# Vestnik of Samara University. Natural Science Series

Journal «Vestnik of Samara University. Natural Science Series» is a scientific publication, where the results of *original* research on sections: **Mathematics; Physics; Mathematical Modelling; Mechanics; Mathematical Metods in Natural Sciences; Informatics, Computer Science and Management, Reviews are published**. Published since 1995.

Since 2003, the journal is included by the Higher Attestation Commission in the List of leading scientific journals and publications in the Russian Federation, where basic scientific results of doctoral theses should be published (Bulletin of the Higher Attestation Commission of the Ministry of Education and Science), included in the international database zbMATH.

The Journal is included in bibliographic databases VINITI, Crossref, ULRICH`S Periodical Directory, Math-Net.ru, MathSciNet. Since 2005, the journal is included in the Russian Science Citation Index (Scientific Electronic Library eLIBRARY.ru).

**Journal founder and publisher**: Samara National Research University.

**Business model: the journal is funded by the founder, all articles are published free of charge.**

**All articles are reviewed in the program «Antiplagiat» and are sent for independent external double-blind peer-review.**

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## Current Issue

### Vol 29, No 2 (2023)

**Year:**2023**Articles:**7**URL:**https://journals.ssau.ru/est/issue/view/613

#### Статьи

##### TRANSFORMATION OF OSCILLATIONS OF AN UNSTABLE SYSTEM IN AN ENERGY HARVESTER

###### Abstract

In this work, a simple model of energy harvester transforming the energy of unstable mechanical vibrations into useful electric energy is proposed. The mechanical part of the system is presented in the form of an inverted pendulum. The electric part consists of a converter of mechanical energy based on a direct piezoelectric effect, and a payload. The dynamics of the system is considered in the linearized production, the areas of stability are determined, various dynamics modes in the parameter space are identified. It was established that the stabilizing pendulum of management based on the principles of feedback allows you to transfer the system into a stable mode of functioning. The optimal characteristics of the system that meets maximum power were found.

**Vestnik of Samara University. Natural Science Series**. 2023;29(2):7-18

##### DYNAMICS OF AN ENERGY HARVESTER WITH HYSTERESIS FRICTION

###### Abstract

A model of an energy harvester converter with hysteresis viscous friction is considered. The mechanical part of the energy harvester is made in the form of an inverted pendulum. The hysteresis is formalized within the framework of the Preisach model, which is a continuum analogue of a system of non-ideal relays connected in parallel. Within the framework of numerical experiments, the dependences of the dynamic parameters, in particular, the angle of deflection of the pendulum and the voltage on the load, as well as phase portraits, on the value of the coefficient characterizing the effect of hysteresis friction, were investigated. The role of nonlinear effects is demonstrated.

**Vestnik of Samara University. Natural Science Series**. 2023;29(2):19-29

##### INFLUENCE OF HIGH-ORDER TERMS IN THE SOLUTION GENERALIZING THE APPROACH OF M. WILLIAMS, TAKING INTO ACCOUNT THE ANISOTROPY OF THE MATERIAL

###### Abstract

The research is devoted to the study of the stress field at the crack tip in an anisotropic material with three mutually orthogonal axes of symmetry of the fourth order (with cubic symmetry). A plane case is considered when one of the axes of symmetry is orthogonal to the cracked plate, and the remaining two axes lie in the plane of the plate. The paper presents an asymptotic analysis of the contribution of higher approximations in the generalized asymptotic decomposition of mechanical fields near the crack tip in a linearly elastic anisotropic material with cubic symmetry of its elastic properties. In the article, based on the obtained solution of M. Nejati and co-authors for an infinite anisotropic plate with a central crack, circumferential apportionments of the stress tensor components at the crack tip at various distances from

the crack tip are constructed, which makes it possible to estimate the contribution of non-singular (regular)

terms to the general asymptotic representation of mechanical fields generated by an acute crack. In the work of M. Nejati, the contribution of exclusively T-stresses is analyzed, then, as shown in this work, the terms following the T-stress play a significant role in describing the fields induced by the crack. A comparison of the angular distributions of the stress tensor components constructed at different distances from the crack tip indicates that with the increase of distances from the crack tip, it is required to preserve in asymptotic series representing stresses, displacements and strains near the tip of the crack, the terms of high order of smallness. The preservation of the terms of high order of smallness can be used to expand the domain in which the asymptotic solution in the series is valid.

**Vestnik of Samara University. Natural Science Series**. 2023;29(2):30-39

##### EQUIVARIANT PROPERTIES OF THE SPACE Z(X) FOR A STRATIFIABLE SPACE X

###### Abstract

In this paper, we prove the action of the compact group G defined by the stratified space X is continuous to the space Z(X) being a stratified space containing the self-stratified space X as a closed subset. An equivariant analogue of some results of R. Cauty concerning A(N)R(S) – spaces is proved. It is presented that the orbit space Z(X)/G by the action of the group G is a S space.

**Vestnik of Samara University. Natural Science Series**. 2023;29(2):40-47

##### ASSOCIATIVE PRODUCTION OF J/ψ -MESONS AND DIRECT PHOTONS AT THE ENERGY OF THE NICA COLLIDER

###### Abstract

The article considers the associated production of J/ψ-mesons and direct photons at the energy of the NICA collider, √s =27 GeV, in the Generalized Parton Model in the leading order of perturbation theory of the quantum chromodynamics. Hadronization of a pair of c¯c-quarks to a J/ψ-meson is described in terms of two approaches: the color singlet model and the color evaporation model. Nonperturbative parameters of the models are fixed from comparison with the available experimental data on inclusive production of J/ψ-mesons obtained at energies from √s = 19 up to √s = 200 GeV. It is shown that the processes of the associative production of J/ψ + γ can be used to study of gluon distribution functions depending on the transverse momentum in a proton.

**Vestnik of Samara University. Natural Science Series**. 2023;29(2):48-61

##### ENTANGLEMENT BETWEEN TWO SUPERCONDUCTING CHARGE QUBITS

###### Abstract

In this paper, we investigated the dynamics of entanglement of two identical charge qubits with Josephson junctions in the case when one of the qubits is exposed to a microwave field in a coherent or thermal state. We have found the exact solution of the quantum time equation of evolution of the system under consideration for the statistical operator in the case of initial separable and entangled states of qubits. The exact solution for the complete statistical operator is used to calculate the qubit entanglement criterion - concurrence. The results of numerical simulation of the time dependence of the concurrence in the case of the coherent field showed that, with a certain choice of model parameters, the system can realize long-lived entangled states. It is also shown that for the thermal state of the field and the entangled initial state of qubits, the qubits retain a certain degree of entanglement during evolution even in the case of very intensive fields. In this case, for any intensities of thermal noise, there is no effect of the sudden death of entanglement.

**Vestnik of Samara University. Natural Science Series**. 2023;29(2):62-71

##### ENTANGLEMENT IN NONLINEAR TWO-QUBIT TAVIS — CUMMINGS MODEL

###### Abstract

In this work, we have studied the dynamics of entanglement of two identical superconducting qubits resonantly interacting with the one-mode field of a coplanar microwave cavity without loss through single-photon transitions in the presence of third- and fifth-order nonlinearities. Based on the solution of the equation of evolution of the system for the Fock initial states of the cavity field, the criterion of qubits entanglement – negativity is calculated. The results of the negativity calculation show that for the initial separable states, the cavity nonlinearity can lead to a significant increase in the maximum degree of qubit entanglement. It is shown that for the initial entangled

states of qubits and intense cavity fields, taking into account nonlinearities leads to stabilization of the degree of entanglement of qubits in the cavity and contributes to the disappearance of the effect of the entanglement sudden death of qubits.

**Vestnik of Samara University. Natural Science Series**. 2023;29(2):72-80