Статьи журнала - Вестник Южно-Уральского государственного университета. Серия: Математика. Механика. Физика
Все статьи: 724
DFT моделирование взаимодействия водорода с вакансией в ОЦК-железе
Статья научная
Впервые представлены результаты первопринципного моделирования взаимодействия атома водорода с вакансией ОЦК-железа в парамагнитном состоянии, которое сопоставляется с аналогичной величиной в магнитоупорядоченном ферромагнитном состоянии. Показано, что расстояния между атомом водорода и соответствующей октапорой для ферромагнитного и парамагнитного состояния оказываются одинаковыми и составляют 0,23 Å. Энергия связи комплекса водород-вакансия составила 0,60 и 0,27 для ферромагнитного и парамагнитного ОЦК-железа, соответственно.
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Description of some weighted exponential classes of subharmonic functions
Статья научная
The role of subharmonic functions in such sections of analysis as complex and real analysis is very significant. Such classes of functions are closely related to analytic harmonic functions and make an important contribution to the general theory of potential and mathematical physics. In the works of R. Nevanlinna and W. Heiman, parametric representations of subharmonic classes in the plane of functions, whose characteristic has a power growth at infinity, are obtained. The question of whether similar representations are true for weighted classes that admit a stronger growth at infinity (for example, the exponential growth) arises in the theory of entire and meromorphic functions. In this article, classes of subharmonic functions with Nevanlinna characteristic that is summable with exponential weight in a complex plane are introduced for consideration, and the representing measures of functions of such classes are studied. When proving the results, methods of complex and functional analysis are used. An important role in the study is played by potentials based on the factors of the modified Weierstrass product. The proof of the main result is based on the use of auxiliary assertions formulated in the form of lemmas.
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Effects of basis set superposition error on DFT model of C2N/graphene bilayer
Статья научная
We investigated the structural and energetic properties of the C2N/graphene bilayer using the electron density functional theory. We compared two approaches for wave function decomposition: plane waves (PW) and localized pseudoatomic orbitals (PAOs). We showed that for the weakly bonded bilayer, it is essential to consider correction to the basis set superposition error in binding energy calculations and geometry optimization. Otherwise, the interlayer binding energy and layer separation could be overestimated by 45-90 % and underestimated by 4-12 %, respectively. Also, to have the quantitative agreement between PAOs and PW results, the atomic-like basis set should be optimized. Overall, calculated with dispersion corrections, the interlayer binding energy (0,17-0,22 J/m2) is of the van der Waals nature.
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Elaboration of atomic model for ab initio calculation of the ferrite / cementite interface
Статья научная
The work describes constructing a supercell for ab initio modelling of ferrite / cementite interface in pearlite microsctructure of iron-carbon alloys. Bagaryatskii type orientation relationship between the two phases was accepted, with habit plane (101) c||(112) α. Optimization of ab initio modelling parameters was also performed using WIEN2k package.
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Статья научная
Intense irradiation and high-speed collision of metals results in the formation and dissemination of shock compression pulses in them. The recent development of experimental technology using high-power subpicosecond laser pulses makes it possible to obtain shock pulses of the picosecond range. A molecular dynamics simulation of high-speed collisions for aluminium samples is conducted. The presence of a nanorelief or precipitated nanoparticles on the back superficies of the sample may essentially enhance the rear splitting threshold. The cooperation of a shock wave with a nanorelief or precipitated nanoparticles results in strong plastic deformation. Consequently, part of the compression pulse energy is spent on plastic deformation, which prevents spall destruction. The effect of increasing the threshold can reach hundreds of meters per second in terms of collision speed and tens of gigapascals in amplitude of the incident shock wave. The distribution of shear strain and temperature in the sample is considered. It is shown that the maximum degree of deformation and maximum heating are observed in those parts of the nanorelief, for which the greatest change in shape is observed. The maximum temperature reaches the melting point, but no obvious traces of melting are found, which may be related to the speed of the processes.
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Exact solutions of the Hirota equation using the sine-cosine method
Статья научная
Nonlinear partial differential equations of mathematical physics are considered to be major subjects in physics. The study of exact solutions for nonlinear partial differential equations plays an important role in many phenomena in physics. Many effective and viable methods for finding accurate solutions have been established. In this work, the Hirota equation is examined. This equation is a nonlinear partial differential equation and is a combination of the nonlinear Schrödinger equation and the complex modified Korteweg-de Vries equation. The nonlinear Schrödinger equation is the physical model and occurs in various areas of physics, including nonlinear optics, plasma physics, superconductivity, and quantum mechanics. The complex modified Korteweg-de Vries equation has been applied as a model for the nonlinear evolution of plasma waves and represents the physical model that incorporates the propagation of transverse waves in a molecular chain model and in a generalized elastic solid. To find exact solutions of the Hirota equation, the sine-cosine method is applied. This method is an effective tool for searching exact solutions of nonlinear partial differential equations in mathematical physics. The obtained solutions can be applied when explaining some of the practical problems of physics.
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First-principles investigations of reference states of Co2CrIn Heusler alloys
Статья научная
In order to identify the reasons for the differences between the available theoretical and experimental values of the total magnetic moment of Co2CrIn Heusler alloy, in this work we studied the effects of various magnetic reference states on the magnetic and electronic properties of the alloys by means of ab initio and Monte Carlo methods. It is shown that the calculated ground state in the L21 phase is ferromagnetic. However, the values for both lattice parameter and magnetic moment calculated for the ferrimagnetic state, where the Cr atoms are ordered antiferromagnetically, are found to be in good agreement with the available experimental data. It is shown that the half-metallic behavior is realized only in the case of the ferromagnetic order. By using the calculated exchange coupling parameters in the Heisenberg Hamiltonian, the temperature dependences of magnetization were simulated.
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First-principles studies of the phase transitions in Fe-Si alloys
Статья научная
In this paper, the structural and magnetic properties of Fe100-xSix alloys (10 ≤ x ≤ 25,0 at. %) were calculated. The structural phase transition temperatures for the crystal structures A2, B2, and D03 were estimated from the geometry optimization. The Curie temperatures were calculated in a molecular-field approximation using the constants of magnetic exchange interaction calculated ab initio. For all the considered concentrations, with the temperature increase, we observed the structural transitions from the ordered cubic phase to a disordered structure, with the intermediate stage of a partially disordered state. The ferromagnet-paramagnet transition was observed for all the compositions, though in various crystal phases.
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Статья научная
Using the solid-phase reaction method we obtained bismuth ferrite based compounds generated by partial substitution of bismuth ions with rare earth metal ions (lanthanum and praseodymium). We used thermogravimetric analysis and X-ray analysis at the temperature range from 297 to 1123 K to study the peculiarities of the processes of phase formation of reaction-products synthesis in the systems which contain oxides of iron, bismuth, lanthanum, and praseodymium; their compositions were also determined. For the final synthesis temperature of 1123 K we determined a homogeneous concentration area, where bismuth ferrite solid solutions with the structure of distorted perovskite exist. We studied the influence of lanthanum and praseodymium oxides on phase composition of bismuth ferrite compounds in the process of isovalent alloying of a part of bismuth ions by lanthanum and praseodymium ions. In the frequency range of 20 Hz - 1 MHz we determined the key parameters, which characterize electrical and magnetic properties of perovskite-like phases. We found that for the considered samples the frequency dependencies of complex magnetic permeability and electrical parameters (real and alleged part of permittivity) are of almost the same type. We showed that for the given frequency range both electrical (complex permittivity) and magnetic (complex magnetic permeability) parameters decrease with the frequency increase.
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H-однородные lambda-пространства
Статья научная
Пусть Х - h-однородное сепарабельное метризуемое несчётное lambda-пространство. Тогда: 1) Х является CDH-пространством, 2) Х гомеоморфно Х \ А для любого счётного множества А из Х.
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Importance of atomic-like basis set optimization for DFT modelling of nanomaterials
Статья научная
Atomic-like orbital basis sets allow efficient calculation of nanomaterial’s surface properties within the density functional theory. However, unlike plane wave basis sets, they require thorough optimization on a reference system before modelling systems of interest. We considered the basis set optimization procedure for several structures: bulk tantalum carbide, oxygen molecule, bulk lithium, and α-carbyne. We showed that during the optimization procedure not only the total energy of a reference system should be monitored but other physical characteristics (bond length and atomic charges) too. Moreover, optimal basis parameters could not correspond to the minimum total energy of a reference system to get the correct physical properties. We obtained optimal orbital parameters, which can be used for modelling of the following systems: oxygen adsorption on tantalum carbide surface, and Li-functionalized carbyne. Considering oxygen adsorption on TaC surface and Li-functionalization of carbyne, we also demonstrated that the basis set optimization influences binding energies and atomic charges of an adsorbent and a surface.
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Invariant spaces of Oskolkov stochastic linear equations on the manifold
Статья научная
The Oskolkov equation is obtained from the Oskolkov system of equations describing the dynamics of a viscoelastic fluid, after stopping one of the spatial variables and introducing a stream function. The article considers a stochastic analogue of the linear Oskolkov equation for plane-parallel flows in spaces of differential forms defined on a smooth compact oriented manifold without boundary. In these Hilbert spaces, spaces of random K-variables and K-“noises” are constructed, and the question of the stability of solutions of the Oskolkov linear equation in the constructed spaces is solved in terms of stable and unstable invariant spaces and exponential dichotomies of solutions. Oskolkov stochastic linear equation is considered as a special case of a stochastic linear Sobolev-type equation, where the Nelson-Glicklich derivative is taken as the derivative, and a random process acts as the unknown. The existence of stable and unstable invariant spaces is shown for different values of the parameters entering into the Oskolkov equation.
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Inverse problem for Sobolev type equation of the second order
Статья научная
The paper deals with the inverse problem for the Sobolev type equation of the second order in Banach spaces. The introduction contains a problem statement and the historiography of Sobolev type equations. The second part includes preliminary information based on the results of the theory of higher-order Sobolev type equations. In the third part the initial problem is reduced to the inverse regular and singular problems. A theorem of unique solvability of regular problem is formulated and proved. Using the results of the third part, the solution for the singular problem is obtained in the fourth part. The sum of regular and singular solutions is a solution to the original problem, thus a theorem on the unique solvability of the inverse problem for Sobolev type equation of the second order is stated and proved.
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Inverse problems of recovering the boundary data with integral over determination conditions
Статья научная
In the present article we examine an inverse problem of recovering unknown functions being part of the Dirichlet boundary condition together solving an initial boundary problem for a parabolic second order equation. Such problems on recovering the boundary data arise in various tasks of mathematical physics: control of heat exchange prosesses and design of thermal protection systems, diagnostics and identification of heat transfer in supersonic heterogeneous flows, identification and modeling of heat transfer in heat-shielding materials and coatings, modeling of properties and heat regimes of reusable heat protection of spacecrafts, study of composite materials, etc. As the overdetrermination conditions we take the integrals of a solution over the spatial domain with weights. The problem is reduced to an operator equation of the Volterra-type. The existence and uniqueness theorem for solutions to this inverse problem is established in Sobolev spaces. A solution is regular, i. e., all generalized derivatives occuring into the equation exists and are summable to some power. The proof relies on the fixed point theorem and bootstrap arguments. Stability estimates for solutions are also given. The solvability conditions are close to necessary conditions.
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Investigation of the diffraction of a focused Gaussian beam by a half-plane near the beam waist
Статья научная
Diffraction of a focused Gaussian beam in the vicinity of the waist region at the edge of the screen is considered on the basis of numerical simulation and experimental investigation. The Gaussian beam propagation has been simulated on the basis of the Helmholtz equation solution by the spectral method. The diffraction of coherent laser radiation (wavelength of 0,63 μm) at the edge of a rectangular screen overlapping half the beam in the transverse direction has been analyzed experimentally. The laser beam is focused by the lens of focal length of 4 cm. A dependence of the diffraction pattern on the screen position relative to the focal waist position is observed. It is found that if the screen is located at distances less than the focal length, then the diffraction pattern is observed in the dark region and represents a semicircle with diffraction fringes. If the screen is placed in the waist region, then the diffraction pattern becomes symmetrical with respect to the screen edge, and if the screen is located at a distance greater than the focal length, then the diffraction pattern is observed in bright area with the diffraction fringes appearing on the other side. The results can be used for the accurate determination of the focused Gaussian beams waist position.
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Making investment decisions in an industrial enterprise under uncertainty
Статья научная
The article is devoted to the issue of selecting investment projects for the modernization of an industrial enterprise in the conditions of uncertainty. Uncertainty in this work is understood as the lack of data on the likelihood of the implementation of scenarios of alternative investment projects. As a methodological base, a set of generally accepted quantitative criteria for reducing uncertainty is proposed, which is characterized by different attitudes towards the probability of future events (pessimistic, optimistic, neutral, etc.). Additionally, a criterion is selected that combines expert and quantitative assessment of uncertainty. Practical calculations are made according to five criteria for three scenarios of five investment projects of an industrial enterprise. The aim of this work is to assess the difficulty of making unambiguous investment decisions under conditions of uncertainty. As a result, each of the four quantitative criteria has pointed to a different project. The fifth criterion has made it possible to limit the range of choice to two projects. This has confirmed the conclusions that making investment decisions requires the responsible person to use not only quantitative indicators, but also existing experience and intuition. The reliability of the findings has been confirmed by the use of generally accepted models and methods, as well as the practical implementation of the results. It is recommended to use these results in the scientific community when conducting subsequent methodological studies aimed at reducing uncertainty, as well as to business owners and investors when making strategic decisions.
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Статья научная
The work is the continuation of the authors' work on the simulation of the structure of the society by the method of random graphs generation. In their previous works, the authors experimentally proved that the social graph has a strict orientation of the information direction propagation from the shares of the graph with high bonds density to the graph parts having a lower bond density. The authors proposed a method for determining the orientation of the social graph by investigating the ratio of the number of outgoing links to the incoming ones. This method found its application in the analysis of postal mailing, but it turned out to be practically inapplicable in the analysis of social networks, since the counting of incoming and outgoing communications required the compilation of the announced social graphs which was a time-consuming and computational resources task that does not have a solution for polynomial time at present. Since the issue of the social networks analysis is not only of a strictly scientific, but also of a practical interest, the authors developed and tested a technique for determining the orientation of social graphs by the method of analyzing the numerical characteristics of a graph. The new method does not require a detailed analysis of the correspondence of users of social networks, but operates with open user information that is a list of friends (Friend List). The ultimate goal of this work is to develop simple and effective methods for analyzing social networks to identify “opinion leaders”, ways of disseminating information, including propagandizing deviant and dependent forms of behavior, identifying anti-systems and separate closed network communities, and general monitoring of the state of social systems.
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Methods of speech and text databases development for QA-systems
Статья научная
The paper is devoted to the problems of question-answer systems development (QA-systems). The subject of the study is discussion of approaches to the automatic filling of the database of the QA-system based on the analysis of the unstructured text sources currently available in the public domain of the Internet. The analysis reveals that the following ways of implementing QA-systems are distinguished: based on inference for ontologies, rules and syntax, using artificial neural networks. The methods for automatically search of question-answer pairs based on the structure of sentences and on the basis of associative-ontological analysis has been developed and tested in the research. The method based on the analysis of the structure of sentences is effective for texts such as lists of frequently asked questions (FAQ), as well as literature texts containing dialogs, direct speech, based on preliminary processing of the text, expressed in the form of a heuristic rule. The method based on associative-ontological analysis is focused to the class of reference and dictionary texts and is based on the assumption that in the descriptive text there is a sentence (or a group of sentences) containing the main idea of the text. In this case, the title of the text can be considered a question, and this sentence (or a group of sentences) is the answer. We need to make the selection of meaning-generating sentences due to the semantic reduction of the text automation. For this purpose, algorithms of self-referencing are applied based on the associative-ontological approach to the processing of texts in natural language. For the experimental verification of the possibility of creating an open QA-system based on the automatic collection of question-answer pairs from the Internet, a prototype of a collection module for the database of the QA-system has been developed.
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Статья научная
The article is devoted to the study of the morphology of the phase space of a degenerate two-component mathematical model of a nerve impulse propagation in the membrane shell. A mathematical model is studied in the case when the parameter at the time derivative of the component responsible for the dynamics of the membrane potential is equal to zero, and the theorem about the fact that the phase space is simple in this case is proved. A mathematical model is also considered in the case when the parameter at the time derivative of the component responsible for the ion currents is equal to zero, and the theorem on the presence of singularities of Whitney assemblies is proved. Based on the results obtained, the phase space of the mathematical model is constructed in the case when the parameters at the time derivative of both components of the system are equal to zero. The author gives examples of the construction of the phase space, illustrating the presence of features in the phase space of the studied problems based on the Galerkin method.
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Non-classical equations of mathematical physics. Linear Sobolev type equations of higher order
Статья научная
The article presents the review of authors' results in the field of non-classical equations of mathematical physics. The theory of Sobolev-type equations of higher order is introduced. The idea is based on generalization of degenerate operator semigroups theory in case of the following equations: decomposition of spaces, splitting of operators' actions, the construction of propagators and phase spaces for a homogeneous equation, as well as the set of valid initial values for the inhomogeneous equation. The author uses a proven phase space technology for solving Sobolev type equations consisting of reduction of a singular equation to a regular one defined on some subspace of initial space. However, unlike the first order equations, there is an extra condition that guarantees the existence of the phase space. There are some examples where the initial conditions should match together if the extra condition can't be fulfilled to solve the Cauchy problem. The reduction of nonclassical equations of mathematical physics to the initial problems for abstract Sobolev type equations of high order is conducted and justified.
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