Statistical characteristics of the current flowing through semiconductor superlattice, with structure fluctuations
Statistical characteristics of the current flowing through semiconductor superlattice, with structure fluctuations
A. О. Selskii, O. I. Moskalenko, A. A. Koronovskii
The paper investigates how fluctuations in the lattice structure, namely the width of the conducting miniband, affect the current flowing through a semiconductor superlattice. To solve this problem, a numerical calculation model is proposed that makes it possible to calculate the current for random changes in the miniband width in the superlattice layers, both in the case of an inclined magnetic field and without it. In order to evaluate the change in current, two integral characteristics were introduced: one for the shape of the current-voltage characteristic, the second for the amplitude of high-frequency current oscillations. The integral characteristics ranked in ascending order make it possible to approximately approximate the variability of the characteristics of the current flowing through a semiconductor superlattice for various fluctuations of the lattice structure.
Show AbstractA.G. Sveshnikov's works in the numerical methods for the irregular waveguides design
A.G. Sveshnikov's works in the numerical methods for the irregular waveguides design
A. A. Bykov
In a series of works by Professor A.G.Sveshnikov in 1963 a mathematical model of the propagation of electromagnetic waves inside a metal waveguide with a complex shape boundary was formulated. This model is based and substantiated on the modified Galerkin method. Later it was named al the incomplete Galerkin method. The solution of the boundary value problem is presented in the form of a linear combina-tion of coordinate functions of the cross-section, the complete set of which is found from the eigenvalues-eigenvectors-problem inside the cross-section of the waveguide. The coefficients of the linear combination depend on the longitudinal coordinate. They are found from the condition of orthogonality of the discrep-ancy to the system of projection functions. In case of the Galerkin method, the set of the projection func-tions is equal to the set of coordinate functions (also cross-section depended). A boundary value problem for a system of linear ordinary differential equations of the second order is obtained as the result of the application of projection relations of orthogonality and boundary conditions of radiation in infinite re-gions. We show that the method created 60 years ago at the Department of Mathematics of the Faculty of Physics of Moscow State University is still relevant today. The increased capabilities of computers, math-ematical and programming tools make it possible to significantly expand the class of problems that are effectively solved using the incomplete Galerkin method. We present the results of solving one problem of optimizing a waveguide transformer in a loaded waveguide using an incomplete Galerkin method.
Show AbstractFeatures of microstructure of promising Pd-Ru alloy
Features of microstructure of promising Pd-Ru alloy
O. V. Akimova$^1$, A. V. Ovcharov$^2$, N. R. Roshan$^3$
The paper shows features of microstructure of palladium-based membrane alloy, which alloyed with ruthenium content of 6 wt.%. The alloy with such ruthenium content has good strength and hydrogen permeability. Samples for the study are made of metals of high purity (99.9%) and are presented in the work in the form of a membrane-foil with a thickness of 30 mkm and a tube with an outer diameter of 0.9 mm and an inner diameter of 0.1 mm. The study of microstructure features of the samples was carried out in the work by methods: X-ray diffraction (XRD), energy dispersive X-ray spectroscopy (EDRS), and scanning electron microscopy (SEM). X-ray diffraction method established formation of solid substitution solutions with substructure of high degree of homogeneity and nanodispersity. EDRS and SEM methods tested the elemental composition of the samples and their surface morphology. SEM images of the samples’ surface confirmed the high homogeneity and nanodispersity established by X-ray diffraction.
Show AbstractState equations and phase diagrams
State equations and phase diagrams
P. N. Nikolaev
In the paper it is investigated the derivation of the thermodynamic systems equation of state and the calculation of phase diagrams on their basis. The main aspects of this problem, as well as its current state, are analyzed. Analytical and geometric representations of the thermodynamic properties of matter are considered.
Show AbstractOptimizing big data distributed processing: Algebraic foundations and the concept of information
Optimizing big data distributed processing: Algebraic foundations and the concept of information
P. V. Golubtsov
An algebraic formalization of distributed processing of big data is considered. The concept of information space is defined for a given data processing procedure and a criterion for its minimality is established. The existence of a minimal information space is proved, which provides the most compact form of representation of the information contained in the data and allows the most efficient parallelization of data processing. An element of this space describes in a consistent way the information contained in the corresponding data set. It is shown that in terms of the information space, the concepts of information addition and information quality are naturally expressed, reflecting the intuitive idea of the very concept of information. The advantages of using the minimal information space in the MapReduce distributed data processing model are also considered. In the context of this model, Map transforms the original data sets into information space elements, and Reduce combines all these pieces of partial information into a single element representing all the original data. By way of illustration, several examples of data processing procedures are analyzed and the corresponding minimal information spaces are presented.
Show AbstractMultilevel research works of schoolchildren on the celestial mechanics problems implementation
Multilevel research works of schoolchildren on the celestial mechanics problems implementation
S. B. Ryzhikov$^1$, Yu. V. Ryzhikova$^2$
The problem of involving schoolchildren in research activities is considered. The reason for the low schoolchildren motivation is indicated - the first research work results appear only after a few weeks. A methodology for conducting multi-level work is proposed, in which the results are obtained already at the first lesson. An example of such multilevel research work based on the celestial mechanics problems is considered.
Show AbstractHeat capacity of neon, argon, krypton and xenon crystals at high temperatures
Heat capacity of neon, argon, krypton and xenon crystals at high temperatures
P. N. Nikolaev
The heat capacity of rare gas crystals is studied in the paper. For this, the cell-cluster expansion for the free energy is used, taking into account three-particle clusters, inclusive. The self-consistent field approximation is used as the basic approximation. The calculations performed for neon, argon, krypton and xenon showed good agreement between the theoretical results and experimental data. This also applies to regions at normal pressure for krypton and xenon, where the heat capacity at constant volume decreases with increasing temperature.
Show AbstractOn the set of solutions to the Schrodinger equation on the example of the description of water clusters
On the set of solutions to the Schrodinger equation on the example of the description of water clusters
K. E. Plokhotnikov
The article discusses a computational procedure for obtaining all possible solutions to the Schrodinger equation by statistical testing or the Monte Carlo method. Clusters of water, namely hexamer, dodecahedra, and tetradecamer, act as a demonstration quantum system illustrating this procedure. Various solutions of the Schrodinger equation are derived from the computational algorithm proposed by the author earlier, based on the intersection of finite-difference, Monte Carlo approaches, the virial theorem, as well as methods tested on water clusters for spatial information of the scattering centers of particle nuclei and electron scattering centers of an arbitrary quantum system. A variety of information schemes are considered, among them are specially highlighted: single-particle, two-, three-, etc. up to the scheme with maximum partiality. Within the framework of any of the information schemes, the dissociation energy of the quantum system under consideration is consistent, on the one hand, and the positioning of the scattering centers of particle nuclei and electrons, on the other hand. The method of solving the Schrodinger equation proposed earlier by the author by the Monte Carlo method acts as a means of selecting configurations acceptable as solutions. As a result, it turned out to be possible to construct an algorithm for generating an unlimited number of different spatial structures of scattering clouds of particle nuclei and electrons at a given dissociation energy of a quantum system. The computational procedure proposed in this paper allows for a natural generalization for the case of describing an arbitrary quantum system whose elemental composition is known. The procedure is computationally efficient, because it allows parallelization of calculations.
Show AbstractImpact of tensor interaction on the structure of silicon isotopes
Impact of tensor interaction on the structure of silicon isotopes
S. V. Sidorov$^{1,2}$, T. Yu. Tretyakova$^{1,2}$
The influence of the tensor interaction of nucleons on the characteristics of neutron-rich silicon isotopes was studied in this work. Tensor forces are taken into account within the framework of the Hartree-Fock approach with the Skyrme interaction. It is shown that the addition of tensor component of interaction improves the description of the splitting between different single-particle states and leads to a decrease in nucleon-nucleon pairing correlations in silicon nuclei.
Show AbstractStudy of petroleum paraffin and resins by NMR relaxation
Study of petroleum paraffin and resins by NMR relaxation
T. .. Kazbayev, D. S. Ivanov
Due to the complexity of the chemical and molecular composition of oil, it is usually used to identify four main components: asphaltenes, resins, paraffins and oils. According to the accepted methods of GOST 11851085, M 01-12-81 paraffins are extracted not directly from oil as, for example, asphaltenes, but from pre-separated oils. In this study, results of research by NMR of benzene and alcohol-benzene resins extracted from oil according to the standardized procedure of GOST 11858-66 were carried out. It was found that benzene resins show hysteresis in NMR characteristics that is typical of systems with the first order phase transition, while alcoholtobenzene resins show no hysteresis over the temperature range from minus 80 to plus 65 degrees Celsius accurate to the experimental error. It has been suggested that as a result of peculiarities of interaction between resins and paraffins, the paraffins are extracted from oil mainly in the composition of benzene resins.
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