Faculty of Physics
M.V.Lomonosov Moscow State University

# Issue 5, 2019

Acoustics and acoustooptics

## Numerical modeling, visualization, and counting of the velocity of shear waves in soft biological tissues

### A. A. Lisin, S. N. Gurbatov, I. Yu. Demin, A. E. Spivak

Memoirs of the Faculty of Physics 2019. N 5.

This article focuses on the use of the Westervelt equation for solving problems in a medical application. A numerical simulation of the ultrasonic wave propagation in space, close to soft biological tissues was carried out, the SWEI mode of operation was modeled, and the shear wave velocity was obtained for media repeating calibrated CIRS phantoms based on the simulation results. The results were compared with the results on the Verasonics research system.

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## Supersonic Shear Imaging: description and implementation of the method on Verasonics research system

### A. E. Spivak, I. Yu. Demin, A. A. Lisin, A. E. Simonov

Memoirs of the Faculty of Physics 2019. N 5.

The work describes the method of shear wave elastography Supersonic Shear Imaging. A scheme for implementing this method on the Verasonics research system and an algorithm for processing and outputting data in the form of an elasticity map are presented. Physical modeling was carried out with a CIRS model 049 elasticity phantom on the Verasonics research system using SSI and SWEI methods, and on the Supersonic Aixplorer ultrasound system. The results were compared and conclusions were drawn about the quality of the method for the research system.

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Wave processes in inhomogeneous media

## On the drift properties of the Stokes wave packet propagating along an electrically charged interface between liquid media

### A. A. Ochirov, D. F. Belonozhko

Memoirs of the Faculty of Physics 2019. N 5.

The analytical asymptotical expretions of velocity of drift flow and expressions for trajectories of individual liquid particles are derived for system of two immiscible liquids shifting with relate to each other along the electrically charged interface with the Stokes's wave paket propogating along the interface.

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Mathematical modeling in radiophysics and optics

## On the modelling and analysis of using a cylindrical jet of fluid as an antenna element

### A. A. Ochirov, T. K. Artyomova, S. V. Khodyrev

Memoirs of the Faculty of Physics 2019. N 5.

A mathematical model of an antenna element made of a cylindrical jet of liquid is considered. The effect of capillary jet decay on the surface shape and, as a consequence, on the gain and directivity characteristics of the antenna is considered. Asymptotic analytical expressions are obtained for the surface shape without taking into account the influence of the electromagnetic field.

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## Modified Hamiltonian algorithm for discrete reduced Vlasov-Darwin model.

### L. V. Borodachev$^1$, S. S. Annenkov$^{1,2}$

Memoirs of the Faculty of Physics 2019. N 5.

Based on the conjugation of dynamic schemes, an approach is proposed for optimizing the procedure for solving the equations of motion of particles in a self-consistent model of a rarefied plasma. The technique was tested in the framework of the discrete Darwin algorithm on the problem of modeling Waibel instability.

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Metamaterials and photonic crystals

## Guided modes in periodic planar system of metal cylinders

### A. A. Anastasiev$^1$, M. I. Gozman$^2$, I. Y. Polishchuk$^{1,2}$, Yu. I. Polishchuk$^{1,2}$, E. A. Tsyvkunova$^3$

Memoirs of the Faculty of Physics 2019. N 5.

Guided modes in periodic systems consisting of silver cylinders are studied. Elementary cell in such systems comprise several identical guides. We employ multiple scattering formalism based on exact solution of Maxwell's equations for single waveguide problem. We also engage the technique that utilizes the transformation of sattice sums into fast convergent series. This method greatly increases the accuracy of calculations and sufficiently optimizes time cost of numerical simulations. It is shown that under the condition of nonzero propagetion constant these systems possess lcosely located guided modes. The number of these modes equals to the number of cylinders inside one elementary cell. The frequency of these modes decreases as quasi-wave vector runs over the Brillouin zone and approaches its edge. The modes are shifted towards high frequency region as propagation constant value increases thus allowing the modes to be found in near infrared or even visible part of the spectrum. It is also possible to simultaneously match the quasi-wave number and the frequency of dispersion curves in zigzag-shaped waveguide systems.

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## The effect of the structure on the optical properties of epicular blue spruce wax (Picea pungens)

### E. R. Bukhanov$^1$, A. V. Shabanov$^1$, M. N. Krakhalev$^1$, M. N. Volochaev$^1$, Yu. L. Gurevich$^2$

Memoirs of the Faculty of Physics 2019. N 5.

The study of morphological and optical characteristics of the epicular wax layer of blue spruce (Picea pungens). The method of scanning electron microscopy revealed structural units - tubes with a diameter of 150-200 nm and a length of 3-5 microns. An iridescence effect from the wax layer domains has been detected. In the reflected light, the domains have a blue color, when observed in transmitted light acquire a pinkish tint. These optical characteristics are the main features of the photonic crystal structure. A numerical simulation of the transmission spectrum with the identified structural optical parameters was carried out using the transfer matrix method. The spectrum of the maximum fluorescence coincides with the defect mode of the calculated transmission spectrum.

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Microwave electronics

## Influence of the Focusing Magnetic Field on the Setup of Terminal Fields in a Relativistic Cherenkov Source

### O. V. Gallyamova$^1$, A. I. Slepkov$^2$, S. V. Khudyakov$^3$

Memoirs of the Faculty of Physics 2019. N 5.

The results of numerical simulation of the interaction of a relativistic electron beam focused by a constant magnetic field with its own steady-state fields in an axisymmetric slowing-down structure of a relativistic Cherenkov source are presented. A theoretical and numerical analysis of the resonant action of a focusing magnetic field has been carried out, and the areas of resonant signal amplification and cyclotron absorption have been investigated. Taking into account the self-consistent interaction of the relativistic beam and the eigenfield of the structure, the influence of the beam parameters on the type of field distribution in the structure at the cyclotron resonance was studied.

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## The steady state oscillations in the generator of the backward wave in the framework of the two-dimensional model

### G. M. Vdovina, A. A. Funtov, A. D. Koval

Memoirs of the Faculty of Physics 2019. N 5.

The processes of establishing steady-state oscillations in the backward wave generator has been considered in the superregenerative mode within the framework of the linear theory. In this case, the electron current exceeds the starting value. In the analysis, a complex frequency is introduced, the imaginary part of which characterizes the increase of oscillations in time. The consideration is carried out in the framework of a two-dimensional model, taking into account the influence of a focusing magnetic field of finite magnitude. In this case, in addition to the longitudinal high-frequency displacements, the appearance of transverse ones is possible in the electron beam. The results are obtained using the method of successive approximations. The conditions for obtaining the characteristic responsible for the wave growth are derived, the dependences of this quantity on the ratio of the electron beam current and the starting current value for various values of the magnetic field are given. Also the dependencies for the time of the establishment of oscillations for different parameters of the system in a linear approximation have been represented. In limiting cases, the results obtained agree well with the well-known results of the one-dimensional theory. The case of cyclotron resonance is considered separately, when only a slow cyclotron wave is excited in the electron beam, which noticeably simplifies the original problem and the initial relations.

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Nonlinear dynamics

## Mutual synchronization of coupled digital phase-locked loops

### E. S. Lutchenkova$^1$, A. R. Safin$^2$, R. S. Kulikov$^1$

Memoirs of the Faculty of Physics 2019. N 5.

There are many artificial neural networks: semiconductors, magnetic, carbon, optical, etc. There are a lot of requirements for the fast operating speed and low power consumption, as well as high stability. Phase systems are good enough to provide required stability and synchronization effects. In addition, phase schemes can be implemented on the basis of different physical principles. In this paper we develop the theory of digital phase locked loop (DPLL) -based neural networks, where a separate neuron is made as a DPLL with a filter. We construct the bifurcation map of a system of coupled DPLL schemes.

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