Faculty of Physics
M.V. Lomonosov Moscow State University

# Issue 2, 2009

Astronomy, astrophysics, and cosmology

## About “black holes” and dark matter

### Yu. M. Loskutov

Moscow University Physics Bulletin 2009. 64. N 2. P. 103

It is shown that the complete system of classical gravitational equations for an isolated centrally symmetric body yields that: (1) in terms of Galilean coordinates all metric coefficients of the Riemannian space induced by the body cannot be equal to zero or infinity anywhere; (2) they, together with the first-order derivatives, should be continuous everywhere. The equations do not contain solutions corresponding to “black holes,” but admit solutions corresponding to objects for which the surface radius (in terms of standard coordinates) is equal to the double mass of matter under this surface. These objects can make the main contribution to the dark matter of the Universe and explain observed effects, such as gravitational microlensing and other effects. Under certain conditions they can become powerful X-ray sources.

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Theoretical and mathematical physics

## A physically realizable whitening filter for cryogenic resonant gravitational-wave antennas

### A. V. Gusev

Moscow University Physics Bulletin 2009. 64. N 2. P. 110

In this paper the problem of a physically realizable whitening-filter (WF) synthesis for cryogenic resonant gravitational-wave antennas is considered in the framework of the optimal linear Kalman-Bucy filtering. A system of equations determining the structure of the Kalman filter for gravitational-wave antennas with a displacement converter is presented. The transfer function of a stationary physically realizable WF is derived. The Kalman approach ensures the possibility of high frequency parameter measurements of Gaussian and non-Gausssian noises in low-dissipation oscillatory systems for observation intervals, which are relatively short in comparison to the relaxation time.

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## Light propagation in a strong external magnetic field with regard to quantum corrections

### I. S. Grinin

Moscow University Physics Bulletin 2009. 64. N 2. P. 115

Linearized motion equations for electromagnetic wave field in the external magnetic field have been solved for the PVLAS experiment configuration within the low-energy approximation of quantum electrodynamics. It has been shown that the wave propagation velocity depends on the initial direction of the plane of wave polarization. Dispersion laws corresponding to the waves with mutually perpendicular directions of polarization have been established. The dependence of ellipticity of laser radiation field on initial polarization and the value of the external magnetic field has been obtained. The ellipticity parameter for the configuration of the system used in the PVLAS experiment has been found.

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## Mathematical model for antisymmetric solutions of N-particle schrodinger equation

### D. S. Golikov

Moscow University Physics Bulletin 2009. 64. N 2. P. 119

We consider equations for a mathematical model system of fermions. Equations for spectrum are determined from the system of variational equations. The eigenvalues of the system of variational equations were defined for a particular solution.

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## Calculation of the resonance frequencies of an open dielectric axially symmetric resonator of piecewise constant radius

### A. N. Bogolyubov, A. I. Erokhin, I. E. Mogilevskii, N. E. Shapkina

Moscow University Physics Bulletin 2009. 64. N 2. P. 124

An algorithm is suggested for calculating the resonance frequencies of open dielectric axially symmetric resonators of piecewise constant radius suitable for an arbitrary layered axially symmetric dielectric filling. The resonator is placed into a case with ideally conducting walls of a sufficiently large radius. Cases are analyzed where the resonator structure is partly coated with a perfect conductor.

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## Cooling kinetics of a granular gas of viscoelastic particles

### A. S. Bodrova, N. V. Brilliantov

Moscow University Physics Bulletin 2009. 64. N 2. P. 128

The evolution of a granular gas of viscoelastic particles in the homogeneous cooling state is studied. The velocity distribution function of granular particles and the time dependence of the mean kinetic energy of particles (granular temperature) are found. The noticeable deviation of the distribution function from the Maxwell distribution and its non-monotonous evolution are established. The perturbation theory with respect to the small dispersion parameter is elaborated and the analytical expressions for the asymptotic time dependence of the velocity distribution function and the granular gas temperature are derived.

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## Effect of tensor g-factor on the spectrum of eigen modes in magnetoactive plasma

### D. V. Vagin, P. A. Polyakov, N. E. Rusakova

Moscow University Physics Bulletin 2009. 64. N 2. P. 133

The influence of the tensorial nature of the gyromagnetic coupling on a spectrum of eigen modes in magnetoactive plasma is studied. A dispersion equation for waves propagating in such a medium is obtained in the approximation of frigid hydrodynamics.

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## Combined analysis of static and dynamic magnetic characteristics of multilayer CoFeZr/α-Si nanostructures

### S. A. Vyzulin$^1$ , A. V. Gorobinskii$^1$ , Yu. E. Kalinin$^2$ , E. V. Lebedeva$^3$ , A. V. Sitnikov$^2$ , N. E. Syr’ev$^3$ , I. T. Trofimenko$^3$ , I. G. Shipkova$^4$

Moscow University Physics Bulletin 2009. 64. N 2. P. 136

The combined method of static and dynamic magnetic measurements is used to study nano-dimensional multilayer amorphous CoFeZr/α -Si films. It is established that at the thickness of magnetic layers x = 5–12 nm their magnetization does not differ from that of the bulk material. It is shown that as x is lowered to 2–3 nm, the magnetization of magnetic layers decreases, which may be due to the formation of mixed layers containing nonmagnetic silicides. At a thickness of nonmagnetic interlayers of less than 1 nm the features characteristic of a weak antiferromagnetic interaction of neighboring layers are observed.

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Optics and spectroscopy. Laser physics

## VUV spectroscopy of Ce$^{3+}$-doped Na$_{0.4}$Lu$_{0.6}$F$_{2.2}$ single crystals

### G. M. Shapochkin$^1$ , V. V. Mikhailin$^1$ , S. P. Chernov$^2$ , D. N. Karimov$^3$

Moscow University Physics Bulletin 2009. 64. N 2. P. 141

The short-wave transmission spectrum of Na$_{0.4}$Lu$_{0.6}$F$_{2.2}$ with the visible/ultraviolet transmission edge of 8 eV was studied. Absorption spectra of the 4f—5d transitions of the Ce$^{3+}$ ion in the region of 4–8 eV were studied in Ce$^{3+}$-doped Na$_{0.4}$Lu$_{0.6}$F$_{2.2}$ single crystals. Luminescence spectra in the ultraviolet and visible spectral regions, luminescence decay kinetics and reflection and luminescence excitation spectra in the visible/ultraviolet and ultraviolet regions (4–20 eV) were investigated at helium and room temperatures.

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## Fraunhofer diffraction on a polygon and calculation of binary mask images

### G. V. Belokopytov, Yu. V. Ryzhikova

Moscow University Physics Bulletin 2009. 64. N 2. P. 146

A simple analytical formula for the spectrum of spatial harmonic components of a diffracted field is derived. It is used for construction of an effective algorithm of image calculation in photolithography.

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## Specific features of excitations of “flow”-type self-oscillations in a two-component active medium of a fast-flow gas laser

### L. S. Kuz’minskii$^1$ , A. I. Odintsov$^1$ , N. E. Sarkarov$^2$ , A. I. Fedoseev$^1$

Moscow University Physics Bulletin 2009. 64. N 2. P. 149

The mechanism of “flow”-type self-oscillations in a two-component active medium of a flow laser with an unstable resonator is studied. It is shown that this mechanism is associated with the excitation of edge self-oscillatory in-phase perturbations of the medium components. These flow perturbations with low damping reach the optical axis of the resonator and result in an instability.

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## Study of the feasibility of optical coatings with a continuous refractive index profile

### T.V. Amochkina, I.V. Kozlov, A.V. Tikhonravov, M.K. Trubetskov

Moscow University Physics Bulletin 2009. 64. N 2. P. 155

The effect of the instability of deposition rates on the spectral characteristics of optical coatings with a continuous refractive index profile was studied. A correlation between the error level in the experimental data and the accuracy of the reproducibility of spectral characteristics of these coatings was found.

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Condensed matter physics

## Hopping conductivity in polycrystalline diamond films

### P. G. Kopylov, A. M. Lotonov, I. A. Apolonskaya, A. N. Obraztsov

Moscow University Physics Bulletin 2009. 64. N 2. P. 161

The results of the experimental study of the conductivity of a polycrystalline diamond film by dielectric spectroscopy are presented. A diamond film about 200 μm thick was grown by microwave plasma-assisted chemical vapor deposition for 180 h. Two pronounced local peaks in the frequency dependence of the conductivity were observed. The relevant frequencies were temperature-dependent. These data permit us to hypothesize that the hopping mechanism of conductivity occurs in the polycrystalline diamond film. Two types of electrically active centers with different activation energies and relaxation times are involved in the conductivity.

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## Analysis of the structure of block copolymer films by atomic force microscopy

### E. A. Menshikov, A. V. Bol’shakova, I. V. Yaminskii

Moscow University Physics Bulletin 2009. 64. N 2. P. 166

The structure of thin films of the polysterene-polymethylacrylate-polysterene triblock copolymer was studied. Universal algorithms to analyze atomic-force-microscopy images of thin block-copolymer films were developed.

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## Features of structure and properties of Na$_n$C$_6$$_0 (n = 2, 3) fullerides synthesized in toluene ## Features of structure and properties of Na_nC_6$$_0$ (n = 2, 3) fullerides synthesized in toluene

### N.B. Brandt$^1$, B.M. Bulychev$^2$, Yu.A. Velikodnyi$^2$, A.V. Zoteev$^1$, E.A. Konstantinova$^1$, A.V. Krechetov$^1$, V.A. Kul’bachinskii$^1$, V.G. Kytin$^1$, V.P. Tarasov$^3$

Moscow University Physics Bulletin 2009. 64. N 2. P. 172

The structure and electron properties of Na$_n$C$_6$$_0 (n = 2, 3) sodium fullerides synthesized from simple compounds in toluene were studied. It was shown that Na_2C_6$$_0$ fulleride forms a face-centered cubic lattice at temperatures above 300 K. As the temperature is lowered, the phase transition to a structure with a simple cubic lattice takes place. The temperature dependences of the properties of Na$_3$C$_6$$_0 with a more complex structure exhibit features that are presumably due to sodium atom redistribution in the Na_3C_6$$_0$ fulleride lattice and the formation of sodium ion clusters.

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## Impurity photovoltaic effect in p-i-n structures of undoped GaAs

### V.A. Morozova$^1$, O.G. Koshelev$^1$, E.P. Veretenkin$^1$, V.N. Gavrin$^2$, Yu.P. Kozlova$^2$

Moscow University Physics Bulletin 2009. 64. N 2. P. 177

Photo-emf in the range hv = 0.76 − 1.35 eV was found in p-i-n structures produced from undoped GaAs crystals with known parameters; the current sensitivities in the impurity and intrinsic (hv > 1.35 eV) regions were comparable. It was proven that the impurity photovoltaic effect results from EL2 and EL3 structural defects creating deep donor levels in the forbidden zone. Calculations were performed that justified the possibility of observing this effect on the investigated structures.

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Chemical physics, physical kinetics, and plasma physics

## Simulation of ignition of a supersonic flow of a propane-air mixture by electric discharge

### A.F. Aleksandrov$^1$, V.G. Gromov$^2$, A.P. Ershov$^1$, V.A. Levin$^2$, V.A. Chernikov$^1$

Moscow University Physics Bulletin 2009. 64. N 2. P. 182

The numerical simulation of the ignition process of a supersonic flow of a preliminary mixed propane-air mixture by electric discharge, with respect to power, geometry, and the duration of energy input, was carried out via a two-dimensional thermo-chemical model. The ignition thresholds evaluated in the framework of this model were in agreement with the experimental values of power density and induction duration.

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## Hysteresis transition between diffuse and constricted modes of dc discharge in argon

### I.A. Shkurenkov, Yu.A. Mankelevich, T.V. Rakhimova

Moscow University Physics Bulletin 2009. 64. N 2. P. 187

The results of theoretical studies of hysteresis transition between the diffuse and constricted modes of a dc glow discharge in argon are presented. It has been shown that the experimentally observed hysteresis of the current voltage characteristic (CVC) at the transition from the constricted to the diffuse mode is caused by the nonlocal formation of the electron energy distribution function (EEDF) while taking into account the heterogeneity of radial fields, namely, the diffusion of high-energy electrons capable of producing gas ionization from the central (constricted) region. The effect of the non-local formation of the EEDF has been described approximately by introducing the effective temperature of the high-energy part of the EEDF and solving the equation for the radial profile of the high-energy part of the EEDF.

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## Changes in adsorption and optical properties near the phase transition of super thin vanadyl phthalocyanine Langmuir films

### V.B. Zaitsev$^1$, N.L. Levshin$^1$, S.G. Yudin$^2$

Moscow University Physics Bulletin 2009. 64. N 2. P. 191

Structural transition in thin vanadyl-phtalocyanine films deposited by Langmuir technology was studied in detail with the help of the vacuum adsorption and optical spectroscopy techniques. The reversible structural transition observed only in super-thin Langmuir films is accompanied by nonreversible changes during heating. This transformation of the film having defects and amorphous regions occurs during the film transition from a metastable state to a more stable one that is characterized by a lower free energy.

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Astronomy, astrophysics, and cosmology

## Periodic motion of a star inside an elliptical galaxy with a variable mass

### S.A. Gasanov

Moscow University Physics Bulletin 2009. 64. N 2. P. 195

Periodic solutions are constructed to the problem of a star’s motion inside a layered inhomogeneous rotating elliptical galaxy with a variable mass using the Lyapunov and the small parameter methods. The stability of periodic solutions in the Lyapunov sense is studied.

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Physics of Earth, atmosphere, and hydrosphere

## The influence of the benthic frontal zone on acoustic wave propagation in the ocean and evaluation of the possibilities of its ray tomography

### V.S. Ivanov, P.N. Kravchun

Moscow University Physics Bulletin 2009. 64. N 2. P. 202

The specificity of ray trajectories in the presence of a benthic front, which is the boundary between the Antarctic deep and bottom waters, has been considered. Deep-water “noncanonical” caustic surfaces confined to the front have been found. The ability to reconstruct a sound velocity profile in the benthic frontal zone has been evaluated using methods of ray tomography in the ocean. A possible reconstruction of the profile using a horizontal displacement of the receiving antenna or transmitter at relatively small depths has been shown.

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## Method of specification of the initial conditions for numerical tsunami modeling

### M.A. Nosov, S.V. Kolesov

Moscow University Physics Bulletin 2009. 64. N 2. P. 208

A new method for the specification of initial conditions in the tsunami problem is suggested. The initial elevation of a water surface is determined from the solution of the three-dimensional problem in the framework of potential theory with account for both the horizontal and vertical components of the bottom deformations and the distributions of depths in the vicinity of the source. The tsunamigenic Central Kuril Islands earthquakes in 2006 and 2007 are taken as examples to demonstrate the efficiency of the new method.

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## The impact of cosmic dust on the Earth’s climate

### V.I. Ermakov$^1$, V.P. Okhlopkov$^2$, Yu.I. Stozhkov$^3$

Moscow University Physics Bulletin 2009. 64. N 2. P. 214

Flows of material particles, viz., cosmic rays and cosmic dust, are perpetually coming from space into the Earth’s atmosphere; these are particles sized from 0.001 μm to dozens or hundreds of μm. The paper shows that cosmic rays influence the main parameters of the atmosphere’s electricity, and cosmic dust influences global cloudiness, albedo and the Earth’s climate.

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Theoretical and mathematical physics

## Classification of acoustic signals of discharge processes in insulation based on the shape of their wavelet spectra

### A.I. Chulichkov, N.D. Tsybulskaya, S.K. Tsvetaev, O.S. Surkont

Moscow University Physics Bulletin 2009. 64. N 2. P. 218

A description of the results of the recording of acoustic signals, which indicate the isolation disruption of high-voltage power equipment, are presented. The description is invariant with relation to the time shift and nonlinear monotonous amplitude distortions. Signal classification, as the basis for the automatic control and monitoring of power equipment, was carried out.

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Optics and spectroscopy. Laser physics

## Image subtraction by polarized light

### Yu.G. Pavlenko

Moscow University Physics Bulletin 2009. 64. N 2. P. 221

It is shown that holographic images can be subtracted by substitution of a mirror for a phase plate.

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## Enhancement of hard X-ray yield under the interaction of Cr: Forsterite femtosecond laser radiation with Xe clusters

### A.P. Golubev$^1$, V.M. Gordienko$^1$, M.S. Dzhidzhoev$^1$, I.A. Makarov$^1$, D.N. Trubnikov$^2$

Moscow University Physics Bulletin 2009. 64. N 2. P. 223

Experiments on the interaction of femtosecond laser radiation (1240 nm, 140 fs,$10^{16}$ W/cm$^2$) with a Xe cluster beam in a Xe-Ne binary mixture are carried out. The formation of Xe clusters in the presence of light carrier gas (Ne) is found to narrow the Xe cluster beam and enhance the x-ray yield (at about 4 keV). X-ray generation efficiency is about 10$^{-8}$.

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Condensed matter physics

## Calculation of the thermodynamic properties of copper by molecular dynamics simulation

### O.V. Stepanyuk, D.B. Alekseev, A.M. Saletskii

Moscow University Physics Bulletin 2009. 64. N 2. P. 226

It is shown that the thermodynamic characteristics of a system can be accurately described using many-body potentials of the interatomic interaction in molecular dynamics calculations.

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Astronomy, astrophysics, and cosmology

## In-situ recordings of the changes in the regimes of heat-mass exchange between sea and atmosphere at the shore

### Yu.Yu. Plaksina$^1$ , V.N. Aksenov$^2$ , E.G. Andreev$^2$

Moscow University Physics Bulletin 2009. 64. N 2. P. 228

Using instrumental investigations at the Black Sea shore, new data on the change in the heat-mass exchange under upwelling are obtained for the first time; the interrelation between the regimes of heat-mass exchange with a difference in air and water temperatures near the interface is established. The increased values of total heat flow at the shore as compared with the same flows in the open sea are recorded.

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