Faculty of Physics
M.V.Lomonosov Moscow State University

# Issue 4, 2017

Biochemical Physics and Medical Physics

## Photon radiation quality factor energy dependence for personal dose equivalent calculation}

### A. V. Belousov$^1$, G. A. Krusanov$^{1,2}$, A. P. Chernyeav$^{1,2}$

Memoirs of the Faculty of Physics 2017. N 4.

Using the Monte Carlo computer simulation (Geant4 code), the energy dependence of the personal dose equivalent $H_p(0.07), H_p(3), H_p(10)$ of photon radiation with energies up to 40 MeV in water phantom was estimated. To estimate the energy dependence of $H_p$, the calculation of linear energy transfer (LET) averaged by dose of all types of secondary particles in a thin layer of a sensitive detector located at depths of 0.07, 3 and 10 mm, respectively, is performed. It is shown that in the given range of photon energies, the quality factor equal to the ratio $H_p / D$, where $D$ is the absorbed dose, can differ significantly from the value recommended for photons of all energies equal to unity. The main reason for the increase in the quality factor is due to the large contribution of photonuclear reaction products.

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Mathematical Physics

## Exact Solution for Hyperbolic Heat Equation and for Guyer–Krumhansl Type Equation

### K. V. Zhukovsky

Memoirs of the Faculty of Physics 2017. N 4.

The heat transfer in the mathematical framework of the Guyer–Krumhansl model is studied. Exact analytical one-dimensional solution for Guyer–Krumhansl equation is obtained The operational approach is employed. With its help the propagation of various pulses of heat in the medium is studied with account for phonon and ballistic heat transport. The obtained results are used for modelling heat transfer in ultra-thin films with account for molecular effects in systems with reduced dimensions. We model propagation of ultra short laser heat pulses and propagation of isolated smooth spatial heat waves with account for the Knudsen . The solution for periodic function is obtained. The exact solutions of the above problems are studied in the model of thin films; the maximum principle and the non-negativity of the solutions are discussed in the context of heat conduction.

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## Nonmonotonicity of FDTD scheme in modeling of dielectric interfaces

### Z. O. Dombrovskaya, A. N. Bogolubov

Memoirs of the Faculty of Physics 2017. N 4.

It is shown that Yee’s scheme of the FDTD method is nonmonotonous. It is demonstrated that for modeling of dielectric layered medium, the actual order of calculations accuracy is reduced to the first. To increase the accuracy, we suggest to carry out computations on thickening grids according to the Richardson-Kalitkin method. As a test problem, the propagation of a Gaussian pulse through a silicon plate placed in the air is considered. Computations are performed with increasing the order of accuracy up to the fourth.

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## Singularities waveguide electromagnetic field in vicinities of silent points

### I. E. Mogilevskiy, A. N. Bogolubov

Memoirs of the Faculty of Physics 2017. N 4.

An asymptotic representation of the inhomogeneous in cross-section waveguide system electromagnetic field in the vicinity of metal-dielectric wedge edge is constructed. It is shown that the longitudinal component is bounded in the neighborhood of the corner point, and its derivative has a power singularity.

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## A method of the study of singularly perturbed differential equations

### E. E. Bukzhalev

Memoirs of the Faculty of Physics 2017. N 4.

We propose an iterative approach to singularly perturbed differential equations. With this approach we construct a sequence that converges (both in the asymptotic and in the usual sense) to the solution to the Cauchy problem for a singularly perturbed first-order weakly nonlinear differential equation with two small parameters. The proof of convergence of the sequence constructed is based on the Banach fixed-point theorem for a contraction mapping, and the estimate of the contraction coefficient allows one to estimate the rate of convergence of the sequence. This sequence can be used for justification of the asymptotics obtained by other asymptotic methods.

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## Mathematical model of periodic waveguide systems with rectangular cross-section

### M. I. Svetkin, A. N. Bogolubov, A. I. Erokhin, V. M. Pikunov

Memoirs of the Faculty of Physics 2017. N 4.

A mathematical model of an ideally conducting periodic waveguide system with piecewise constant rectangular cross-section is proposed. This type of geometry is finding application in the development of terahertz devices more often recently. The problem to solve is a system of Maxwell equations supplemented by metal boundary conditions and Floquet conditions on cross-sections spaced by one period of the structure. The solution of the problem is based on incomplete Galerkin's method and projection field conjunction in the region of cross-sections jumps. Direct use of this approach leads to matrix problems with ill-conditioned matrices due to simultaneous presence of exponentially increasing and decreasing matrix coefficients. In this context the method to be proposed additionally takes into account the directions of wave propagation in any regular section in the system, which makes it possible to eliminate exponentially increasing elements and make the matrices well-conditioned. Internal wave reflections occurring within the considering period of the system are taken into account explicitly. Based on the proposed model the dispersion characteristics of various structures are constructed. The convergence of the method to the limiting cases is investigated.

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Method of teaching

## Modern physics in the course "History and methodology of physics"

### P. N. Nikolaev

Memoirs of the Faculty of Physics 2017. N 4.

The principles of the construction the exposition of the modern physics in the course "History and methodology of physics" is investigated. The causal link between the state of modern physics and the content of the course "History and the methodology of physics" has been noted.

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## Dynamics of academic performance of the 1st and 2nd year groups of students at the Faculty of Physics according to the results of computer testing and examinations

### M. A. Terentyev

Memoirs of the Faculty of Physics 2017. N 4.

We present data on the dynamics of academic performance of the 1st and 2nd year groups of students during the fall semester of the 2016/2017 academic year, and compare the progress of groups in some of the disciplines studied. The data were obtained on the basis of the results of computer testing in the relevant disciplines, conducted at the Center for Education Quality Control at the Faculty of Physics, as well as the results of examinations.

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Physics of the Earth

## Application of the signals of COMPASS/BeiDou geostationary satellites for the studies of ionospheric effects of geomagnetic storms and sudden stratospheric warmings

### G. A. Kurbatov$^1$, E. A. Kozlovtseva$^1$, A. S. Yasyukevich$^2$, Yu. V. Yasyukevich$^2$, A. M. Padokhin$^1$

Memoirs of the Faculty of Physics 2017. N 4.

We consider ionospheric effects of strong (G3) geomagnetic storm of the end of May, 2017 and sudden stratospheric warming events of 2015-2016 winter season and discuss the possibilities of using the signals of COMPASS/BeiDou geostationary satellites for studing ionospheric variability caused by different geomagnetic and meteorological disturbing factors.

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## Applicability of long-wave approximation to the description of tsunami dynamics

### M. A. Nosov

Memoirs of the Faculty of Physics 2017. N 4.

The quantitative criteria defining areas of applicability of the equations of a shallow water theory and the Boussinesq equations at simulation of tsunami dynamics are presented. Approach to use of the received criteria in practice is described.

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## Generation of free gravity waves in the ocean by packet of surface seismic waves

### K. A. Sementsov$^1$, S. V. Kolesov$^1$, M. A. Nosov$^{1,2}$, V. A. Karpov$^1$, H. H. Matsumoto$^3$, Y. Y. Kaneda$^4$

Memoirs of the Faculty of Physics 2017. N 4.

Generation of free gravity waves in the ocean by surface seismic waves is examined with use of numerical simulation by example of the 2011 Tohoku earthquake. Results of numerical simulation are in a good agreement with the records of deep-ocean stations DONET. It is shown, that ocean-bottom oscillations during the passage of low-frequency surface seismic waves play the key role in free gravity waves generation whereas the role of residual deformation is negligible.

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## Storm waves in ocean

### N. K. Shelkovnikov

Memoirs of the Faculty of Physics 2017. N 4.

A study of the formation of solitary waves and wave trains was made in a ring aero-hydrochannel. It is shown that with increasing wind speed in deep water conditions, wave trains are formed in the aerobasin, and solitary waves are observed only in shallow water.

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Optics and laser physics

## Anisotropic micro- and nanostructuring of amorphous silicon films by femtosecond laser pulses

### S. V. Zabotnov$^1$, A. G. Kazansky$^1$, P. K. Kashkarov$^1$, A. V. Pavlikov$^1$, D. E. Presnov$^{1,2}$, I. A. Romanov$^3$, D. V. Shuleiko$^1$

Memoirs of the Faculty of Physics 2017. N 4.

In this paper it was shown that irradiation of amorphous hydrogenated silicon films by femtosecond laser pulses (1.25 μm) leads to formation of a one-dimensional surface relief with 1.20 ± 0.02 μm period. Orientation of the formed structures is determined by polarization vector of the radiation used and the total exposure dose. Nanocrystalline silicon phase with volume fraction from 40 to 67% is detected in the irradiated films, according to the analysis of Raman spectra. Observed micro- and nanostructuring processes are due to surface plasmon-polariton excitation and near-surface region nanocrystallisation, respectively, caused by high-power femtosecond laser pulses. Also, after the laser treatment with a large exposure dose, the formation of Si-III and Si-XII silicon polymorphous modifications was observed. The conductivity of the film increased by 3 orders of magnitude after femtosecond laser nanocrystallization compared to the untreated amorphous surface. The conductivity anisotropy of the irradiated regions was also observed due to the non-uniform intensity distribution in the laser beam cross-section and depolarizing effect of the surface structure.

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## Influence of structural features of fractal system approximants on their optical properties

### Yu. V. Ryzhikova$^1$, P. V. Korolenko$^1$, S. B. Ryzhikov$^2$

Memoirs of the Faculty of Physics 2017. N 4.

Optical characteristics of approximants of aperiodic gratings and multilayer systems with different geometries and fractal features are considered. Equivalence of optical characteristics of approximants of Fibonacci structures formed by projection and block methods is shown.

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Applied Mathematics and Mathematical Modeling

## The results of recording the quadrature components of the signal by means of the ground measuring complex of installation of coherent sounding in the short-wave range of radio waves at the test site of the Moscow State University

### S. Yu. Belov

Memoirs of the Faculty of Physics 2017. N 4.

The problem of remote diagnostics of a "rough" earth's surface and dielectric subsurface structures in the shortwave radio wave band is considered. A new incoherent method for estimating the signal-to-noise parameter is proposed. Specification was carried out for the ionospheric case. This range makes it possible to diagnose a subsurface layer of the earth, since the scattering parameter is also formed by inhomogeneities in the dielectric permeability of subsurface structures. By using this method in the organization of monitoring sounding, it is possible to identify the areas of variation of these media, for example, for assessing seismic hazard, hazardous natural phenomena, changes in ecosystems, and also for some extreme events of anthropogenic nature. Also, these techniques can be used to develop a system for monitoring, monitoring and forecasting emergencies of natural and man-made nature, as well as for assessing the risks of emergencies. The idea of the method for determining this parameter is that, by having synchronous information about a wave reflected from the ionosphere and about a wave reflected from the earth and the ionosphere (or having passed the ionosphere twice when probing from a satellite), it is possible to extract information about the scattering parameter. The paper presents the results of recording the quadrature components of the signal by means of the ground measuring complex of installation of coherent sounding in the short-wave range of radio waves at the test site of the Moscow State University (Moscow). A comparative analysis is performed and it is shown that according to the analytical (relative) accuracy of the definition of this parameter the new method is an order of magnitude larger than the widely used standard method. An analysis of the analytical errors in estimating this parameter allowed us to recommend a new method instead of the standard one.

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

### L. V. Borodachev

Memoirs of the Faculty of Physics 2017. N 4.

A reduced Vlasov-Darwin model is formulated in a compact Hamiltonian representation. A discrete (by the particles method) Lagrangian-Hamiltonian algorithm is constructed. An applied plasma code, adapted to mass PCs of an average perfomance was developed. Numerical algorithm was approbated during the research of the parametric instability of a magnetoactive plasma.

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## Direct and Backward Waves Propagation in Anisotropic Filled Waveguides

### A. L. Delitsyn$^{1,2}$

Memoirs of the Faculty of Physics 2017. N 4.

The effect of transformation of direct to backward waves in the waveguide with anisotropic filling is considered. The dependence of dispersion curves from anisotropic parameters is investigated. It is proved that the curve of special points is ellipse.

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## The MHD model of high-latitudinal current sheet in the heliosphere

### K. R. Anatolevich

Memoirs of the Faculty of Physics 2017. N 4.

It is developed an analytical MHD model of quasi-stationary conic-like current sheet (magnetic “tube”), which was detected by Ulysses over the South pole of the Sun. We can describe the main features of the observed structure in frame of stationary one-fluid MHD model: the sharp increase of the magnetic field compared to the surrounding magnetic field of solar wind, the sharp increases of plasma concentration, electric field, temperature, and drops in value of solar wind speed and plasma beta.

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## Modelling of quasi-adiabatic plasma dynamic in current sheets in the solar wind

### V. Yu. Popov$^1$, H. V. Malova$^2$, E. E. Grigorenko$^3$, O. V. Khabarova$^4$, L. M. Zeleny$^3$, A. A. Petrukovich$^3$

Memoirs of the Faculty of Physics 2017. N 4.

The quasi-adiabatic dynamics of charged particles in strong current sheets (SCS) in the solar wind (SW), including the heliospheric current sheet (HCS), is modeling. A self-consistent hybrid model in which the ion dynamics is described as the quasi-adiabatic approach, and the motion of magnetized electrons is considered in the leading center approximation is developed. The simulation showed that the SCS profile is determined by the relative contribution of the current of demagnetized protons on open quasi-adiabatic orbits and by the drift current of magnetized electrons. It is shown that a multiscale structure, which is a thin current sheet (TCS), embedded in a thicker plasma sheet (PS), is a universal feature of SCS in SW. These results are in good agreement with the observations of the SCS.

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## Morphological methods of image analysis and their applications

### A. I. Chulichkov, O. V. Falomkina, Yu. P. Pytyev, A. V. Zubjuk

Memoirs of the Faculty of Physics 2017. N 4.

The paper contains a brief overview of the methods of morphological image analysis. The mathematical models of signal (image) shapes are formulated, particularly, the models that incorporate subjective judgments of a researcher. The mathematical methods and the numerical algorithms for calculating the measures of proximity of signal (image) shapes based on the oblique projection technique are described. Some applications of the methods of morphological image analysis to the real-wold problems are considered.

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## Analysis of information search capabilities in physics: the problem of internet searching on the example of acoustics

### V. G. Shamaev$^1$, A. B. Gorshkov$^2$, L. G. Guschina$^3$, V. I. Yakimenko$^4$

Memoirs of the Faculty of Physics 2017. N 4.

Problems of online access to scientific information are discussed. Brief information on foreign information retrieval systems is given. The state of information support for Russian-language sources in the USSR and now is described. The absence of a single center for collecting and providing information on Russian-language scientific publications is noted. A scheme is proposed for use in the creation of such a center. A possible cluster of this center is described on the example of acoustic topics, already implemented at the Acoustics Department of the Physics Department of the M.V. Lomonosov Moscow State University. The corresponding portal «Acoustics» (http://akdata.ru) is in the public domain on the Internet. Entrance points of the portal: full-text archive of «Acoustic Journal», «Signaling information» on acoustics and «Information retrieval system. Acoustics. Russian-language sources». Brief description of the work with the system is provided. The developed technologies for the preparation of information resources and the resources themselves constitute a complete system of information support for acoustic research in the Russian-speaking segment. They also make it possible to provide a full reflection of the Russian-language scientific literature for monitoring and expert evaluation of the scientific activities of Russian scientists, which can contribute to strengthening the positive image of Russian sci-ence in the world. Questions of priority and preservation of intellectual property are being raised. It is concluded that only properly organized information support can guarantee the pu-rity and novelty of the scientific results that underlie the research process.

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## Nonlinear elastic phenomena in the propagation of acoustic waves on a flat rough boundary of solid

### N. V. Shirgina, A. I. Kokshayskiy, A. I. Korobov

Memoirs of the Faculty of Physics 2017. N 4.

The paper presents the results of experimental studies of the effect of static pressure applied to the flat rough boundary of two solid materials on its nonlinear elastic properties. The investigations were carried out by the spectral method on the efficiency of generation of higher acoustic harmonics that were caused by a longitudinal elastic wave passes through the boundary and when a surface acoustic wave propagates along the boundary of two solid bodies. The experimentally determined power law dependence of the higher acoustic harmonics on the amplitude of the first acoustic harmonic was significantly different from the classical values for these harmonics. According to the measured amplitudes of the first and second harmonics of the surface acoustic wave passing along the boundary, a second-order nonlinear acoustic parameter was calculated as a function of the external pressure applied to the sample. It is found that the nonlinear parameter of the SAW does not depend monotonically on the pressure at the boundary. An analysis of the experimental results was carried out on the basis of a nonclassical acoustic nonlinearity.

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Theoretical Physics

## Gamma metrics with the Newman-Unty-Tamburino parameter

### D. V. Gal’tsov, K. V. Kobialko

Memoirs of the Faculty of Physics 2017. N 4.

In this paper we study some geometric and physical characteristics of new gamma metrics with the Newman-Unti-Tamburino parameter. The mass and angular momentum of singularity and Mizner's strings, the properties of time-like geodesics, including the appearance of geodesic chaos, the appearance of the horizon at δ = 2 are determined.

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## Account for the CP-violation in the exponential parameterization of neutrino mixing

### K. V. Zhukovsky

Memoirs of the Faculty of Physics 2017. N 4.

The exponential parameterization of the neutrino mixing is studied; it allows distinguishing of pure rotational part of the mixing matrix and of the part, in charge of the CP-violation. The logarithm of the mixing matrix is computed. Based on the last experimental data on the neutrino mixing, the exact values of the parameters of the exponential neutrino mixing matrix are calculated. The real part, corresponding the real rotation in space, and the imaginary part, corresponding CP-violation and rotation around the axis with imaginary coordinates, are distinguished. Factorization of the mixing matrix is demonstrated in the form of two rotations around real and imaginary axes. The complementarity hypothesis is confirmed.

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## Neutrino oscillations in homogeneous moving medium

### A. E. Lobanov, A. V. Chukhnova

Memoirs of the Faculty of Physics 2017. N 4.

We obtain the probabilities of the spin-flavor transitions in unpolarized moving matter in the two-flavor model using the solution of the quasi-classical equation, which describes both neutrino flavor oscillations and its spin rotation. Neutrino spin behaviour is investigated taking into account neutrino flavor oscillations.

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## Methods of accelerated convergence in statistical physics

### P. N. Nikolaev

Memoirs of the Faculty of Physics 2017. N 4.

In the work the classification of the methods of accelerated convergence used in statistical physics is given. Among them a combined method using physical analysis of the system and mathematical methods of accelerated convergence is picked out. Its effectiveness is shown for obtaining the Carnahan-Starling equation. The proposed method is of a general nature and is applicable to a wide class of systems.

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Condensed matter physics

## Peculiarities of dielectric properties of proton conducting (K$_{0.3}$(NH$_{4}$)$_{0.7}$)$_3$H(SO$_4$)$_2$ single crystals (to discussion of negative dielectric permittivity)

### N. D. Gavrilova$^1$, I. A. Malyshkina$^1$, V. K. Novik$^2$, E. V. Selezneva$^3$, I. P. Makarova$^3$

Memoirs of the Faculty of Physics 2017. N 4.

On the example of superprotonic crystal (K$_{0.3}$(NH$_{4}$)$_{0.7}$)$_3$H(SO$_4$)$_2$, a first attempt was made to detect, by means of dielectric investigations, the presence of structure elements in the material, which are devoid of elastic bonds or having loosen bonds with crystal matrix. It was shown that it is possible to separate contributions from structure elements with elastic bonds, which are devoid of elastic bonds or having loosen bonds in comparison with influence of measuring field. A supposition was stated about sequence of physical mechanisms which determine the reaction of quasi-free structure elements on the growth of measuring field.

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## Influence of the reactive atmosphere during magnetron sputtering on evolution of the phase composition of diamond-like coatings doped with chromium

### I. S. Levin$^{1,2}$, V. M. Avdyukhina$^1$, M. M. Khrushchov$^2$, V. A. Schergunov$^2$

Memoirs of the Faculty of Physics 2017. N 4.

In the work, samples of diamond-like carbon coatings doped with chromium, obtained with the help of magnetron sputtering technology in active gas media, were investigated. The influence of the features of coating deposition (first of all, the composition of the sputtering atmosphere) on their phase composition and the fine atomic structure was studied. X-ray diffractometry was used as the main research method.

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## The extension of the software package for the calculation of the crystallographic characteristics of martensite transformations

### A. G. Khundjua$^1$, B. A. Volodin$^2$, E. A. Brovkina$^1$, M. M. Melnikov$^1$

Memoirs of the Faculty of Physics 2017. N 4.

In the paper the extension of the software package for the simulation of diffraction patterns and determination of crystallographic characteristics of alloys with martensite transformations is presented. The block of calculation of martensite crystals habitus planes using ellipsoid of homogeneous deformation is added.

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