Vol 30, No 1 (2024)

Cover Page

Full Issue

Articles

In memory of Vladimir Ivanovich Astafyev (30.11.1948 – 08.02.2024)

Stepanova L.V., Osipov M.N., Fedina M.E., Voropaeva N.V., Krutov A.N., Bondarenko V.V.

Abstract

The article is dedicated to the memory of Doctor of Physical and Mathematical Sciences, Professor Vladimir Ivanovich Astafiev, whose professional activity for more than 35 years has been associated with Samara University. Scientific, teaching and organizational activities of V.I. Astafiev largely determined and will determine the scientific directions developed at the Faculty of Mechanics and Mathematics, and the educational activity at the Faculty of Mechanics and Mathematics. His boundless dedication to the university, his broad and deep education, and high mathematical culture allowed him to educate the whole pleiades of scientists and professors currently working at the university.

Vestnik of Samara University. Natural Science Series. 2024;30(1):7-22
pages 7-22 views

Mathematics

Some auxiliary estimates for solutions to non-uniformly degenerate second-order elliptic equations

Huseynov S.T., Aliyev M.J.

Abstract

We consider a class of second order elliptic equations in divergence form with non-uniform exponential degeneracy. The method used is based on the fact that the degeneracy rates of the eigenvalues of the matrix ||aij(x)|| (function λi(x)) are not the functions of unusual norm |x|, but of some anisotropic distance |x| a. We assume that the Dirichlet problem for such equations is solvable in the classical sense for every continuous boundary function in any normal domain Ω.

Estimates for the weak solutions of Dirichlet problem near the boundary point are obtained, and Green’s functions for second order non-uniformly degenerate elliptic equations are constructed.

Vestnik of Samara University. Natural Science Series. 2024;30(1):23-30
pages 23-30 views

Relaxation oscillations in the Darie wind power plant model

Kirsanova A.S.

Abstract

The article discusses the mathematical model of the Daria small wind power plant. This installation is a type of vertical axis wind turbine named after its inventor, Georges Jean Marie Darrieux. The design consists of a vertically oriented shaft with curved blades or airfoils attached to it, forming a shape similar to an egg whisk. In today’s world, against the backdrop of climate change and steadily increasing energy demand, wind energy acts as a critical pillar of the transition to renewable energy sources. This technology helps reduce carbon emissions and mitigate humanity’s impact on the environment. In this context, wind energy is emerging not only as a means of supplying electricity, but also as a powerful catalyst for building a more sustainable and energy-efficient future. The equation of stationary modes is studied at the value of the external resistance of the dynamic model specified by the simplest equation. Conditions have been found under which relaxation oscillations are observed in the system.

Vestnik of Samara University. Natural Science Series. 2024;30(1):31-39
pages 31-39 views

Mechanics

On one solution of the problem of vibrations of mechanical systems with moving boundaries

Litvinov V.L., Litvinova K.V.

Abstract

An analytical method of solving the wave equation describing the oscillations of systems with moving boundaries is considered. By changing the variables that stop the boundaries and leave the equation invariant, the original boundary value problem is reduced to a system of functional-difference equations, which can be solved using direct and inverse methods. An inverse method is described that makes it possible to approximate quite diverse laws of boundary motion by laws obtained from solving the inverse problem. New particular solutions are obtained for a fairly wide range of laws of boundary motion. A direct asymptotic method for the approximate solution of a functional equation is considered. An estimate of the errors of the approximate
method was made depending on the speed of the boundary movement.

Vestnik of Samara University. Natural Science Series. 2024;30(1):40-49
pages 40-49 views

On the boundary conditions for a thin circular plate conjugated to a massive body

Ustinov K.B., Gandilyan D.V.

Abstract

The problem of deformation under the action of uniform pressure of a circular plate coupled with a massive base is considered, while the condition for the coupling of the plate with the base is modeled using boundary conditions of the generalized elastic embedding type, i.e. the relationship between the bending moment and forces at the edge of the plate with displacements and rotation angles through the compliance matrix. The main goal of the work is to study the influence of the elasticity of the embedding on the elastic response of the plate. The solution to the problem was obtained in the formulation of the linear theory of plates, the theory of membranes in the approximation of homogeneity of longitudinal forces, and the Foppl — von Karman theory, also in the approximation of the assumption of homogeneity of longitudinal forces. The values of the coefficients of the compliance matrix were obtained using the finite element method for the auxiliary problem and compared with the values of the coefficients obtained for related problems by analytical methods. Numerical results were obtained for an aluminum wafer on a silicon base. The obtained solution was compared with the solution obtained for the rigid embedment condition for all three models used. It is shown that in the case of large deflections (several plate thicknesses), taking into account the compliance of the embedment becomes essential.

Vestnik of Samara University. Natural Science Series. 2024;30(1):50-63
pages 50-63 views

Mathematical Modelling

Modeling of semiconductor heterostructures for energy converters and sensors

Dolgopolov M.V., Elisov M.V., Radzhapov S.A., Rakhmankulov I.R., Chipura A.S.

Abstract

A set of modeling programs for constructing a sequence of energy zones of heterojunctions is presented for analyzing the distribution of charge carriers in the heterostructure and internal characteristics, for describing the processes of charge transfer and accumulation. Wolfram Mathematica analytical system and Delphi programming language were used. The main elements of materials are semiconductors, metals of contact structures and injection regions of nonequilibrium carriers. The programs allow determining the structural characteristics of materials, active zones and spatial charge regions, calculating quasi-Fermi levels and built-in potentials, as well as the efficiency of heterostructures in general and for separation-charge collection, charge accumulation, determining the type of metallization of barrier or ohmic contact.

Vestnik of Samara University. Natural Science Series. 2024;30(1):64-81
pages 64-81 views

Physics

Dynamics of entangled Greenberger — Horne — Zeilinger states in three qubits thermal Tavis — Cummings model

Bagrov A.R., Bashkirov E.K.

Abstract

In this paper, we investigated the dynamics of systems of two and three identical qubits interacting resonantly with a selected mode of a thermal field of a lossless resonator. We found solutions of the quantum time-dependent Liouville equation for various three- and two-qubit entangled states of qubits. Based on these solutions, we calculated the criterion of the qubit entanglement — fidelity. The results of numerical calculations of the fidelity showed that increasing the average number of photons in a mode leads to a decrease in the maximum degree of entanglement. It is shown that the two-qubit entangled state is more stable with respect to external noise than the three-qubit entangled Greenberger — Horne — Zeilinger states (GHZ). Moreover, a genuine entangled GHZ-state is more stable to noise than a GHZ-like entangled state.

Vestnik of Samara University. Natural Science Series. 2024;30(1):82-95
pages 82-95 views

Prompt polarized J/ψ production at NICA within NRQCD and generalized parton model

Karpishkov A.V., Saleev V.A., Shilyaev K.K.

Abstract

In our work we consider prompt J/ψ and ψproduction within the approaches of nonrelativistic quantum chromodynamics and generalized parton model. We use various experimental data (s = 200 GeV and s =19.4 GeV) of charmonium production to fit octet nonperturbative matrix elements and averaged values of initial partons’ transverse momenta. Further, we make evaluation with the extracted parameters and predict J/ψ production cross section and polarization of J/ψ and ψat NICA collider energy s = 27 GeV.

Vestnik of Samara University. Natural Science Series. 2024;30(1):96-111
pages 96-111 views

Dynamics of atom-atom entanglement in two-atom model with degenerate two-photon raman transitions

Othman A., Bashkirov E.K.

Abstract

The exact dynamics of a model consisting of two two-level atoms interacting with the electromagnetic field mode of an ideal resonator through degenerate Raman transitions are found for coherent and thermal field states. The exact solution is used to calculate atom-atom negativity. It is shown that for separable initial states of atoms, their interaction with the resonator field does not lead to the occurrence of atom-atom entanglement. It was found that for the Bell initial states of atoms in the case of a coherent resonator field, the effect of sudden death of entanglement takes place for large average values of the number of photons in the resonator, while in case of thermal noise, this effect is absent for any intensities of the resonator field.

Vestnik of Samara University. Natural Science Series. 2024;30(1):112-121
pages 112-121 views

Model of decomposition of the native absorption spectrum of Porphyridium purpureum culture

Chernyshev D.N., Klochkova V.S., Lelekov A.S.

Abstract

A model of the native absorption spectrum of the red seaweed Porphyridium purpureum culture was developed in this work. The mathematical model of each pigment is the sum of Gaussian curves. To level the light scattering, the spectra of the culture were recorded on a spectrophotometer with an integrating sphere. To verify the model, a series of parallel measurements of photosynthetic pigment concentrations using standard biochemical methods and the Gaussian curve method were performed. It was shown that the proposed model with sufficient accuracy makes it possible to determine the concentration of the main photosynthetic pigments of Porphyridium purpureum culture without interfering with its growth processes.

Vestnik of Samara University. Natural Science Series. 2024;30(1):122-131
pages 122-131 views

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