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 AbstractThe results of 3D – three-dimensional numerical simulation of low-depth vibroseismic sounding of local inhomogeneities in the upper layers of sedimentary strata are presented. The possibilities of developing monitoring and reconstruction of soil parameters, improving methods for diagnosing local anomalies and remote monitoring of underground engineering structures are considered. For this purpose, an analysis of the spatial distribution of acoustic responses – elastic waves scattered by the inhomogeneity of a spherical shape (hollow, water-filled) lying at some depth under the free boundary of the elastic half-space is presented. The analysis uses harmonic and pulse dependence on time in probing parcels created by non-explosive sources of vibrations. When modeling radiation, a model of a radiator in the form of a monopole located under a free surface is used. Registration of scattered wave signals is carried out along the free boundary along the line running from the source point to the removal through the epicenter of the foreign sphere. The spatial distribution of responses by amplitude is demonstrated on graphs and on reliefs in planar and vertical sections. Based on the simulation data of the scattering wave fields, informative signs have been established for the diagnosis of the material and geometric parameters of local inhomogeneities lying in the geo-environment.
Show AbstractKeldysh non-equilibrium diagram technique is used for a detailed description of electronic transport through a system of localized states. Particular attention is paid to the predictive ability of the theory, for which the number of free parameters in the second-quantized Hamiltonian is reduced. The employed formalism accounts for Coulomb interaction and rigorously treats multi-electron effects and the discreteness of the energy spectra of such structures as induced quantum dots, systems of impurity atoms, or charge centers of metal-organic framework polymers. The proposed algorithm for calculating electric currents and occupation numbers of localized states is implemented in software and tested on a model system with two consecutive two-level quantum dots. The calculated volt-ampere characteristic and current stability diagram are intuitively explained using illustrative energy diagrams. The model successfully reproduces typical single-electron effects: resonant tunneling, negative differential resistance, population inversion in a multilevel system, Coulomb correlations and an indirect manifestation of the memory effect.
Show AbstractThe 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 AbstractThis work details the physical and mathematical foundations of an algorithm to determine the optical profile of thin gradient films using the surface plasmon resonance (SPR) method. The algorithm minimizes the discrepancy function, which quantifies the deviation between experimental data and model data of the targeted gradient layer, approximated using a cubic Hermite interpolant known as PCHIP. Powell's method optimization, implemented in Python, determines the optimal coordinates for the spline nodes approximating the gradient optical layer. To enhance stability, accuracy, and search speed, the algorithm operates in three stages. Each stage refines the search area and sets initial parameters for the subsequent stage to align closely with the targeted gradient layer. The algorithm incorporates angle, wavelength, and external environment scan data derived via SPR.
Show AbstractExperimental equipment for determining the impact resistance of composite materials by the method of impact pendulum copra and low-speed ballistic method is described. Two types of polymer nanocomposites have been studied: consisting entirely of epoxy resin reinforced with carbon nanotubes and layered composites of fiberglass and basalt fabric impregnated with epoxy resin reinforced with carbon nanotubes. Measurement methods are proposed.
Show AbstractRecurrent analysis is a good correlation method of processing EEG data of the human brain. It is aimed at identifying links between channels. In particular, the modified recurrent analysis is designed to identify the most significant channels with a certain activity. At the same time, recurrent analysis is a method that strongly depends on frequency. The paper proposes a method for correcting the results obtained by recurrent analysis of the EEG processing of the brain data of the subjects, taking into account the frequency based on the Fourier transform.
Show AbstractThis article discusses the statistical analysis of recurrent indicators calculated for different stages of sleep in three groups of subjects: healthy people, with Parkinson's disease, and with sleep apnea. Statistical analysis included the calculation of recurrent indicators and parameters associated with the estimation of the spread of recurrent indicators for sleep stages compared with the average value for this stage and for the entire night recording. It has been shown that for patients with Parkinson's disease, the spread of the recurrent indicator for the wakefulness stage is extremely large, which makes further analysis difficult, but can be a good biomarker for early recognition of the disease. For apparently healthy subjects and patients with sleep apnea, sleep stages 3 and 4 differ most from the overnight averages, but have the smallest deviations from the average for this stage. Patients with sleep apnea have a higher dispersion for REM sleep compared to healthy subjects.
Show AbstractThe article is devoted to the analysis of hydrogen, helium and calcium emission in spectral lines of the quiescent prominence observed on the horizontal solar equipment HSFA-2 (Ond\u{r}ejov observatory, Astronomical Institute of the Czech Academy of Sciences). After crossing of theoretical and observed fluxes of spectral lines the prominence parameters are derived under the assumption of optically thin continuum and possible self absorbtion in lines. Comparison of 5 lines allow us to find out the parameters of the emitting gas with high validity. Three of four observational moments need to take into account the non-uniform structure of the gas.
Show AbstractThe study of the origin and propagation of cosmic rays in the range from 1 to 1000 PeV is important. A new facility, SPHERE-3, with higher luminosity and better optical resolution, is being developed, based on the experience gained from the operation of the balloon facility SPHERE-2. This paper presents a simulation complex for the generation of Cherenkov light images on the detector mosaic of the SPHERE-3 telescope.
Show AbstractThe subject of consideration is the features of teaching a course on optics of fractal objects for physics students. The classification of fractal objects according to their Fourier spectra is given. The scheme for analyzing fractals in the proposed educational course “Optics of Fractal Objects” is given. The main problems of the fractal optics course are discussed. The analysis of fractal objects is being systematized to obtain a qualitative and quantitative correspondence between the structure of the object being studied and its optical characteristics.
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