Faculty of Physics
M.V.Lomonosov Moscow State University
Biophysics and medical physics

## Evolution of chaotic dynamics of collective modes as a way of behavioral description of living systems

### V.M. Eskov, V.V. Eskov, J.V. Vochmina, T.V. Gavrilenko

Moscow University Physics Bulletin 2016. 16. N 2. P. 143

Complex and multi-dimensional biological systems possess a unique feature - a continuous, random motion of many components of the state vector (of living) systems x = x(t). Taking this property into consideration causes the denial of any known types of stationary modes (e.g., dx/dt = 0) and requires the revision of chaos. A new approach proposed to the understanding the living systems (as a third paradigm of natural science) and new methods for the study of living systems (as theory of chaos and self-organization). Common grounds of physics and theory of chaos and self- organization are revealed as a generalized uncertainty principle and limits on the parameters of quasi-attractors.

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Theoretical and mathematical physics

## Electromagnetic wave propagation in a medium with defects

### P.I. Pronin, N.Ed. Smirnov

Moscow University Physics Bulletin 2016. 16. N 2. P. 155

The equations of the electromagnetic field in a solid with defects was obtained and found an approximate solution of the wave by the Debye-Rytov

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## A method of constructing trajectory for an unmanned aerial vehicle in the city

### O.O. Tsaryova, V.Y. Popov, D.N. Suzansky

Moscow University Physics Bulletin 2016. 16. N 2. P. 161

A synthesis method of reference trajectory for unmanned aerial vehicle, which flies around of obstacles of urban buildings in horizontal and vertical planes, is proposed. To solve this problem for the first time a conformal mapping is constructed for a collection of rectangles approximating the obstacles on the digital map of the terrain.

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## Vacuum polarization in the model of Dirac fermions with anomalous magnetic moment interacting with background axial-vector condensate and magnetic field

### A.F. Bubnov, N.V. Gubina, V.Ch. Zhukovsky

Moscow University Physics Bulletin 2016. 16. N 2. P. 168

In this paper, we consider vacuum polarization in the model of Dirac fermions with anomalous magnetic moment and axial-vector interaction term in a uniform magnetic field. Quadratic corrections from the anomalous moment and axial-vector term are calculated with account for various configurations of parameters of the model.

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## A Neural-Network Method for the Synthesis of Informative Features for the Classification of Signal Sources in Cognitive Radio Systems

### S. S. Adjemov$^1$, N. V. Klenov$^{1,2}$, M. V. Tereshonok$^1$, D. S. Chirov$^1$

Moscow University Physics Bulletin 2016. 16. N 2. P. 174

This paper discusses possible methods for the synthesis of informative features for the classification of signal sources in cognitive radio systems using artificial neural networks. A synthesis method based on the use of autoassociative neural networks is proposed. From the point of view of the classification of the signals, informativeness of synthesized features is estimated using a modified artificial neural network based on radial basis functions that contains an additional self-organizing layer of neurons that provide the automatic selection of the variance of basis functions and a significant reduction of the network dimension. It is shown that the use of autoassociative networks in the problem of the classification of signal sources makes it possible to synthesize the feature space with a minimum dimension while maintaining separation properties.

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Condensed matter physics

## Modeling of the Angular Dependences of Nuclear Resonant Reflectivity for Different Types of Noncollinear Magnetic Ordering

### R. A. Baulin, M. A. Andreeva

Moscow University Physics Bulletin 2016. 16. N 2. P. 180

The peculiarities of nuclear-resonance reflectometry (NRR) for different types of magnetic ordering in multilayers are considered. The theory of NRR for noncollinear magnetic structures is briefly presented. Model calculations are carried out for the [$^{57}$Fe(8Å)/Cr(20 Å)]$_{30}$ structure, in which the magnetization varies with depth in different ways. The results show that the <<magnetic>> maximum on the NRR curve occurs only when the directions of the hyperfine fields in adjacent iron layers have different projections on the synchronous beam direction. Spiral alignment of the multilayer magnetization causes the emergence of satellites near the Bragg maximum, while the <<magnetic>> maximum does not occur. With more complicated magnetic ordering profiles the characteristic features of available experimental curves can be explained.

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## The Effect of Alloying on the Structure and Peculiarities of Tribological Behavior of Vacuum-Deposited Diamond-Like Coatings

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

Moscow University Physics Bulletin 2016. 16. N 2. P. 186

In this work, we report the results of a study of the atomic and crystalline structures, phase and chemical compositions and tribological properties of DLC coatings deposited by plasma-assisted (PA) CVD (a-C:H:Si and a-C:H:Si:Mo) and magnetron reactive sputtering (a-C:H:Cr). The a-C:H:Si:Mo coatings revealed the formation of ultra-dispersed inclusions of either molybdenum carbides or silicides, whereas no such inclusions were found in the a-C:H:Si compound. The a-C:H:Cr coatings that were deposited in an acetylene–nitrogen gas mixture exhibited a nanocomposite structure composed of chromium, its carbide and nitride phases. The tribological tests showed that the DLC coatings with silicon and silicon–molybdenum have a high friction coefficient and a low working performance, while the chromium-containing coatings have high levels of their mechanical and tribological characteristics, making them promising materials for operation under high contact pressures.

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## A Mössbauer Study of Iron and Iron–Cobalt Nanotubes in Polymer Ion-Track Membranes

### V.S. Rusakov$^1$, K.K. Kadyrzhanov$^2$, A.L. Kozlovskiy$^2$, T.Yu. Kiseleva$^3$, M.V. Zdorovets$^2$, M.C. Fadeev$^1$

Moscow University Physics Bulletin 2016. 16. N 2. P. 193

Iron and iron–cobalt nanostructures that were synthesized in polymer ion-track membranes have been studied via Mössbauer spectroscopy combined with raster electron microscopy, energy-dispersion analysis, and X-ray diffraction data. The obtained nanostructures are single-phase bcc Fe$_{1 – x}$Co$_x$ nanotubes with a high degree of polycrystallinity, whose length is 12 μm; their diameter is 110 ± 3 nm and the wall thickness is 21 ± 2 nm. Fe$^{2+}$ and Fe$^{3+}$ cations were detected in the nanotubes, which belong to iron salts that were used and formed in the electrochemical deposition. The Fe nanotubes exhibit eventual magnetic moment direction distributions of Fe atoms, whereas Fe/Co nanotubes have a partial magnetic structure along the nanotube axis with a mean value of the angle between the magnetic moment and nanotube axis of 34$^{\circ} \pm 2^{\circ}$. Substituting the Fe atom with Co in the nearest environment of the Fe atom within the Fe/Co structure of nanotubes leads to a noticeable increase in the hyperfine magnetic field at the $^{57}$Fe nuclei (by 8.7$\pm$ 0.4 kOe) and to a slight decrease in the shift of the Mössbauer line (by 0.005$\pm$0.004 mm/s).

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## The Construction of Phenomenological Models of Phase Transitions Using Equivariant Catastrophe Theory Methods

### Pavlov S.V.

Moscow University Physics Bulletin 2016. 16. N 2. P. 202

A method for the construction of phenomenological models of phase transitions using the equivariant theory of singularities of differentiable maps with the symmetry of the order parameter (the equivariant catastrophe theory) is considered. This method differs from the traditional series expansion in powers of the order parameter in that, firstly, there is no requirement that the order parameters be small, and only the number of thermodynamic parameters that are varied in the experiment (temperature, pressure, etc.) is given; secondly, derived models have structural stability for an adequate description of the anomalies of the physical properties near the phase transitions. As an example to illustrate the method, a model of phase transitions with a two-component order parameter is constructed.

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## Determination of Surface-Layer Parameters on Pure Liquids via Ellipsometry

### S.G.Ili'ina, E.A. Alexeeva

Moscow University Physics Bulletin 2016. 16. N 2. P. 208

In this work we describe a method for evaluating such parameters of an interfacial layer as the refractive index and thickness of the liquid–vapor interface, based on the measured ellipticity coefficient, ρ, at different wavelengths of the probing light and the data [1] for several pure fluids. In particular, the change in the main angle of incidence was evaluated in the <<layer on the substrate>> structure. The surface layer is assumed to be homogeneous.

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