Кафедра фізико-математичних наук
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Item Visualization in Maple for Learning Differential Calculus(2025) Shevtsova, OksanaMaple is a comprehensive general-purpose computer algebra system. It is used primarily in educational and scientific research in mathematics and engineering. Maple offers many visualization tools. Using Maple, students can explore functions, analyze their derivatives, and draw tangent lines. In this paper, we consider two problems and their visualization in Maple by providing graphical representations of a function and its tangent.Item The Poisson bracket and Hamilton's equations of motion(2025) Shevtsova, OksanaIn mathematics and classical mechanics, the Poisson bracket is a fundamental binary operation in Hamiltonian mechanics, serving as a key component in Hamilton’s equations of motion. This binary operation can be computed for any two physical quantities.Item Three Degrees of Freedom System in the Frame of Lagrangian and Hamiltonian Approaches(2025) Shevtsova, OksanaThe Lagrangian and Hamiltonian approaches are key structural elements in classical mechanics courses for undergraduate students and a powerful part of the physics education culture. The paper is created as a project for students aimed at applying the Lagrangian and Hamiltonian formalism for the description of an illustrative three degrees of freedom system, learning the peculiarities of these formalisms, identifying the conservation laws and finding the integrals/constants of motion. Students can develop using these different independent techniques and obtaining the coinciding results. In other words, this paper is an attempt to present clear interrelations of these approaches training new skills, useful for students learning classical mechanics.Item The dependence of electrical conductivity of MgxZn1-xO ceramics on phase composition(2024) Korsunska, Nadiia; Polishchuk, Yulia; Markevich, Iryna; Kozoriz, K.; Ponomaryov, Semyon; Melnichuk, Olexandr; Stara, Tetyana; Melnichuk, Lyudmyla; Khomenkova, LarysaThe structural and electrical characteristics of (Mg,Zn)O ceramics produced using the solid state reaction at 1100 °C for 3 hours were studied applying X-ray diffraction and IR reflection spectroscopy as well as means of direct current measurements versus MgO content in initial charge (varied from 0 to 100 mol.%). It has been shown that electrical conductivity extracted from the IR reflection spectra corresponds to that of hexagonal phase in a solid solution, while plasmon in cubic phase was not observed. The electron concentration in the hexagonal grains of solid solution prepared with MgO content below 30 mol. % in the charge was found to be close to that of ZnO grains. It shows the tendency to decrease with further growth of the MgO content, which was explained by extraction of zinc interstitials, responsible for ZnO conductivity, from ZnO under formation of the MgZnO cubic phase. The direct current measurements have shown the lower conductivity as compared to the value estimated from IR reflection spectra. This fact along with the superlinearity of current-voltage characteristics has been explained by the presence of intergranular barriers, which does not allow obtaining information on the concentration of free electrons in the grain by this method. The possible nature of intergranular barriers as well as the role of grain boundaries in the DC conductivity of samples has been discussed.Item Magneto-reflectance effect in ZnO and ZnO:Mn ceramics(2025) Korsunska, Nadiia; Melnichuk, Olexandr; Tarasov, G.; Markevich, Iryna; Melnichuk, Lyudmyla; Khomenkova, LarysaThe effect of a magnetic field on the infrared reflectance spectra of undoped and manganese doped ZnO ceramics has been studied. In the undoped samples, an increase in the reflection coefficient was found mainly in the spectral region ν > 580 cm 1 with a slight change in the residual rays range. In the manganese-doped ceramics, the magnetic field results in an increase in the reflection coefficient mainly in the residual rays interval while in the high-frequency region the changes are present also. Based on the modeling of the experimental spectra, it was determined that in the undoped samples, the magnetic field leads to a noticeable increase in the plasmon damping coefficient with an almost unchanged phonon one. In the case of ZnO:Mn ceramics, in addition to an increase in the plasmon damping coefficient, there is a significant decrease in the phonon ones. It is proposed that for the undoped samples the dominant effect is an increase in the effective electron mass, which also occurs in ZnO:Mn samples. In the case of Mn doped samples, it is assumed that the decrease in the phonon damping coefficient may relate to an appearance of defects causing the phonon scattering and reducing their effect in a magnetic field.Item Green's Function Technique in the Theory of Disordered Crystals: Application to Potassium-Doped Graphene(2025) Repetsky, Stanislav; Vyshyvana, Iryna; Lizunov, Viacheslav; Melnyk, Ruslan; Reznikov, Mykhailo; Radchenko, Taras; Tatarenko, ValentynThe method of describing the energy spectrum, free energy, and electrical conductivity of disordered crystals based on the use of the Hamiltonian of electrons and phonons is reviewed, analysed, and developed. The electron states of a system are described through the tight-binding model. A simple procedure for calculating the matrix elements of the Hamiltonian within the Wannier’s representation is proposed. Expressions for the Green’s functions, free energy, and electrical conductivity are derived using the diagram method. Using this procedure, the vertex parts of the mass operators of the electron–electron and electron–phonon interactions are renormalized. A set of exact equations is obtained for the spectrum of elementary excitations in a crystal. This enables the performance of numerical calculations on the energy spectrum and the prediction of system properties with predetermined accuracy. Expressions are obtained for the static waves of concentrations, charge and spin densities, which determine the phase state of a disordered crystal. In contrast to other approaches, which account for electron correlations only within the limiting cases of infinitely large and alinfinitesimal electron densities, this method describes electron correlations in the general case of an arbitrary density. In addition to the theory, the results of a numerical calculation of the energy spectrum of a graphene layer with adsorbed potassium (K) atoms are presented. As established, at the K-atoms’ concentration such that the unit cell includes two carbon (C) atoms and one K atom, the latter being located (adsorbed) on the graphene layer surface 0.286 nm above the C atom, the energy gap is 0.25 eV. The location of the Fermi level (εF) in the energy spectrum depends on the potassiumatoms’ concentration and is in the energy interval −0.36 Ry ≤ εF ≤ −0.23 Ry.Item Magnetically tunable surface phonon polaritons in ZnO and ZnO:Mn ceramics(2025) Melnichuk, Olexandr; Korsunska, Nadiia; Melnichuk, Lyudmyla; Khomenkova, LarysaThe excitation conditions and spectra signatures of surface phonon polaritons and plasmon–phonon polaritons in ZnO and Mn-doped ZnO ceramics have beentheoretically analyzed and experimentally probed. Specular infrared reflection and attenuated total reflection spectroscopy were employed to investigate their dispersion relations. A single-oscillator model was used to describe the dielectric permittivity of ZnO ceramics, accounting for additive phonon and plasmon contributions. Theoretical and experimental dispersion curves were examined in the 100–4000 cm−1 and 240–4000 cm−1 spectral range, respectively. Additionally, the effect of an external magnetic field on surface polaritons was explored, revealing magnetically tunable optical responses. These findings contribute to the development of ZnO-based plasmonic and photonic devices, particularly in infrared and terahertz applications.Item Effects of DNA-Induced Confinement on Interaction with Metallic or Molecular Flexible Counterion(2024) Perepelytsya, Sergiy; Vasiliu, Tudor; Laaksonen, Aatto; Engelbrecht, Leon De Villiers; Mocci, FrancescaIn the presentation, the problem of DNA-counterion interaction reviewed, beginning with the earliest research papers related to the modeling of the system at the atomistic level up to the most recent results. The prominent effects due to the increased confinement induced by the DNA structure emphasized.Item Investigating the influence of polyamines on G-Quadruplex structures: Insights from Molecular Dynamics(2024) Puf, Razvan; Cibotariu, Narcis; Perepelytsya, Sergiy; Pinteala, Mariana; Laaksonen, Aatto; Vasiliu, Tudor; Mocci, FrancescaAbstracts of the report of the participants of the 1st Virtual meeting WG2 of COST action CA21101 COSY "From quantum to classical dynamics of isolated molecules and 3D materials", 6th February 2024, Belgrade, Serbia.Item Exploring Intricate Interactions: A Comprehensive Study of Novel Bis-Acridine Orange Dyes with Double-Stranded DNA(2024) Mocci, Francesca; Kulyk, Olesia; Svoiakov, Rostyslav; Kolosova, Olga; Prylutska, Ivanna; Vasiliu, Tudor; Puf, Razvan; Laaksonen, Aatto; Perepelytsya, Sergiy; Krivoshey, Alexander; Kobzev, Dmytro; Tkachuk, Zenoviy; Tatarets, AnatoliyAbstracts of the report of the participants of the 1st Virtual meeting WG2 of COST action CA21101 COSY "From quantum to classical dynamics of isolated molecules and 3D materials", 6th February 2024, Belgrade, Serbia.Item α + t and α + 3He Interactions and the Excited-State Spectrum of 6Li Nucleus(2025) Povoroznyk, Orest; Gorpinich, Olha; Roznyuk, Yu.; Jachmenjov, O.A kinematically complete analysis of the 3He(α, pα)d reaction on 3He nuclei of radiogenic origin accumulated in titanium-tritium targets, as well as the 3H(α, dα)n and 3H(α, τt)n reactions on tritium nuclei accumulated on the same targets, has been carried out to study the excitation spectrum of 6Li nucleus at excitation energies E* < 26 MeV with the energies of accelerated alpha particles Eα = 27.2 and 67.2 MeV. Three unbound excited levels are observed in the excitation energy interval of 6Li nucleus from 7 to 16 MeV, as well as two excited levels of 6Li with excitation energies of 21.30 and 21.90 MeV, which are consistent with theoretical calculations, but were not reliably confirmed experimentally. The application of the particle decay spectroscopy method made it possible to eliminate some ambiguities in the energy parameters of the excited states of the 6Li nucleus.Item Взаємодiя 𝛼α + t i α + 3He та спектр збуджених станiв ядра 6Li(2025) Поворозник, Орест; Горпинич, Ольга; Рознюк, Ю.; Ячменьов, О.Проведено кiнематично повне дослiдження реакцiй 3He(α, pα)d на ядрах 3He радiогенного походження, накопичених у титан-тритiєвих мiшенях та 3H(α, dα)n, 3H(α, τt)n на ядрах тритiю на цих же мiшенях для вивчення спектра збудження ядра 6Li до енергiй збудження E*< 26 MeВ при енергiї пучкiв прискорених альфа-частинок Eα = 27,2 i 67,2 МеВ. Спостерiгались три незв’язанi збудженi рiвнi в енергетичному дiапазонi енергiї збудження ядра 6Li вiд 7 до 16 МеВ та два збудженi рiвнi 6Li з енергiями збудження 21,30 та 21,90 MeВ, якi узгоджуються з теоретичними розрахунками, але не були достовiрно пiдтвердженi експериментально. Використання методу спектроскопiї розпаду збуджених рiвнiв (particle decay) дозволило усунути деякi неоднозначностi в енергетичних параметрах збуджених станiв ядра 6Li.Item Про застосування форми хвильового фронту альвенових мод для діагностики просторового каналювання(Інститут ядерних досліджень, 2024) Яковенко, ЮрійАнотація до доповіді на XXXI Щорічній науковій конференції Інституту ядерних досліджень НАН України, (м. Київ, 27-31 травня 2024 року). Метою цієї роботи є розробка числових засобів для дослідження такого зв’язку в складніших альвенових власних модах, які не можна задовільно наблизити однією полоїдною гармонікою, – RSAE-модах (Reversed-Shear Alfven Eigenmode) та TAE-модах (Toroidicity-induced Alfven Eigenmode).Item Числове дослідження швидких магнітозвукових мод у токамаках(Інститут ядерних досліджень, 2024) Бурдо, Олена; Колесниченко, Ярослав; Яковенко, Юрій; Руденко, Т.Анотація до доповіді на XXXI Щорічній науковій конференції Інституту ядерних досліджень НАН України, (м. Київ, 27-31 травня 2024 року). У цій доповіді робиться огляд числових кодів, призначених для моделювання FMM з частотами в йонно-циклотронному діапазоні, які було розроблено в останній час авторами.Item Primordial black holes and their gravitational-wave signatures(2025) Bagui, Eleni; Clesse, Sébastien; De Luca, Valerio; Ezquiaga, Jose María ; Franciolini, Gabriele; García-Bellido, Juan; Joana, Cristian; Kumar Jain, Rajeev; Kuroyanagi, Sachiko; Musco, Ilia; Papanikolaou, Theodoros; Raccanelli, Alvise; Renaux-Petel, Sébastien; Riotto, Antonio; Ruiz Morales, Ester; Scalisi, Marco; Sergijenko, Olga; Ünal, Caner; Vennin, Vincent; Wands, DavidIn the recent years, primordial black holes (PBHs) have emerged as one of the most interesting and hotly debated topics in cosmology. Among other possibilities, PBHs could explain both some of the signals from binary black hole mergers observed in gravitational-wave detectors and an important component of the dark matter in the Universe. Significant progress has been achieved both on the theory side and from the point of view of observations, including new models and more accurate calculations of PBH formation, evolution, clustering, merger rates, as well as new astrophysical and cosmological probes. In this work, we review, analyze and combine the latest developments in order to perform end-to-end calculations of the various gravitational-wave signatures of PBHs. Different ways to distinguish PBHs from stellar black holes are emphasized. Finally, we discuss their detectability with LISA, the first planned gravitational-wave observatory in space.Item 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, LarysaIn 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.Item Luminophores for luminescent solar concentrators(2024) Rudko, GalynaThe war in Ukraine demonstrated the vulnerability of the energy supply system with centralized power supply. Moreover, it showed that the country must not rely on imported gas and oil, and also highlighted the danger of using nuclear plants. Under these circumstances solar energy gains the acute attention especially because of possibility to decentralize energy production. However, using of traditional solar cells in Ukraine encounters a problem of rather low amount of sunny days thus there is a demand for the devices capable of operating under diffuse illumination.Item Mn2+ як ЕПР зонд для вивчення структури мікро- та нанорозмірних порошків ZnS(2024) Ворона, Ігор; Іщенко, С.; Баран, Н.; Носенко, Валентина; Грачов, В.Матеріали доповіді учасників міжнародного наукового семінару "ЕПР-орієнтири еволюції методології пізнання"Item Радіаційні дефекти в термічно відпаленому карбонатвмісному гідроксилапатиті(2024) Носенко, Валентина; Ворона, Ігор; Іщенко, С.; Окулов, СергійМатеріали доповіді учасників міжнародного наукового семінару "ЕПР-орієнтири еволюції методології пізнання".Item DNA condensation induced by Li+ counterions(2024) Bubon, Tetiana; Piatnytskyi, Dmytro; Perepelytsya, SergiyMaterials 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