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

## Formation of a Kerr black hole from two stringy NUT objects

### V.S. Manko$^1$, E.D. Rodchenko$^2$, E. Ruiz$^3$, M.B. Sadovnikova$^2$

Moscow University Physics Bulletin 2009. 64. N 4. P. 359

In this paper we show that an isolated Kerr black hole can be interpreted as arising from a pair of identical counter-rotating NUT objects placed on a symmetry axis at the appropriate critical distance from each other.

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## Distribution of guided mode power flow between the layers of circular and elliptical multilayer optical fibers

### V.I. Krivenkov

Moscow University Physics Bulletin 2009. 64. N 4. P. 362

An invariant expression in the form of a contour integral for guided mode power flow via an arbitrary area of the cross section of an optical fiber with constant permittivity is presented in polar and elliptical coordinates. Expressions for guided mode power flows via the cross sections of circular and elliptical multilayer optical fibers are obtained.

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## An approach to introducing fractional integro-differentiation in classical electrodynamics

### A.N. Bogolyubov$^1$, A.A. Potapov$^2$, S.Sh. Rehviashvili$^3$

Moscow University Physics Bulletin 2009. 64. N 4. P. 365

Analogs for Maxwell’s equations with fractional derivatives are obtained using the concepts of an effective current and the velocity of a charged particle in a medium. The calibration invariance is considered and a diffusion-wave equation is found and analyzed for scalar and vector potentials. It is shown that the stochastic nature of charged particle motion in a medium influences the dynamics of an electromagnetic field.

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Physics of nuclei and elementary particles

## Effects of minimal supersymmetry standard model in neutral $K^0$ meson mixing

### A.I. Sukachev

Moscow University Physics Bulletin 2009. 64. N 4. P. 374

Mixing of neutral $K^0$ mesons is studied in the framework of the minimal supersymmetric model (MSSM) with a Yukawa type II sector and explicit violation of $CP$ invariance in the Higgs potential. Mixing parameters$\Delta m_{LS}$ and $\varepsilon$ are calculated in the limit of the four-fermion approximation with charged Higgs boson exchange. This work specifies the data presented in [1] more precisely and, taking into account the influence of new contributions on the above observables, proves the small degree of supersymmetric effects for a system of $K^0$ mesons.

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## Recursive method for calculation of tree-level elements of arbitrary order $S$ matrix in scalar electrodynamics

### E.E. Boos$^1$, V.E. Bunichev$^2$, A.V. Tolokonnikov$^3$

Moscow University Physics Bulletin 2009. 64. N 4. P. 379

The possibility of creating a recursive method for the calculation of tree-level elements of an $S$-matrix based on the functional integration method is considered, as exemplified by scalar electrodynamics. One of the advantages of this method is the gauge invariance of amplitudes provided without additional operations with them.

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## Using a focused ion beam for the creation of a molecular single-electron transistor

### I.V. Sapkov$^1$, V.V. Kolesov$^2$, E.S. Soldatov$^1$

Moscow University Physics Bulletin 2009. N 4.

Blank chips for a molecular single-electron transistor were created with the use of etching technology with a focused ion beam. Etching can be characterized as a process with a high speed of production, great reproducibility, mild requirements for prior lithographic operations, and rather good possibilities for decreasing gap width. The optimal parameters of scission of the metallic jumper of the electrodes were found, so that it is possible to create a 70 nm gap suitable for the production of a system with “overhanging” electrodes.

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## Specificity of multiwave interaction of an electronic beam and electromagnetic field in a relativistic diffractive generator

### A.I. Slepkov, O.V. Gallyamova

Moscow University Physics Bulletin 2009. 64. N 4. P. 389

The mechanisms of self-consistent interaction of tubular relativistic electronic beams with the fields of super-dimensional periodic structure of a relativistic diffractive generator have been studied in the area of $2\pi$-type oscillations of fundamental mode. Numerical analysis was carried out with the use of the matrix multimode method in its nonstationary variation. The electromagnetic field profiles, their mode structure, and their radiation spectrum have been studied. The conditions for generating frequency stabilization concerned with the longitudinal resonance of the surface spatial harmonics and volume resonance at the cutoff frequency of the E 0n mode of cylindrical waveguide have been revealed.

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## Novel combined optoacoustic and laser-ultrasound transducer array system

### V.A. Simonova$^1$, E.. Savateeva$^1$, A.A. Karabutov$^2$

Moscow University Physics Bulletin 2009. 64. N 4. P. 394

A new multichannel integral system enabling simultaneous laser-optoacoutic and laser-ultrasonic and optical-acoustic images in real time has been proposed. The new potential of such a system and the advantages of both methods (large depth of penetration, high image contrast, and spatial resolution) are discussed in detail.

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## Joint diffusion of rays in a homogeneous medium with random inhomogeneities

### O.K. Vlasova$^{1,3}$, L.I. Prikhod’ko$^{2,3}$

Moscow University Physics Bulletin 2009. 64. N 4. P. 397

Fluctuations of the direction and amplitude of two rays propagating in a homogeneous, on aver-age, medium with random inhomogeneities of dielectric permittivity are considered. The solution to the problem is based on the method of ray diffusion, which enabled us to obtain the probability densities of the distribution of the relative amplitude and the relative direction of the rays.

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Optics and spectroscopy. Laser physics

## Interference effects in the theory of multiphoton laser-simulated bremsstrahlung for electron wave packets that are broad in their momentum representation

### I.A. Burenkov, O.V. Tikhonova

Moscow University Physics Bulletin 2009. 64. N 4. P. 402

The interference peculiarities of absorption and emission of external laser field quanta by a spatially narrow electron wave packet during its scattering at a potential center are considered. The angular and energy distributions for an electron due to scattering in a laser field are obtained and analyzed within the framework of the perturbation theory based on interaction with the potential center. A new mechanism of effective heating of plasma produced in a cluster under the effect of intense external laser field is found. Drastic changes in angular distribution due to the interference of incident and scattered parts of an electron wave packet are revealed.

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## The Golden Mean and self-similar structures in optics

### N.V. Grushina, A.M. Zotov, P.V. Korolenko, A.Yu. Mishin

Moscow University Physics Bulletin 2009. 64. N 4. P. 407

Based on numerical modeling it has been found that if self-similarity (which often connects with the Golden proportions) is present in structures of Fibonacci gratings and multilayer systems, it appears in their optical characteristics. Properties of Fibonacci optical structures have been compared with those of other aperiodic systems. It has been shown that structures based on the Golden and Silver means have highly related optical properties.

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## Fluorescent characteristics of probes of the fluorescein family in human serum albumin solutions

### I.M. Vlasova, A.M. Saletsky

Moscow University Physics Bulletin 2009. 64. N 4. P. 412

Differences in human serum albumin solutions of fluorescein family probes in their molecular association, in the type of dependence of fluorescence on pH, and in fluorescence anisotropy have been shown. These are due to the electronegativities of the atoms of the lateral radicals in the structural formula and the pK values of the ionizable groups of the probes.

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## Refocusing of a high-power femtosecond laser pulse after a layer of atmospheric aerosol

### E.P. Silaeva, V.P. Kandidov

Moscow University Physics Bulletin 2009. 64. N 4. P. 417

The refocusing of a high-power femtosecond laser pulse after filamentation in a layer of atmospheric aerosol has been numerically investigated. It is shown that the presence of an on-path cloud of aerosol particles in the atmosphere results in the decrement of the filament energy, and the process of pulse refocusing becomes stochastic after the aerosol layer due to the competition between the influence of perturbations induced by aerosol scattering and filtration of radiation spatial modes.

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Condensed matter physics

## Hot electrons in indium nitride: a new numerical approach to solving the electron transport problem

### N.A. Masyukov, A.V. Dmitriev

Moscow University Physics Bulletin 2009. 64. N 4. P. 423

The electron transport in indium nitride in a heating electric field has been calculated. The results obtained are in good agreement with the known experimental data. The Boltzmann transport equation in the isotropic spatially homogeneous case has been solved using a new numerical approach based on the approximation of the distribution function from the points of a relatively thin grid in momentum space and the iterative search for a stationary solution.

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## Long-range order in a polycrystalline Pd-30 at % Au solid solution

### V.M. Silonov$^1$, T.V. Skorobogatova$^2$, O.V. Kris’ko$^3$, G.P. Zhmurko$^1$

Moscow University Physics Bulletin 2009. 64. N 4. P. 430

Using x-ray analysis, at % the existence of regions with a long-range order of the Cu$_3$Au type has been established in a polycrystalline Pd-30 at % Au solid solution.

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## Thermal oxidation of detonation nanodiamond

### I.A. Apolonskaya, A.V. Tyurnina, P.G. Kopylov, A.N. Obraztsov

Moscow University Physics Bulletin 2009. 64. N 4. P. 433

In this work the results of investigation of detonation ultradispersed diamond (UDD) powder by means of thermogravimetric analysis (TGA) and Raman scattering (RS) are presented. Using the TGA method the temperature regions corresponding to the oxidation of different carbon fractions included in the composition of UDD powder were determined. In particular, it was established that heat treatment in the air at a temperature not exceeding 550°C leads to the oxidation and removal of nondiamond carbon, while the diamond part of the UDD remains unchanged. The form of the diamond RS band in the spectra of the UDD powder oxidized at 550°C shows good agreement with the model of phonon confinement. Based on the comparison of the results of experimental data and theoretical calculations for the RS band forms the size of the UDD crystal grains was defined as 4–5 nm.

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## Localization of an ultrathin buried Fe layer in a multilayer structure Nb/Fe/[Mo/Si]$_{40}$/SiO$_2$ by means of X-ray standing waves

### M.A. Andreeva$^1$, A.D. Gribova$^1$, E.E. Odintsova$^1$, M.M. Borisov$^2$, M.V. Kovalchuk$^2$, E.Kh. Mukhamedzhanov$^2$

Moscow University Physics Bulletin 2009. 64. N 4. P. 437

An analysis of the influence of standing waves on the angular dependencies of the fluorescent yield from an ultrathin iron layer buried inside a multilayer structure of Nb(50 nm)/Fe(3.9 nm)/[Si/Mo(6.77 nm)]$_{40}$/SiO$_2$ is presented. These angular dependencies of reflectivity and FeK α-fluorescence yield were measured at the Station for high-precision X-ray optics (HPXO) of the Kurchatov Center for Synchrotron Radiation and Nanotechnology. The measured data was analyzed with the help of our FLUO software package. As a result of the complex treatment of reflectivity and Fe fluorescent yield data, the depth profile for iron atomic density was restored.

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Biophysics and medical physics

## The impact of collisions on platelet distribution in the blood flow

### V.N. Buravtsev$^1$, A.V. Nikolaev$^1$, A.V. Ukrainets$^2$

Moscow University Physics Bulletin 2009. 64. N 4. P. 442

The impact of platelet collisions on their distribution in a viscous liquid flow has been analyzed. It has been shown that platelet distribution in the flow perpendicular to current lines resulting from their collisions can be described as “shear” diffusion. In the wide physiological range of shear velocities specific for blood, the coefficient of “shear” diffusion is much larger than the coefficient of “Brownian” diffusion. For a parabolic fluid velocity profile (Poiseuille flow) in cylindrical vessel “shear” diffusion causes uneven radial distribution of platelets over the vessel radius. “Shear” diffusion causes platelet concentration to grow from the wall toward the center (vessel axis). This effect appears to be a consequence of the specific distribution of platelet collision frequency reaching its maximum at the vessel wall.

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## Molecular mobility in protein solutions containing metal ions with various ionic radii

### I.A. Sergeeva, N.V. Sokol, M.S. Ivanova, G.P. Petrova, Yu.M. Petrusevich

Moscow University Physics Bulletin 2009. 64. N 4. P. 446

Using methods of photon-correlation spectroscopy and polarized fluorescence pH, the dependencies of the translation and rotary diffusion coefficients of collagen and bovine serum albumen in solutions on NaCl and KCl salts at various ion forces have been obtained. It is shown that the size of the metal ionic radius affects intermolecular interactions and the mobility of albumen molecules in solution. The effect of the potassium ion, with its large ionic radius, compared with Na ions, is analogous to the effect of heavy metals ions, since it results in albumen molecule aggregation near the isoelectric point.

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Astronomy, astrophysics, and cosmology

## Atmospheric UV light and comparing of its intensity with the electron flux variations at satellite orbit (“Universitetsky-Tatiana" satellite data)

### N.N. Veden’kin, A.V. Dmitriev, G.K. Garipov, P.A. Klimov, V.S. Morozenko, I.N. Myagkova, M.I. Panasyuk, S.N. Petrova, I.A. Rubinshtein, U. Salazar, S.I. Svertilov, V.I. Tulupov, B.A. Khrenov, V.M. Shakhparonov, A.V. Shirokov, I.V. Yashin

Moscow University Physics Bulletin 2009. 64. N 4. P. 450

The ultraviolet radiation of the night atmosphere and electron fluxes with energies higher than 70 keV are measured simultaneously onboard the satellite Universitetskii-Tatiana. It has been revealed that the mean intensity of ultra-violet radiation increases and this could be due to electron acceleration in atmospheric electric discharges with further capture by the geomagnetic field and electron precipitation in conjugated points of the geomagnetic field.

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Physics of Earth, atmosphere, and hydrosphere

## Analysis of high-frequency geoacoustic emissions using a receiving unit based on a vector receiver

### V.A. Gordienko$^1$, T.V. Gordienko$^1$, J.V. Marapulets$^2$, A.O. Sherbina$^2$

Moscow University Physics Bulletin 2009. 64. N 4. P. 455

The features of the use of a combined receiver that is able to record acoustic pressure and three mutually orthogonal components of its gradient simultaneously in a region of small wave sizes are discussed. This method can be used to record geoacoustic emission signal anomalies, which could be treated as useful earthquake precursors. Possible methods of solving this problem are considered using an example of the analysis of such anomalies that occurred during strong seismic events in Kamchatka.

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## Estimation of the melting temperature of the Earth’s mantle material

### G.I. Petrunin, V.V. Lupachik

Moscow University Physics Bulletin 2009. 64. N 4. P. 460

This paper presents an approach that makes it possible to calculate the Lindemann constant for polyatomic crystal compounds (minerals) with a different type of bond and to directly estimate the constancy of the ratio between the mean-square amplitude of atomic oscillations and the average distance between atoms on a melting curve using the Lindemann hypothesis within the Debye acoustic approximation. The ratio obtained was used to estimate the melting temperature of the Earth’s mantle material under conditions of natural occurrence without assigning fixed points only from the data of modern seismic and mineralogical models.

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Optics and spectroscopy. Laser physics

## Application of the model of a set of harmonic oscillators in intense femtosecond laser pulsed field for the estimation of the limits of electron heating in insulators

### I.B. Bogatyrev$^1$, A.N. Vasil’ev$^2$, U.V. Popov$^2$

Moscow University Physics Bulletin 2009. 64. N 4. P. 465

We study dynamics of harmonic oscillators system with continuously distributed frequencies irradiated by femtosecond laser pulse. This system is applied to the description of vertical transitions with conservation of the quasi-momentum between different branches of the conduction band at those points of the Brilloin zone at which the effective heating is possible. The model can be applied for the estimation of the high-energy tail of the electron distribution in insulators at intensities under optical breakdown. Analytic solution for electron energy distribution in oscillators system after heating by femtosecond laser pulse is obtained. It is shown that at laser field intensities above 3 TW/cm$^2$ with photon energy of 1.55 eV and pulse duration of 40 fs the electrons with energy above 10 eV are appeared.

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Astronomy, astrophysics, and cosmology

## Frequency spectra of variations of cosmic rays, parameters of solar activity and the interplanetary environment

### V.P. Okhlopkov

Moscow University Physics Bulletin 2009. 64. N 4. P. 470

The periodicities that take place in cosmic rays in the stratosphere, in the neutron component, and in various parameters of solar activity and the interplanetary environment for the period from 1958 to 2007 were investigated by means of spectral analysis.

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