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

## Complication of the spectrum of electromagnetic waves scattered by charged nanoparticles with allowance for radiation reaction

### A.A. Vlasov

Moscow University Physics Bulletin 2007. 62. N 3. P. 131

Peculiarities of the scattering of electromagnetic waves by charged nanoparticles have been revealed, given the proper expression for the radiation reaction force. These peculiarities (the change in maximum intensity, the appearance of additional peaks in the spectrum, and others) can be used, in particular, in near-Earth plasma physics and charged nanoparticle physics.

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## On the value of an element of Sobolev space W˚2 1 (X) at a point of domain $X$

### M.D. Malykh

Moscow University Physics Bulletin 2007. 62. N 3. P. 134

A concept of cosheaf of Sobolev spaces is introduced; the value of an element of Sobolev space at a point is defined. Some theorems relating the convergence in norm with pointwise convergence are presented.

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## Quasi-gasdynamic equations for gas flows with external heat sources

### T.G. Elizarova$^1$, A.A. Khokhlov$^2$

Moscow University Physics Bulletin 2007. 62. N 3. P. 138

A system of quasi-gasdynamic equations for gas flows with external forces and heat sources is constructed. An entropy balance equation is derived that demonstrates the dissipative nature of the additional terms appearing in the system.

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## Radial distribution function and the speed of sound in dense gases and liquids

### O.P. Nikolaeva

Moscow University Physics Bulletin 2007. 62. N 3. P. 143

An expression for the speed of sound is derived in terms of the radial distribution function and its temperature derivative. Since the radial distribution function and the speed of sound can be determined independently from experiments, the relation found can be used to analyze the substance’s phase diagram and the thermodynamic consistency of the equations of state.

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## A variational approach to the reconstruction of galactic peculiar velocities

### A.A. Kurnosov, A.N. Sobolevskiĭ

Moscow University Physics Bulletin 2007. 62. N 3. P. 147

A variational method for determining the peculiar velocities of galaxies using a catalog of their positions and masses is suggested. The method is based on an approximate reconstruction of the dynamical history of the patch of the Universe covered by the catalog through the optimization of a suitable integral action functional and is an improvement on the method of the Monge-Kantorovich mass transportation problem developed in [1].

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## The finite element method for calculating the propagation constant in a rectangular chiral waveguide

### A.N. Bogolyubov, N.A. Mosunova

Moscow University Physics Bulletin 2007. 62. N 3. P. 151

The problem of finding the propagation constant of a rectangular chiral waveguide is solved using the finite element method. The method proved to be highly accurate and can be used for solving similar problems.

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Atomic and nuclear physics

## Study of the acoustic field produced by a 50-MeV electron beam in water

### V.B. Bychkov$^1$, V.S. Demidov$^2$, E.V. Demidova$^2$, A.N. Ermakov$^3$, O.D. Ershova$^3$, B.S. Ishkhanov$^3$, V.P. Maslyanyi$^1$, A.Yu. Sokolov$^2$, N.A. Khaldeeva$^2$

Moscow University Physics Bulletin 2007. 62. N 3. P. 155

For the first time, a detailed space-time dependence of acoustic pressure produced by a 50-MeV electron beam in water are obtained at the electron accelerator of Moscow State University. Measurements are performed at 100 points taken along one line parallel to the beam axis and spaced 6.5 cm apart from this axis. The 2D (time-distance) patterns display two paths corresponding to signals from two sound sources: a cylindrical acoustic antenna produced by the electron beam and the entrance cap separating the water and air media.

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## Efficiency of collinear acoustooptic interaction in an anisotropic medium

### Yu.S. Dobrolenskii, V.B. Voloshinov

Moscow University Physics Bulletin 2007. 62. N 3. P. 160

Collinear acoustooptic interaction in crystals with different values of birefringence is theoretically studied. The crystal medium is considered as a system of thin layers where the orientation of optical indicatrix varies from layer to layer due to the presence of an ultrasonic wave. For collinear diffraction inLiNbO$_3$, $\alpha$-SiO$_2$, Te, CaMoO$_4$ and Tl$_3$AsSe$_3$ crystals, expressions for the transmitted and diffracted intensities are obtained by means of acoustooptic methods and a new method based on the Jones calculus.

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## Directivity of multidipole antennas in microwave energy transmission systems

### Yang Chun, V.L. Savvin

Moscow University Physics Bulletin 2007. 62. N 3. P. 165

Reception characteristics of multidipole antennas of the rectenna converters used in the microwave energy transmission systems are calculated. The effect of the number, mutual positions, and possible failures of dipole elements on the antenna pattern is investigated.

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Optics and spectroscopy

## Spectroscopic study of the purple sulfur bacteria Chromatium sp. cultured in an aqueous medium

### A.S. Milyukov$^1$, S.V. Patsaeva$^1$, V.I. Yuzhakov$^1$, E.L. Rostovtseva$^2$

Moscow University Physics Bulletin 2007. 62. N 3. P. 170

A spectroscopic study of the photosynthetic purple sulfur bacteria of the Chromatium genus is performed at various growth stages and under different culture conditions. Absorption and luminescence spectra of the bacterial cells are found to be useful in estimating their populations within certain concentration ranges. The relative proportion between the porphyrin and blue-band luminescence intensities can be used as an indicator of the physiological state of the culture.

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## Pixelated phase masks and their synthesis

### G.V. Belokopytov, Yu.V. Korotkova

Moscow University Physics Bulletin 2007. 62. N 3. P. 174

An approach to the design of holograms and masks for optical lithography is proposed on the basis of digitizing an image and dividing the sample into three phase components defined on a special bitmap. The equivalence conditions of the continuous and discrete methods of specifying a transmission function are studied. Computer modeling is used to reconstruct the images generated by means of the discrete phase masks synthesized. The locality principle has proven to hold: the transmission function at a given mask point is determined by the position of the nearest aperture.

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Solid state physics

## Dynamic theory of resonant X-ray Bragg diffraction in perfect crystals

### A.P. Oreshko

Moscow University Physics Bulletin 2007. 62. N 3. P. 179

An exact solution is found to the problem of mirror reflection and resonant Bragg diffraction of X rays in a perfect crystal. An anomalous transmission of radiation with the energy close to the $K$-edge absorption of the atoms is shown to be feasible.

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## Antiferromagnetic ordering arising in Mn$_{19.8-x}$Fe$_x$Sn$_{0.2}$ alloys with the $\beta$-Mn-type structure

### I.Yu. Gaidukova$^1$, A.S. Ilyushin$^1$, K. Inoue$^2$, I.A. Nikanorova$^1$, A.S. Markosyan$^1$, Z.S. Umhaeva$^3$

Moscow University Physics Bulletin 2007. 62. N 3. P. 184

The magnetic state of the Mn$_{19.8-x}$Fe$_x$Sn$_{0.2}$ alloys is revealed and the mechanisms of changing their properties depending on the iron content are determined.

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## Mössbauer studies of natural glasses of impact and volcanic origin

### V.S. Rusakov$^1$, M.V. Volovetskii$^2$, O.A. Lukanin$^2$

Moscow University Physics Bulletin 2007. 62. N 3. P. 187

Mössbauer spectroscopy of natural silicate glasses of impact (tektites, impactites, and irghizites) and volcanic origin (obsidians) is performed. The resulted spectra are processed by the method of reconstructing the distribution functions of superfine parameters of partial spectra. The content of Fe$^{3+}$: is determined to be 5–10% in tektites, 15–25% in impactites, 25–35% in irghizites, and ∼20% in obsidians. The oxygen coordination sphere of Fe$^{3+}$ is found to be octahedral in the tektites, tetrahedral in the impactites, and intermediate in the other glasses. The coordination of Fe$^{2+}$ is intermediate between the octahedral and pentahedral ones.

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## A method of determining the distribution of photoconductivity and its relaxation time over the semiconductor wafer thickness

### O.G. Koshelev$^1$, E.A. Guseva$^2$

Moscow University Physics Bulletin 2007. 62. N 3. P. 193

A noncontact method is proposed to determine the depth profiles of photoconductivity and its relaxation time in a high-resistance plane-parallel semiconductor wafer placed at the center of an open confocal cavity normally to its axis and exposed to intensity-modulated light. The method is based on measuring the cavity transmission modulation depth at several frequencies for which the wafer optical thickness equals an integer number of half-waves and the wafer positions in which the phase difference between the interfering waves on the wafer surfaces is a multiple of $\pi/2$. The effect of experimental errors on the accuracy of the method is studied by computer simulation.

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Theoretical and mathematical physics

## Phase transitions in dense quark matter in a gravitational field of constant curvature

### V.Ch. Zhukovsky$^1$, A.V. Tyukov$^1$, D. Ebert$^2$

Moscow University Physics Bulletin 2007. 62. N 3. P. 198

The impact of the gravitational field on the formation of quark and diquark condensate in the framework of the extended Nambu-Jona-Lasinio (NJL) model is studied. In the mean field approximation, an expression for the effective potential with regard to a finite temperature and density of quark matter in the static gravitational field of constant curvature is obtained.

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Geophysics

## Effect of hydrostatic pressure on isothermal remanent magnetization of rocks

### V.I. Trukhin$^1$, N.S. Bezaeva$^1$, P. Rochette$^2$, J. Gattacceca$^2$

Moscow University Physics Bulletin 2007. 62. N 3. P. 201

The effect of hydrostatic pressure (up to 1.3 GPa) on the isothermal remanent magnetization of rocks is studied experimentally using a new-type nonmagnetic high-pressure cell produced at the Institute of High-Pressure Physics (Troitsk, Moscow oblast). The experiments were carried out at the European Center for Research and Education in Environmental Geoscience (CEREGE), France.

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## On the decametric radiation of Jupiter

### V.I. Grigor’ev, V.S. Rostovskii

Moscow University Physics Bulletin 2007. 62. N 3. P. 203

A possible mechanism of the influence of Io’s and Jupiter’s tidal baroelectric fields on the decametric radiation is discussed on a qualitative level.

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