO2 phases, respectively. Comparing experimental and theoretical spectra, the parameters of various phonons were determined. It was found that the distinct position of the high-frequency FTIR reflection minimum is a unique feature for each crystalline phase. It was centered at 700–720 cm−1, 790–800 cm−1, and 820–840 cm−1 for cubic, tetragonal, and monoclinic phases, respectively, showing minimal dependence on phonon damping coefficients. Based on the complementary nature of results obtained from structural and optical methods, an approach for monitoring powder properties and predicting catalytic activity can be proposed for ZrO2–based nanopowders.
Effect of MgO/ZnO ratio on the formation process of MgxZn1-xO ceramics
(2024) Korsunska, Nadiia; Polishchuk, Yuliya; Ponomaryov, Semyon; Kozoriz, K.; Chusnutdinow, S.; Melnichuk, Olexandr; Melnichuk, Lyudmyla; Khomenkova, Larysa
The structural characteristics, chemical composition, and element spatial distribution in MgxZn1-xO ceramics were investigated using X-ray diffraction, scanning electron microscopy, Auger electron spectroscopy, energy-dispersive X-ray spectroscopy, and cathodoluminescence techniques. The study revealed that the morphology of the ceramic samples, as well as the mechanism of solid solution formation, depend on the relative contribution of both oxides in the charge. It was discovered that hexagonal and cubic phases of the solid solution were found to form simultaneously. An increase in the MgO content in the charge results in the magnesium content rise in the hexagonal grains continuously, reaching approximately 13 at.%. It was discovered an enrichment of grain boundaries with zinc and magnesium playing a significant role in doping ZnO and MgO grains. Obtained results allowed to propose two mechanisms involved in the formation of solid solution ceramics: i) diffusion of Mg and Zn along grain boundaries, followed by their incorporation into ZnO or MgO grains, respectively, and ii) interdiffusion of Mg into ZnO and Zn into MgO due to direct contact of ZnO and MgO grains. The second mechanism appears to dominate when both ZnO and MgO contribute comparably, increasing the probability of their direct contact. This study significantly advances the understanding of the process of the formation of MgxZn1-xO ceramics under thermodynamic conditions. These insights are crucial for optimizing the doping process and improving the material properties, thereby promoting innovations in the ceramics industry.
Effects of Electron Correlation inside Disordered Crystals
(2022) Kruchinin, Sergei; Eglitis, Roberts; Babak, Vitaliy; Vyshyvana, Iryna; Repetsky, Stanislav
We propose a novel approach for characterising the electron spectrum of disordered crystals constructed from a Hamiltonian of electrons as well as phonons and a diagram approach for Green’s function. The system’s electronic states were modelled by means of the multi-band, tight-binding approach. The system’s Hamiltonian is described based on the electron wave functions at the field of the atom nucleus. Our novel approach incorporates the long-range Coulomb interplay of electrons located in different lattice positions. Explicit interpretations of Green’s functions are derived using a diagram method. Equations are obtained for the vertex components for the mass operators of the electron–electron as well aselectron–phonon interplays. A system of equations for the spectrum of elementary excitations in the crystal is obtained, in which the vertex components for the mass operators of electron–electron as well as electron–phonon interplays are renormalised. Thismakes it possible to perform numerical computationsfor the system’s energy spectrum with a predetermined accuracy. In contrast to other approaches in which electron correlations are only taken into account in the limiting cases of an infinitely large and infinitesimal electron density, in this method, electron correlations are described in the general case of an arbitrary density. We obtained the cluster expansion of the density of states (DOS) of the disordered systems. We demonstrate that the addition of the electron-scattering mechanismsto the clusters is decreasing. This happens due to a growing number of positions in the cluster, which hang ontothe small parameter. The computing exactness is fixed by a small parameter for cluster expansion of Green’s functions of electrons as well as phonons.
Effects of metallic and molecular counterions in structural dynamics of the DNA double helix
(2024) Perepelytsya, Sergiy
The aim of this paper is to derive the hydrodynamics for a cold Bose gas from the microscopic platform based on the many-body Schr¨odinger equation and general assumptions of the hydrodynamic approach (HA) applicable to any dimension.
Effects of thermal treatment on the complex structure of luminescence emission of Li-doped ZnO screen-printed films
(2023) Chukova, O.; Borkovska, L.; Khomenkova, L.; Korsunska, N.; Ponomaryov, S.; Androulidaki, M.; Stratakis, E.
The ZnO–Li films were synthesized and investigated in an attempt to explore and develop RE-free phosphor materials capable of emitting intense visible light in a wide spectral range. The effects of both heterovalent doping with lithium and high-temperature annealing on the optical properties of ZnO films were studied. The films were deposited on the Al2O3 substrate using the screen-printing method and annealed at 800–1,000°C in air for 0.5–3 h. Both doping and annealing result in the transformation of the shape of reflectance spectra in the range of 300–400 nm and the shift of absorption edge to the long-wavelength region. At the same time, the bandgap value estimated taking into account the exciton peak position and its binding energy is independent of Li-doping. The feature at 300–400 nm and the shift of absorption edge are ascribed to the appearance of the absorption band that excited the yellow photoluminescence band. The photoluminescence spectra of undoped and Li-doped films show the emission bands in the ultraviolet and visible spectral ranges. The ultraviolet emission is due to ZnO exciton recombination. The visible emission band comprises several components peaked at 430, 482, 540, 575, and 640 nm. Their relative intensities depend on Li-doping, annealing temperature, and annealing duration. The 430- and 482-nm luminescence bands were observed in Lidoped films only. Their excitation spectra show the peak located at 330–340 nm, indicating that the energy significantly exceeds the ZnO bandgap energy. Consequently, the 430- and 482-nm luminescence bands are attributed to an additional crystal phase formed under annealing. Other components of visible emission bands are ascribed to the defect-related emission of ZnO. The possible nature of these bands is further discussed. Li-doping and annealing at intermediate temperatures result in blue emission and an enhancement of other visible bands, which makes ZnO–Li films a perspective material in photonic applications.
Electronic Spectrum and Conductivity in Graphene with Impurities
(2023) Kruchinin, Sergei; Repetsky, Stanislav; Vyshyvana, Iryna; Polishchuk, Arkadiy
In the tight-binding one-electron model, the influence of substitutional impurity atoms on the energy spectrum and electrical conductance of graphene is studied. It is established that the ordering of substitutional impurity atoms on nodes of the crystal lattice causes the appearance of a gap in the energy spectrum of graphene 𝜂|𝛿| in width centered at the point 𝑦𝛿, where 𝜂 is the parameter of ordering, 𝛿 is the difference of the scattering potentials of impurity atoms and carbon atoms, and 𝑦 is the impurity concentration. If the Fermi level is located outside the gap, then the electrical conductance increases with the parameter of order 𝜂. It is shown that an increase in the electrical conductance with the order parameter is a result of both the growth of the density of states at the Fermi level and the time of relaxation of electron states. We have demonstrated the presence of a domain of localized states on the edges of the energy gap arising at the ordering of atoms of the admixture.

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