Vol 31, No 6 (2023)

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Purpose of this work is to use analytical and numerical methods to consider the problem of the structure and dynamics of the kinks in the sine-Gordon model with “impurities” (or spatial inhomogeneity of the periodic potential). Methods. Using the method of collective variables for the case of three identical point impurities located at the same distance from each other, a system of differential equations is obtained. Resulting system of equations makes it possible to describe the dynamics of the kink taking into account the excitation of localized waves on impurities. To analyze the dynamics of the kink in the case of extended impurities, a numerical finite difference method with an explicit integration scheme was applied. Frequency analysis of kink oscillations and localized waves calculated numerically was performed using a discrete Fourier transform. Results. For the kink dynamics, taking into account the excitation of oscillations in modes, a system of equations for the coordinate of the kink center and the amplitudes of waves localized on impurities is obtained and investigated. Significant differences are observed in the dynamics of the kink when interacting with a repulsive and attractive impurity. The dynamics of the kink in a model with three identical extended impurities, taking into account possible resonant effects, was solved numerically. It is established that the found scenarios of kink dynamics for an extended rectangular impurity are qualitatively similar to the scenarios obtained for a point impurity described using a delta function. All possible scenarios of kink dynamics were determined and described taking into account resonant effects. Conclusion. The analysis of the influence of system parameters and initial conditions on possible scenarios of kink dynamics is carried out. Critical and resonant kink velocities are found as functions of the impurity parameters.

The purpose of this work is the study of design of new short-circuited coaxial transducer with thin linear jumper, that circuits on one side of the grounded coaxial cylinder, located above the rectangular iron-yttrium garnet (YIG) film, in homogeneous constant magnetic field with rectangular film along its length or width. The thin linear jumper is directed parallel to the width of the YIG film. Methods. In the CST Microwave Studio environment, an electrodynamic analysis of the model was carried out using the finite element method. To study the efficiency of modes excitation in a ferrite film at different distances between the coaxial transducer and the surface of the YIG film, the frequency dependences of the inverse losses S11 of the model were calculated. Results. 1. The identification of modes in a homogeneous static magnetic field H , directed parallel to the plane of a rectangular YIG film along its width (z-axis) was carried out. 2. The identification of modes in a homogeneous static magnetic field H directed parallel to the plane of the rectangular YIG film along its length (y-axis) was carried out. 3. A comparison of modes spectra was made at H, directed parallel to the plane of the YIG film along its width (z-axis) and length (y-axis). Conclusion. In this paper short-circuited transducer with a thin linear jumper, circuited on one side of the grounded coaxial cylinder, is investigated. By the electrodynamic method distributions of high-frequency magnetic field of the excited magnetostatic modes were calculated and their identification was carried out for two directions of homogeneous static magnetic field H: along width and along length of rectangular YIG film. The dependence of number of excited modes on the distance between a short-circuited transducer and rectangular YIG was also studied. A comparison of modes spectra is carried out at H, directed parallel to the plane of the YIG film along its width and length. With this rotation of vector, the band of effectively excitable modes shifts from 4.6...4.9 GHz to 4.5...4.75 GHz. However, the excitation of these modes in the case of the vector H, directed along the width of YIG film (z-axis), is much more effective in the band 4.65...4.9 GHz than in the case when this vector is directed along the length of YIG film (y-axis). At the same time, excitation of these modes in the case of the vector H, directed along the length of YIG film (y-axis) is effective in the band 4.4...4.6 GHz.

The purpose of this work is to study the collective dynamics of a neural network consisting of excitatory and inhibitory populations. The method of reducing the network dynamics to new generation neural mass models is used, and a bifurcation analysis of the model is carried out. As a result the conditions and mechanisms for the emergence of various modes of network collective activity are described, including collective oscillations, multistability of various types, and chaotic collective dynamics. Conclusion. The low-dimensional reduced model is an effective tool for studying the essential patterns of collective dynamics in large-scale neural networks. At the same time, the analysis also allows us to elicit more subtle effects, such as the emergence of synchrony clusters in the network and the shifting effect for the boundaries of the existence of dynamical modes.

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