# Vol 28, No 1-2 (2022)

**Year:**2022**Articles:**11**URL:**https://journals.ssau.ru/est/issue/view/575

## Full Issue

## Статьи

### PROPERTIES OF MEASURES ON ”STABLE” BOOLEAN ALGEBRAS

#### Abstract

We study the properties of finitely additive measures with values in a topological abelian group and defined on a wide class of Boolean algebras, which covers algebras with SIP and algebras ???? ( if ν satisfies some conditions). We establish sufficient conditions for the sequences of such measures to be uniformly strongly continuous. Novelty in this theme is that we do not require uniform exhaustivity and, in some theorems, even exhaustivity for measures. Applications to weak convergence of measures are presented.

**Vestnik of Samara University. Natural Science Series**. 2022;28(1-2):7-22

### HOW THE DISTANCE BETWEEN SUBSPACES IN THE METRIC OF A SPHERICAL OPENING AFFECTS THE GEOMETRIC STRUCTURE OF A SYMMETRIC SPACE

#### Abstract

A relationship is found between the metric of a spherical opening on the space of all subspaces of a symmetric space and some numerical characteristic of the subspace. It is known that, for example, in L1 this characteristic takes only two values (i.e. this is a binary space), while in L2 there are infinitely many values. Using the connection found, the necessary conditions for the binarity of a symmetric space were generalized.

**Vestnik of Samara University. Natural Science Series**. 2022;28(1-2):23-31

### PROBLEMS OF DIFFERENTIAL AND TOPOLOGICAL DIAGNOSTICS. PART 8. AIRCRAFT MOVEMENT AND ALGORITHMS FOR ITS DIAGNOSIS

#### Abstract

This work is the eighth work of the cycle on differential and topological diagnostics. In it, a qualitative and numerical mathematical experiment is carried out to diagnose the control system of an aircraft during its planning from altitudes close to orbital, with an initial velocity close to the first cosmic velocity. And we have shown that the proposed diagnostic algorithms work successfully when searching for various kinds of reference faults, in particular, malfunctions of control signal sensors from a gyrostabilized platform, malfunctions close to to the reference ones, for trajectory measurements with an error, as well as in the case of continuous express diagnostics. At the same time, a certain diagnostic algorithm is built and used in accordance with the previously developed methodology.

**Vestnik of Samara University. Natural Science Series**. 2022;28(1-2):32-45

### GENERAL THEORY OF ORTHOTROPIC SHELLS. PART I

#### Abstract

Modern mechanical engineering sets the tasks of calculating thin-walled structures that simultaneously combine sometimes mutually exclusive properties: lightness and economy on the one hand and high strength and reliability on the other. In this regard, the use of orthotropic materials and plastics seems quite justified.

The article demonstrates the complex representation method of the equations of the orthotropic shells general theory, which allowed in a complex form to significantly reduce the number of unknowns and the order of the system of differential equations. A feature of the proposed technique for orthotropic shells is the appearance of complex conjugate unknown functions. Despite this, the proposed technique allows for a more compact representation of the equations, and in some cases it is even possible to calculate a complex conjugate function. In the case of axisymmetric deformation, this function vanishes, and in other cases the influence of the complex conjugate function can be neglected.

Verification of the correctness of the proposed technique was demonstrated on a shallow orthotropic spherical shell of rotation under the action of a distributed load. In the limiting case, results were obtained for an isotropic shell as well.

**Vestnik of Samara University. Natural Science Series**. 2022;28(1-2):46-54

### EVOLUTION OF THE FIELD OF DISTRIBUTED DEFECTS IN A CRYSTAL DURING CONTACT INTERACTION WITH A SYSTEM OF RIGID STAMPS

#### Abstract

The article discusses the mathematical modeling for the evolution of the stress-strain state and fields of defects in crystals during their contact interaction with a system of rigid punches. From a macroscopic point of view, the redistribution of defects is characterized by inelastic (viscoplastic) deformation, and therefore the processes under study can be classified as elastic-viscoplastic. Elastic and inelastic deformations are assumed to be finite. To take into account inelastic deformations, it is proposed to use a differential-geometric approach, in which the evolution of the fields of distributed defects is completely characterized by measures of incompatible deformations and quantified by material connection invariants. This connection is generated by a non-Euclidean metric, which, in turn, is given by a field of symmetric linear mappings that define (inconsistent) deformations of the crystal. Since the development of local deformations depends both on the

contact interaction at the boundary and on the distribution of defects in the bulk of the crystal, the simulation problem turns out to be coupled. It is assumed that the local change in the defect density is determined by the first-order Alexander Haasen Sumino evolutionary law, which takes into account the deviatoric part of the stress field. An iterative algorithm has been developed to find coupled fields of local deformations and defects density. The numerical analysis for the model problem was provided for a silicon crystal in the form of a parallelepiped, one face of which is rigidly fixed, and a system of rigid stamps acts on the opposite face. The three-constant Mooney Rivlin potential was used to model the local elastic response.

**Vestnik of Samara University. Natural Science Series**. 2022;28(1-2):55-73

### QUANTUM MODELS IN BIOLOGY

#### Abstract

The penetration of quantum concepts into biological science, which began shortly after the creation of quantum mechanics, over the past two decades has taken shape in a new interdisciplinary scientific discipline — quantum biology. One of the key questions of quantum biology has been formulated as follows: are there biological systems that use quantum effects to perform a task that cannot be done classically? More broadly, do some kinds of organisms adapt efficient quantum mechanisms in the process of their evolutionary development in order to gain an advantage over their competitors? The range of topical problems of the new discipline discussed in this brief review includes questions of a general, historical and methodological character, and generalizes some theoretical models aimed at describing quantum processes, including bacterial

photosynthesis, bird magnetoreception, and the mechanism of olfactory sense in living organisms.

**Vestnik of Samara University. Natural Science Series**. 2022;28(1-2):74-94

### DYNAMICS OF THE THREE-QUBITS TAVIS — CUMMINGS MODEL

#### Abstract

In this article, we have studied the entanglement dynamics of three identical qubits (natural or artificial two-level atoms) resonantly interacting with the one mode of the thermal field of a microwave lossless resonator via one-photon transitions. An exact solution of the quantum time Schrodinger equation is found for the total wave function of the system for the initial separable and entangled states of qubits and the Fock initial state of the resonator. On the basis of this solution, an exact solution of the quantum Liouville equation for the total time-dependent density matrix of the system in the case of a thermal field of the resonator is constructed. The exact solution for the full density matrix is used to calculate the criterion of entanglement of pairs of qubits – negativity. The results

of numerical simulation of the time dependence of the negativity of pairs of qubits showed that with an increase in the intensity of the thermal resonator field, the degree of entanglement of pairs of qubits decreases. It is also shown that In the model under consideration, for any initial states of qubits and intensities of the thermal field of the resonator, the effect of sudden death of entanglement takes place. This behavior of the entanglement parameter in the model under consideration differs from that in the two-qubit model. For two-qubit model, the effect of the sudden death of entanglement takes place only for the initial entangled states of qubits and intense thermal fields of the resonator.

**Vestnik of Samara University. Natural Science Series**. 2022;28(1-2):95-105

### THE STRUCTURE OF THE SWIRLING FLOW IN THE COUNTERFLOW VORTEX REACTOR

#### Abstract

Two promising designs of counterflow vortex reactor were numerically investigated. Such apparatus utilizes reverse flow to withdraw thermal energy and products from interelectrode area. Complex gasdynamic structure of the water-vapor flow was investigated using turbulent three-dimensional simulation employing Reynolds averaged Navier-Stokes equations along with SST k − ω turbulence model – technique tested in earlier papers. Presented velocity profiles and heat flux reports demonstrate viability of both approaches.

**Vestnik of Samara University. Natural Science Series**. 2022;28(1-2):106-112

### GROWTH TIME OF ACOUSTIC PERTURBATIONS IN ISENTROPICALLY UNSTABLE HEAT-RELEASING MEDIUM

#### Abstract

Isentropic instability is a type of thermal instability that leads to the growth of acoustic waves. As a result of wave growth in such media, autowave structures are formed, the parameters of which depend only on the properties of the medium and can be predicted both analytically and numerically. This study aims to answer the question of how quickly these structures can form in an isentropically unstable medium with parameters similar to Orion Bar. It is shown that the growth time depends on the characteristic size of the initial perturbation. The fastest growing structures take 3-6 thousand years to reach half their maximum amplitude. Further growth to the maximum value takes 15-20 thousand years.

**Vestnik of Samara University. Natural Science Series**. 2022;28(1-2):113-119

### FAST AND SLOW MHD WAVES IN THERMALLY ACTIVE PLASMA SLAB

#### Abstract

We considered the combined influence of the thermal activity and the magnetic structuring on properties of the compressional magnetohydrodynamic (MHD) waves. To model MHD waves we use the single magnetic slab geometry. To derive dispersion equations for the symmetric (sausage) and anti-symmetric (kink) waves, we apply the assumption of strong magnetic structuring. In our calculations we use parameters corresponding to the highly magnetized coronal loop. The thermal activity leads to the changes in the phase velocity and in the wave increment/decrement. We show that the spatial scales where the dispersion effects caused by the thermal activity is most pronounced are longer than the geometry dispersion spatial scale. The thermal activity and wave-guide geometry have comparable effect on the slow-waves phase velocity dispersion. However, the main source of the phase velocity dispersion for the fast MHD waves remains the wave-guide geometry. We also show that the damping of slow MHD waves caused by the thermal activity is greater than the damping of fast MHD waves.

**Vestnik of Samara University. Natural Science Series**. 2022;28(1-2):120-127

### PRODUCTION OF ηc WITH TWO-PHOTON DECAY IN THE GPM AT THE ENERGIES OF NICA COLLIDER

#### Abstract

The article discuss the production of c-mesons with decays into the photon pairs at the energy of the NICA collider, √s =27 GeV, in the generalized parton model and the leading order approximation of the perturbation theory of quantum chrodynamics. The hadronization of a cc-pair into c-meson is described in the color singlet model and in the color evaporation model. In the calculation of the background process of two photon production with invariant mass near the mass of c-meson, we take into account direct as well as fragmentation mechanisms of the prompt photon production. The results of calculations are compared with predictions of the collinear parton model. We study the signal/background ratio as a function of the

different kinematical variables.

**Vestnik of Samara University. Natural Science Series**. 2022;28(1-2):128-136