Faculty of Physics
M.V.Lomonosov Moscow State University
Theoretical and mathematical physics

## Mathematical Methods of Subjective Modeling in Scientific Research. 2: Applications

### Yu. P. Pyt'ev

Moscow University Physics Bulletin 2018. 73. N 2. P. 125

This article considers applications of the formalism of subjective modeling proposed in [36], based on modeling of uncertainty reflecting unreliability of subjective information and fuzziness common of its content. A subjective model of probabilistic randomness is defined and studied. It is shown that a researcher–modeler (RM) defines a subjective model of a discrete probability space as a space with plausibility and believability that de facto turns out to be a subjective model of the class of subjectively equivalent probability spaces that model an arbitrary evolving stochastic object, and the same space with plausibility and believability is its subjective model. This enables us to empirically recover a subjective model of an evolving stochastic object accurately and using a finite number of event observations, while its probabilistic model cannot be empirically recovered. A similar connection is established between equivalence classes of plausibility and believability distributions and classes of subjectively equivalent absolutely continuous probability densities. For two versions of plausibility and believability measures, entropies of plausibility and believability distributions of the values of an uncertain element (UCE) that model RM’s subjective judgments as characteristics of the information content and uncertainty of his judgments are considered. It is shown that in the first version entropies have properties that are formally similar to those of Shannon entropy but due to absence of the law of large numbers (LLN) their interpretation fundamentally differs from the interpretation of Shannon entropy. In the third version there is an analog of the LLN, and its connection to the Shannon entropy was obtained for the expected value of subjective informational content/uncertainty. A subjective model $M(\tilde{x}) = (\Omega, P(\Omega), P^{\zeta, x}(\dot,\dot;\tilde{x}), N^{\zeta, x}(\dot,\dot;\tilde{x}))$ of an uncertain fuzzy element is considered, and an optimal subjective rule of identification of its states using observation data is obtained and studied. Methods of expert-aided reconstruction of fuzzy and uncertain fuzzy element models are also considered.

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Astronomy, astrophysics, and cosmology

## Space Navigation by X-Ray Pulsars

### M. Sazhin$^1$, V. Zharov$^2$, V. Milyukov$^1$, M. Pshirkov$^1$, V. Sementsov$^1$, O. Sazhina$^1$

Moscow University Physics Bulletin 2018. 73. N 2. P. 141

This review considers the problem of autonomously determining the position of a spacecraft in space based on the analysis of pulses emitted by X-ray pulsars. The characteristics of the prospective equipment and lists of pulsar candidates for reference sources are given. The navigation algorithm and resulting accuracy characteristics are substantiated.

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Theoretical and mathematical physics

## Fluorescence in a Quantum System with Violated Symmetry

### A. V. Soldatov, N. N. Bogolubov

Moscow University Physics Bulletin 2018. 73. N 2. P. 154

The model of a single multilevel one-electron atom with violated symmetry such that its transition dipole-moment operator has constant diagonal matrix elements, among which not all are pairwise equal to each other, has been studied. It has been shown that the expression for the far electromagnetic field of such an atom does not contain any appreciable contributions from the diagonal matrix elements of the transition dipole moment in an explicit form; thus, these matrix elements have an effect on fluorescence via the time dependence of non-diagonal matrix elements due to quantum non-linear processes of higher orders. It has also been demonstrated that a two-level quantum system, whose transition dipole operator has constant unequal diagonal matrix elements, can continuously fluoresce under excitation with monochromatic laser radiation at a much lower frequency than the frequency of the exciting radiation. The possibility of the experimental detection and practical application of this effect are discussed

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## Analytical Solution of the Problem of the Electrovortex Flow in the Hemisphere with Finite Size Electrodes in the Stokes Approximation

### E. A. Mikhailov$^1$, I. O. Teplyakov$^2$

Moscow University Physics Bulletin 2018. 73. N 2. P. 162

An analytical solution was obtained for a stationary axisymmetric motion equation for a flow caused by an inhomogeneous electric current propagating through an electrically conducting liquid. The problem was solved in the variables for vorticity and velocity vector potential in hemispherical geometry with the finite size electrodes. Stokes and electrodynamic approximations were used.

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## Second Harmonic Generation under the Influence of the Earth’s Gravitational Field

### A. Korolev, N. Koshelev

Moscow University Physics Bulletin 2018. 73. N 2. P. 168

The effect of the generation of tsunami waves caused by collapse of the continental slope and by formation of a submarine landslide near the east coast of Sakhalin Island is reproduced within the framework of a hydrodynamic model. The calculations performed using the numerical hydrodynamic model showed that such a submarine landslide can generate a tsunami wave up to 18 m high on the Sakhalin coast.

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## The Evolution of Acoustic Radiation by an Ensemble of Vortex Rings in Air

### D. Cherkasov, F. Shugaev

Moscow University Physics Bulletin 2018. 73. N 2. P. 173

The evolution of acoustic radiation emitted by an ensemble of vortex rings in air is studied on the basis of nonstationary Navier–Stokes equations. We use the expansions of required functions into a power series of the initial vorticity which is a small value. The Navier–Stokes equation system reduces to a parabolic system with constant coefficients for the higher derivatives. The problem is posed as follows. The vorticity is defined inside the toroid at t = 0. The other parameters of the gas are assumed to be constant throughout the space at the initial instant of time. The solution is expressed in terms of multiple integrals, which are calculated using Korobov grids. The density oscillations were investigated. The results show that the frequency spectrum depends on time; high-frequency oscillations are observed at small times and low-frequency oscillations then occur. At the same time, the amplitude of high-frequency oscillations decreases in comparison with low-frequency oscillations. Thus, a transition of energy from the high-frequency spectrum to the lowfrequency spectrum occurs. These results can be useful for modeling decaying grid turbulence.

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Physics of nuclei and elementary particles

## A Method for Estimation of the Parameters of the Primary Particle of an Extensive Air Shower by a High-Altitude Detector

### V. Galkin$^{1,2}$, A. Borisov$^3$, R. Bakhromzod$^{1,4}$, V. Batraev$^1$, S. Latipova$^5$, A. Muqumov$^{1,4}$

Moscow University Physics Bulletin 2018. 73. N 2. P. 179

method for estimation of the parameters of the primary particle of an extensive air shower (EAS) by a high-altitude detector complex is described. This method was developed as part of the Pamir-XXI project. The results may be useful for other high-altitude projects and the EAS method in general. The specific configurations of optical detectors for Cherenkov EAS radiation and charged-particle detectors, the methods for data processing, and the attainable accuracy of reconstruction of parameters of primary particles (energy, direction, mass/type) are presented. The results primarily cover optical detectors that are suitable for studying EASs from primary nuclei in the range of energies $E_{0}$ = 100 TeV–100 PeV and showers from primary $\gamma$-quanta with energies of $E_{\gamma}$ ≥ 30 TeV. Grids of charged-particle detectors designed to determine the EAS direction and energy in the $E_{0}$ = 1 PeV–1 EeV range are also considered. The obtained accuracy estimates are the upper limits of the actual experimental accuracies.

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## Spatial Autocorrelation of the Level of Radio Signal Amplitude at Oblique Propagation in the Ionosphere

### L. I. Prikhodko$^1$, A. G. Vologdin, I. A. Shirokov$^2$

Moscow University Physics Bulletin 2018. 73. N 2. P. 187

Fluctuations of the amplitude level of a wave that propagates through a randomly inhomogeneous medium with regular reflection are considered. Analytical expressions for dispersion and amplitude correlation functions are derived in the parabolic model of a regular ionospheric layer inside the layer and at the exit from it. Special attention is paid to the study of the reflection area, where the conditions for the applicability of the geometric-optics method are violated. The results are analyzed numerically for ionospheric sounding under different conditions.

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## A Coulomb Blockade in a Nanostructure Based on Single Intramolecular Charge Center

### V. R. Gaydamachenko$^1$, E. K. Beloglazkina$^2$, R. A. Petrov$^2$, S. A. Dagesyan$^1$, I. V. Sapkov$^1$, E. S. Soldatov$^1$

Moscow University Physics Bulletin 2018. 73. N 2. P. 193

A novel technique for the production of metal electrodes of a nanotransistor with a nanogap less than 4 nm between them is developed on the basis of controlling the electromigration of previously suspended nanowires of the system. A method that allows the embedding of a molecule of Rh(III) terpyridine with aurophilic ligands between electrodes is elaborated, as well. The characteristics of electron transport through a system that consists of the specified molecule with a single-atom charge center indicate the correlated (singleelectron) tunneling of electrons.

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Optics and spectroscopy. Laser physics

## Antireflection Layers for Solar Cells Based on Silicon Nanowires Produced on a Doped Wafer

### A. V. Pavlikov$^{1,2}$, O. Rakhimova$^1$, P. Kashkarov$^{1,2}$

Moscow University Physics Bulletin 2018. 73. N 2. P. 199

In this work the layers of silicon nanowires produced on highly-doped silicon wafers were studied by means of Raman spectroscopy and IR reflection. The IR reflection data and effective medium approximation approach allowed us estimate the porosity of layers. Analyzing Raman scattering spectra we make a conclusion that the free carriers concentration in silicon nanowires reduces in comparison to wafer concentration. According to the data obtained we deduce, that 2 μm thick layer of silicon nanowires is optimal as antireflection layer for solar cells. The layers of 15 and 20 μm thickness were studied as well. It was demonstrated that there is no effect of Raman scattering enhancement in these layers.

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## The Optical Properties of Polydisperse Glass Microsphere Ensembles in the Infrared Spectral Region

### A. Efimova, V. Zaitsev

Moscow University Physics Bulletin 2018. 73. N 2. P. 205

Semitransparent composites with glass microspheres are promising modern materials. In particular, they contribute to the increase of the efficiency of heat-insulating coatings. An experimental study of the transmission and scattering of infrared radiation (at wavelengths from 2 to 25 μm) by a sodium borosilicate glass microsphere powder is presented. The spectra, angular-scattering patterns, and the degree of polarization of scattered radiation were studied.

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Condensed matter physics

## The Influence of the McCumber Parameter on Parametric Amplification of High-Frequency Radiation by Josephson Junctions

### V. C. Zhukovskii$^1$, O. D. Pozdnyakova$^3$, V. D. Krevchik$^2$, M. B. Semenov$^2$, A. V. Shorokhov$^3$

Moscow University Physics Bulletin 2018. 73. N 2. P. 211

The influence of the internal capacity of a Josephson junction on the parametric amplification of external electromagnetic radiation was studied in terms of a resistively and capacitively shunted junction model. The influence of the McCumber parameter on parametric amplification was clarified. It is shown that the additional regions of amplification can occur near subharmonic Shapiro steps in the case of Josephson junctions with internal capacity

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Astronomy, astrophysics, and cosmology

## Cyclic Variations in the Solar Radiation Fluxes at the Beginning of the 21st Century

### E. A. Bruevich, V. Bruevich, G. Yakunina

Moscow University Physics Bulletin 2018. 73. N 2. P. 216

The solar activity in the current, that is, the 24th, sunspot cycle is analyzed. Cyclic variations in the sunspot number (SSN) and radiation fluxes in various spectral ranges have been estimated in comparison with the general level of the solar radiation, which is traditionally determined by the radio emission flux $F_{10.7}$ at a wavelength of 10.7 cm (2.8 GHz). The comparative analysis of the variations in the solar constant and solar indices in the UV range, which are important for modeling the state of the Earth’s atmosphere, in the weak 24th cycle and strong 22nd and 23rd cycles has shown relative differences in the amplitudes of variations from the minimum to the maximum of the cycle. The influence of the hysteresis effect between the activity indices and $F_{10.7}$ in the 24th cycle, which is taken into account here, makes it possible to refine the forecast of the UV indices and solar constant depending on the quadratic regression coefficients that associate the solar indices with $F_{10.7}$ depending on the phase of the cycle.

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## Quasiperiodic Variations of Solar Activity and Cosmic Rays

### V. Okhlopkov

Moscow University Physics Bulletin 2018. 73. N 2. P. 223

Quasiperiodic variations of various manifestations of solar activity, parameters of the interplanetary medium, and the flux of galactic cosmic rays (GCRs) are studied using the data of stratospheric sounding and measurements with neutron monitors. Groups of spectral components with periods of ~2, 1.3, and ~1 year are identified in the range of periods shorter than 5 years. Particular attention is paid to quasi-2-year GCR variations that are induced by similar variations of the mean magnetic field of the Sun and are integral to the processes of solar activity.

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Physics of Earth, atmosphere, and hydrosphere

## Generation of a Tsunami from the Submarine Landslide Near the East Coast of Sakhalin Island

### A. A. Ivanova$^1$, E. A. Kulikov$^1$, I. V. Fine$^2$, B. V. Baranov$^1$

Moscow University Physics Bulletin 2018. 73. N 2. P. 234

The effect of the generation of tsunami waves caused by collapse of the continental slope and by formation of a submarine landslide near the east coast of Sakhalin Island is reproduced within the framework of a hydrodynamic model. The calculations performed using the numerical hydrodynamic model showed that such a submarine landslide can generate a tsunami wave up to 18 m high on the Sakhalin coast.

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