Faculty of Physics
M.V. Lomonosov Moscow State University

# Issue 4, 2015

Theoretical and mathematical physics

## The Hamiltonian formalism and quantum-mechanical analogy in the probabilistic description of turbulence

### V.P.Yushkov

Moscow University Physics Bulletin 2015. 70. N 4. P. 217

It is shown here that (i) the interaction of adiabatic waves with incompressible turbulence makes it possible to statistically describe the transfer of the energy of turbulent pulsations over the spectrum, (ii) the fundamental parameter that allows the effect of adiabatic motions on incompressible turbulence to be parameterized is the entropy dissipation coefficient in the equation that is called the Obukhov equation in this paper, and (iii) the generalized coordinates or canonical variables of the Zakharov equation should be interpreted as wave functions.

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## The Zeeman effect in a modified Gross–Neveu model in (2 + 1)-dimensional space–time with compactification

### R.N. Zhokhov, V.Ch. Zhukovsky, P.B. Kolmakov

Moscow University Physics Bulletin 2015. 70. N 4. P. 226

The influence of the magnetic field, temperature, and chemical potential on the phase structure of a system in (2 + 1)-dimensional space–time with one compactified spatial dimension (cylinder) was studied in the framework of the modified Gross–Neveu model. The Zeeman effect that is induced by an external magnetic field parallel to the cylinder axis is considered. The system magnetization that is created due to the Zeeman effect was plotted. The possible generalization of these results to carbon nanotubes is noted.

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### K. Zhukovsky

Moscow University Physics Bulletin 2015. 70. N 4. P. 232

Undulator radiation (UR) was studied taking the broadening of spectral lines via homogeneous and nonhomogeneous contributions into account. Exact analytical expressions for the UR spectrum and intensity in the case of relativistic highenergy electrons were obtained. Analytical expressions that characterize the interrelation between the constant components of the magnetic field in undulators and the electron beam divergence within them were derived. These expressions suggest that this divergence may be partially compensated. The radiation of a doublefrequency undulator and the higher harmonic radiation in an ordinary planar undulator were investigated taking the broadening of spectral lines into account. We discuss examples of UR in actual devices and demonstrate that the developed method and the results may be used in the calculation of induced UR.

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## An analytical solution for the profile of nonLinear gravity waves on the surface of an ideal liquid

### V.M. Budanov

Moscow University Physics Bulletin 2015. 70. N 4. P. 240

A nonlinear system of hydrodynamic equations that describe the 2D motion of an incompressible liquid with a free surface in a pond with a fixed depth is studied in this work. It has been shown that a known solution to the linearized system is also a solution to the initial nonlinear system. Description of a wave pro file is also reduced to the solution of one ordinary differential nonlinear firstorder equation.

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## Acoustic radiation frequency of a cylindrical vortex

### T.A. Petrova, F.V. Shugaev

Moscow University Physics Bulletin 2015. 70. N 4. P. 245

Acoustic radiation frequency of a cylindrical vortex in the air has been calculated. Calculations are based on the NavierStokes equations using the expansion of the functions in powers of small parameter char acterizing the initial vorticity. Nonuniform system of parabolic differential equations with constant coefficients is obtained. The initial radius of the cylinder varies over a wide range. The problem is considered for the case of plane flow. In contrast to previously results, it is shown that at small values of vorticity, the frequency of the acoustic radiation depends only on the geometric size (the initial radius of the vortex).

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## The effect of a magnetic field on longitudinal–transverse discharge in the high-speed flow of an air–hydrocarbon mixture

### A.I. Alekseev, V.A. Chernikov, D.N. Vaulin

Moscow University Physics Bulletin 2015. 70. N 4. P. 251

The results of experimental studies on the influence of an inhomogeneous magnetic field on the nature of the ignition and combustion of an air–propane mixture in a supersonic flow that is initiated by a longitudinal–transverse dc discharge are presented. It is shown that the nature of a mixturecombustion regime strongly depends on the orientation of the magnetic field with respect to both the direction of the discharge current and the flowvelocity vector.

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Optics and spectroscopy. Laser physics

## An optical theorem for local sources in diffraction theory

### Yu.A. Eremin$^1$, A.G. Sveshnikov$^2$

Moscow University Physics Bulletin 2015. 70. N 4. P. 258

The optical theorem is generalized for the case of excitation of local structures by point sources. It is shown that an essential parameter, the Purcell factor, can be represented in analytical form. The results are generalized for the case of an interface between two semispaces. These results are of paramount impor tance for averaging of the coefficient of fluorescence amplification and the efficiency of an optical antenna by the position of an excitation source.

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## On the theory of parametric light generation

### A.V.Belinsky, T.M. Tarasova

Moscow University Physics Bulletin 2015. 70. N 4. P. 263

A theory of parametric light generation in a resonator with dissipative losses is presented. Approximate analytical solutions are obtained for schemes with two and three resonating waves and their adequacy criteria are formulated. Computer simulation confirmed the accuracy of the analytical solutions.

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Condensed matter physics

## The features of tunneling currentvVoltage characteristics in a combined atomic force/scanning tunneling microscope System with Quantum Dots of Colloidal Gold

### V.Ch. Zhukovsky$^1$, V.D. Krevchik$^2$, M.B. Semenov$^2$, D.O. Filatov$^3$, R.V. Zaytsev$^2$, P.V. Krevchik$^2$, I.A. Egorov$^2$, V.A. Vasilyev$^4$

Moscow University Physics Bulletin 2015. 70. N 4. P. 271

Tunneling current–voltage characteristics for growing quantum dots of colloidal gold in a combined atomic force/scanning tunneling microscope system were obtained. It was assumed that ionic conduction produces the largest contribution to the tunneling current. The tunneling current–voltage characteristics were compared qualitatively to the theoretical curve of the field dependence of the probability of 2D dissipative tunneling that was calculated taking the influence of two local phonon modes of a widebandgap matrix into account. It was demonstrated that the experimental and theoretical curves agree qualitatively. This suggests that the dissipative tunneling mechanism may produce a contribution to the tunneling current through a growing quantum dot under a cantilever needle. This current may be amplified in clusters with sizes of 1–5 nm in thinner films.

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## The influence of an air atmosphere on the electrical properties of two-phase films of hydrogenated silicon

### M.V. Khenkin$^1$, D.V. Amasev$^1$, A.S. Vorontsov$^1$, P.A. Forsh$^{1,2}$, A.G. Kazanskii$^1$, P.K. Kashkarov$^{1,2}$

Moscow University Physics Bulletin 2015. 70. N 4. P. 277

Amorphous and microcrystalline hydrogenated silicon is an important material in modern thin film electronics. In some cases, the electrical parameters of silicon film samples depend on the ambient environment, in particular, the air. In this work we studied the effect of air exposure on the electrical properties of two-phase silicon films with a volume fraction of the crystalline phase of 0 to 80%. It was shown that the change in the conductivity of the twophase films that were exposed to the air atmosphere depends on the proportion between the amorphous and microcrystalline phases that form the film microstructure. The use of two differing methods for film manufacturing allowed us to qualitatively evaluate how the conductivity of the films with a nonuniform structure across the thickness is affected by gas adsorption from air onto the film surface. Air exposure of the samples with a small amount of the crystalline phase located near the film surface leads to the specific features of temperature dependence of their conductivity.

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Astronomy, astrophysics, and cosmology

## The cyclic activity of the sun from observations of the activity indices at different time scales

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

Moscow University Physics Bulletin 2015. 70. N 4. P. 282

With the time–frequency analysis of the series of observations of one of the global indices of solar activity, viz., the radio flux F$_{10.7}$ at a wavelength of 10.7 cm (2.8 GHz), the most probable value of the main cycle period has been determined. This value is 10.2 yr, which is consistent with the generally accepted estimates. Simultaneously with the main cycle of activity, several lowamplitude cycles with cyclicity periods from 1.3 to 100 yr were identified. With the method of continuous wavelet transform with Morlet mother wavelets, we analyzed the other solar indices that are associated with the radiation at different heights in the solar atmosphere: the relative number of sunspots, SSN, the chromospheric index, $\textit{Mg II}$, at 280 nm, the fluxes in the coronal line at 530.3 nm, F$_{530}$, the $\textit{Flare Index}$, and the index of a total number of flares, $\textit{Counts of flares}$. The obtained time–frequency characteristics turned out to be generally similar. Differences in the results for the solar indices occur during the strengthening of stochastic processes in the maxima and minima of the main cycle.

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## The formation of a transient current system near the inner edge of the magnetospheric tail current

### V.V. Kalegaev, I.S. Nazarkov

Moscow University Physics Bulletin 2015. 70. N 4. P. 291

The structure of the magnetic field near the inner edge of the magnetospheric tail during the preliminary phase of the magnetic storm on Feb. 14, 2009 was studied based on the data of THEMIS satellites. The magnetic field of the currents that were flowing in the magnetospheric tail was obtained by subtracting the effect of the geomagnetic dipole and the magnetic field of magnetospheric currents other than the tail currents (mainly magnetopause currents) from the magnetic field measured on board the satellites. The parabo loid model of the magnetosphere (A2000) was used for calculating the magnetic field of magnetospheric currents. The comparison of calculations and measurements at five satellites in geomagnetically quiet periods allows one to obtain typical radial profiles of magneticfield components along the magnetospheric tail. It was demonstrated that the nonstandard structure of the magnetic field near the inner edge of the tailcurrent sheet before the onset of the magnetic storm on February 14, 2009 is connected with the formation of the transient current system in the magnetosphere. A circular current in the equatorial plane was formed before the onset of the storm in the course of adiabatic compression of the magnetosphere by the solar wind to maintain the magnetic flux through the tail lobes. The spatial position and intensity of the current were determined.

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Physics of Earth, atmosphere, and hydrosphere

## Contrasting secular changes in average ocean levels of the northern and southern hemispheres

### Yu.V. Barkin

Moscow University Physics Bulletin 2015. 70. N 4. P. 299

The origin and mechanisms of the South–Northdirected secular ocean tide are discussed. The average rates of the rise in ocean levels in the Northern and Southern Hemispheres are determined. The secular tide of ocean waters from the Southern Hemisphere to the Northern Hemisphere that were predicted and discovered by the author in 2005 is caused by gravitation of the core, which drifts to the north relative to the mantle. This tide was reliably confirmed by modern studies of the coastal changes in ocean level. Further studies of this tide are important and may play a key role in understanding the asymmetry and inversion of many natural processes in the Northern and Southern Hemispheres, as well as in explanation of the high endogenic activity of the Earth and other bodies of the Solar System.

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## The combination of methods for analyzing the amplitude and phase of satellite radar images for the estimation of displacements on LandslideAffected Slopes

### E.A. Kiseleva$^1$, V.O. Mikhailov$^{1,2}$, E.I. Smolyaninova$^1$, E.P. Timoshkina$^1$, P.N. Dmitriev$^1$

Moscow University Physics Bulletin 2015. 70. N 4. P. 303

The efficiency of combining methods for analyzing the amplitude and phase of radar images from the ENVISAT, ALOS, and TerraSARX satellites is shown based on a case study of a landslide in Baranovka Settlement, Greater Sochi. The offset tracking method in the amplitude field of the reflected radar signal allowed us to define the contour of the area where the landslide occurred in the night between January 23 and 24, 2012 and to estimate the displacements in different parts of the landslide body. The maximum displace ment was 7.5 ± 1 m. The displacements prior to the landslide from January 22, 2007 until September 17, 2010, as obtained from the ALOS satellite by the persistent scatterer method, demonstrate seasonal autumn–winter accelerations. The time series of displacements from the ENVISAT satellite shows that from November 29, 2010 until July 27, 2011 the displacement rates in the lineofsight direction vLOS were relatively small (21 mm/yr), but in the period from September 25, 2011 to December 24, 2011 the slide rate increased to 50 mm/yr. As obtained by the TerraSARX satellite, the slide rate vLOS after landsliding in the period from February 17, 2012 to March 10, 2012, reached 30 mm/month, but after June 6, 2012 it decelerated to 2–3 mm/month. Similar slide rates were also obtained for the same periods based on differential interferograms.

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## Solar flare forcing on ionization of upper atmosphere. comparative study of several major X-class events of 23rd and 24th Solar Cycles1

### V.E. Kunitsyn$^{1,2}$, M.O. Nazarenko$^{1}$, I.A. Nesterov$^{1}$, A.M. Padokhin$^{1}$

Moscow University Physics Bulletin 2015. 70. N 4. P. 312

By analyzing the GNSS (Global Navigational Satellite Systems) signals recorded at the IGS (International GNSS Service) network, we compare the effects of ionization of the upper atmosphere by a series of intense X-class solar flares during the 23rd and 24th solar cycles. We develop the methods for esti mating the geoeffectiveness of solar flares from the GNSS data and suggest using the rate of change of the ionospheric total electron content averaged over all the receiving stations located on the sunlit side of the Earth reduced to the solar zenith angle during the flare as the characteristic of the flare’s geoeffectiveness.

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## The influence of wind on the development of a thermal bar and currents in reservoirs of different depths during Ice Cover Melting

### N.S. Blokhina

Moscow University Physics Bulletin 2015. 70. N 4. P. 319

The influence of wind on the development of a thermal bar and currents in reservoirs of different depths during ice cover melting was studied using mathematical modeling. It is shown that the reservoir depth, as well as the wind velocity and direction, determine the behavior and lifetime of vortex structures in a reservoir that form on both sides of a thermal bar, as well as the location of their convergence zone and the 4$^{\circ}$C isotherm. The dominant mechanisms of the instability of water masses in reservoirs of different depths under wind action on their surface are identified. It is shown that the higher wind speed is, the deeper the reservoir should be in order to get the zone of divergence of water masses close to 4$^{\circ}$C isotherm. In this situation it is justified to use a classical interpretation of a thermal bar as a region of water convergence near 4$^{\circ}$C, unlike shallow reservoirs where even slight winds lead to the significant divergence of these zones.

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## Tsunami forecasting based on deepwaterStation data

### M.A. Nosov, S.S. Grigorieva

Moscow University Physics Bulletin 2015. 70. N 4. P. 326

Shortterm forecasting of tsunamis is proposed by sealevel prediction based on the data of a dense network of deepwater stations. This approach was applied to calculate tsunami waves on March 11, 2011 in the Kii Peninsular coast (Japan). Variations in bottom pressure recorded by DONET stations were used as the input data. The calculation results were compared with the data of JMA coastal tide gauges. Only the two to three first waves that were recorded with coastal tide gauges that were closest to the DONET system were reconstructed with sufficient accuracy. The reasons for the inconsistency between the measured and predicted sealevel variations are discussed. Principles of optimal layout of deepwater stations for tsunami fore casting are suggested

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