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

## Algebra of individual inaccuracies of intervals

### V.I. Grigor’ev

Moscow University Physics Bulletin 2008. 63. N 4. P. 229

A version of the geometry of non-arithmetizable physical space-time based on the hypothesis of individual inaccuracies of the spatial and temporal intervals is discussed.

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## Calculating lateral distribution functions of the Cherenkov light from extensive atmospheric showers in terms of a multilevel scheme

### L.G. Dedenko$^2$, T.M. Roganova$^2$, G.F. Fedorova$^2$, D.A. Podgrudkov$^2$, G.P. Shoziyoev$^2$

Moscow University Physics Bulletin 2008. 63. N 4. P. 232

A new technique for calculating the lateral distribution function of the Cherenkov light in very-high-energy extensive atmospheric showers is proposed. It is shown that the calculation results are in good agreement with the experimental data.

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## Internal energy of ordered multicomponent systems in a correlation approximation

### P.N. Nikolaev

Moscow University Physics Bulletin 2008. 63. N 4. P. 238

An expression for the internal energy of a multicomponent ordered many-body system has been obtained by means of the correlation expansion technique. This expression has proved to be useful for strongly anharmonic crystals in wide temperature and pressure ranges. The relation between the fundamental characteristics of a solid that are used in the correlation expansion and in the phonon approximation has been found. This is, in particular, the relation between the Debye and Einstein temperatures and the average speed of sound.

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## A study of the applicability of a method for successive determination of the kinetic coefficients of sorption on the basis of mathematical modeling

### M.G. Tokmachev$^1$, M. Riegel$^2$, W. Hoell$^2$

Moscow University Physics Bulletin 2008. 63. N 4. P. 242

This paper presents the results of mathematical modeling and experimental studies of ion-exchange process between a weakly concentrated uranium solution and sorbent grains. On the basis of mathematical modeling, we analyze the method of successive determination of the kinetic coefficients of sorption, determining its practicality.

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## Energy spectrum and optical properties of $D^{-}$− centers in structures with quantum disks

### V.Ch. Zhukovsky$^1$, V.D. Krevchik$^2$, M.B. Semenov$^2$, V.A. Proshkin$^2$

Moscow University Physics Bulletin 2008. 63. N 4. P. 245

The impurity absorption of light in a quasi-zero-dimensional structure with disk-like quantum dots is theoretically investigated using the zero-range potential model. It is shown that the singularity of the geometric and potential confinement of a quantum disk manifests itself in spatial anisotropy of the coupling energy of the $D^{-}$ − state and in a significant dependence of the impurity absorption edge on the characteristic dimensions of disk-like quantum dots.

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## Diffraction of monochromatic waves on a metallic cylinder with longitudinal slots

### A.V. Lychev

Moscow University Physics Bulletin 2008. 63. N 4. P. 251

The projection matching method is applied to the calculation of a circular cylindrical slot line with one and two slots. The diffraction problem is studied at near-resonance frequencies.

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Physics of nuclei and elementary particles

## Compact linear electron accelerator for radiation technologies

### A.S. Alimov, B.S. Ishkhanov, V.I. Shvedunov

Moscow University Physics Bulletin 2008. 63. N 4. P. 256

A prototype of a commercial compact continuous-beam linear electron accelerator has been designed and constructed. With its energy of 600 keV and a beam with 30 kW maximum power, the accelerator can be used in various radiation technologies. Its compact size, easy operation, reliability, wide adjustment range for the main parameters, and possible local shielding allow it to be integrated into the majority of radiation technology processes.

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## Mixing of $K^0$ and $B^0$ neutral mesons within the minimum supersymmetry model

### M.N. Dubinin, A.I. Sukachev

Moscow University Physics Bulletin 2008. 63. N 4. P. 259

Mixing of $K^0$ and $B^0$ mesons is studied in the scope of the minimum supersymmetry model (MSSM) with a type II Yukawa sector and explicit violation of $CP$ invariance in the Higgs potential. The mixing parameters $\Delta m_{LS}$ and $\varepsilon$ are calculated in the limit of the low-energy four-fermion approximation with a charged Higgs boson exchange. It is shown that supersymmetric effects are very small for $K^0$ mesons and may be quite significant for $B_s^0$ and $B_d^0$ mesons, which imposes constraints on the MSSM parameter space.

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## Experimental determination of sensitivity of piezoquartz microweighing using an electrochemical method

### Yu.K. Aleshin, A.P. Sukhorukov

Moscow University Physics Bulletin 2008. 63. N 4. P. 264

The sensitivity of a piezoquartz microweighing device was determined experimentally using an electrochemical method working in a real time mode. The results obtained confirmed the linearity of the dependence of the piezoquartz generator’s basic frequency drift on the mass of an applied metal for a wide measurement range.

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Optics and spectroscopy. Laser physics

## Peculiar properties of hot plasma formation under the influence of intense femtosecond pulses on the surface of molten metal

### D.S. Uryupina$^{1,2}$, M.V. Kurilova$^2$, N. Morshedian$^2$, R.V. Volkov$^{1,2}$, A.B. Savel’ev$^{1,2}$

Moscow University Physics Bulletin 2008. 63. N 4. P. 267

The peculiar properties of plasma formation on the surface of different liquid metals by femtosecond laser radiation have been studied. It is shown that plasma formation and generation of hard X-radiation on the surface of molten metal depends substantially on the contrast and weakly on the polarization of laser radiation, which clearly distinguishes the plasma produced in our experiments from the plasma generated on the surface of a solid target.

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Condensed matter physics

## Frequency dependence of low-temperature phononless conductivity in disordered systems

### I.P. Zvyagin, M.A. Ormont

Moscow University Physics Bulletin 2008. 63. N 4. P. 272

The frequency dependence of resonant phononless hopping conductivity in disordered systems with pointlike centers of localization in the low-temperature limit is considered within the framework of the pair approximation. It is shown that the existing theory that predicts the power-mode frequency dependence of the low-frequency phononless hopping conductivity $\sigma(\omega)$ and a transition from linear to quadratic dependence (crossover) when frequency increases may become invalid, and the quadratic frequency dependence may never manifest itself at all.

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Astronomy, astrophysics, and cosmology

## Primordial black holes and the asteroid hazard

### A.A. Shatskii

Moscow University Physics Bulletin 2008. 63. N 4. P. 276

The probability of a primordial black hole (PBH) entering into the Kuijper asteroid belt in the Solar System is calculated. It is shown that primordial black holes of certain masses can significantly modify asteroid trajectories and orbits. Such events can result in local solar-system catastrophes and global terrestrial catastrophes (e.g., the Tunguska event). The rate of such events is estimated.

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Theoretical and mathematical physics

## Generation of second and third harmonics by a rotating pulsar in parametrized post-Maxwellian electrodynamics

### V.A. Sokolov

Moscow University Physics Bulletin 2008. 63. N 4. P. 279

We consider the generation of multiple harmonics by a rotating pulsar in parametrized post-Maxwellian electrodynamics, and evaluate angular distributions of the emission intensity and conversion ratios for emission at a doubled or tripled pulsar rotation frequency.

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## Conformal behavior of a single chain $АВ$ block copolymer with mobile $В$-blocks

### O.S. Pevnaya, E.Yu. Kramarenko, A.R. Khokhlov

Moscow University Physics Bulletin 2008. 63. N 4. P. 281

Monte-Carlo computer modeling was used to investigate the conformal behavior of a single chain $AB$ block copolymer with mobile hydrophobic $B$-blocks and hydrophilic $A$-links. The formation of a “tailed globule” was observed with an increase of the energy of attraction between hydrophobic links. A comparison between the collapsing of a chain with mobile blocks and the behavior of regular and random block copolymers of the same structure was conducted.

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Physics of nuclei and elementary particles

## Macroscopic calculation of air shower radio emission

### N.N. Kalmykov$^1$, A.A. Konstantinov$^1$, R. Engel$^2$

Moscow University Physics Bulletin 2008. 63. N 4. P. 284

Two patterns of calculation of radio emission from extensive air showers (EAS), the so-called microapproach and macroapproach, are considered. The predictions of these approaches are compared by calculating the spatial distribution of the 40 MHz radio emission at the EAS energy $10^{16}$ eV.

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Optics and spectroscopy. Laser physics

## Local transverse diffusion of light due to laguerre laser beam diffraction

### Yu.V. Vasil’ev, A.V. Kozar’, D.A. Kuvshinov, A.E. Luk’yanov, A.V. Seliverstov

Moscow University Physics Bulletin 2008. 63. N 4. P. 287

When shading half of a Laguerre laser light beam with a semi-infinite metal screen with an imperfect edge the effect of fine structure formation in a transverse diffusion of “half-beam” light and its further evolution in the process of half-beam space propagation were experimentally revealed.

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Condensed matter physics

## Redistribution of chromium atoms between the components of an intermetallic/oxide nanocomposite in the course of its production

### T.Yu. Kiseleva, A.A. Novakova, A.N. Falkova, T.L. Talako, T.F. Grigor’eva

Moscow University Physics Bulletin 2008. 63. N 4. P. 290

Structural studies of nanocomposites produced by the method combining mechanical preactivation of the mixture comprising 8.1% Сr$_2$O$_3, 65.9% Fe, and 25% Al by mass and self-propagating high-temperature synthesis (SPHTS) have been carried out by Mössbauer spectroscopy methods. It was found that a FeAlCr$_2$O$_3$composite with a small Fe$_2$Al$_5$intermetallic impurity is produced at the mechanical activation stage. At the SPHTS stage, interaction between the activated components of the mixture results in formation of the Fe$_{0.70-x}$Сr$_{x}$Al$_{0.3}$($x=$0-0.2)/Al$_2$O$_3$composite. Show Abstract Chemical physics, physical kinetics, and plasma physics ## Combustion of a supersonic flowing propane-air mixture within a DC longitudinal-transverse discharge ## Combustion of a supersonic flowing propane-air mixture within a DC longitudinal-transverse discharge ### A.F. Aleksandrov, A.Yu. Baurov, A.P. Ershov, A.A. Logunov, V.A. Chernikov Moscow University Physics Bulletin 2008. 63. N 4. P. 293 The findings of experimental investigations on the combustion of a supersonic flowing propane-air mixture with initiation by a dc discharge are given. It was found that the pattern of combustion depended on a number of initial conditions associated with the generation of plasma and with the external parameters of the supersonic flow. Show Abstract Biophysics and medical physics ## Dynamics of collagen molecules in aqueous solutions containing metal ions with different ionic radii ## Dynamics of collagen molecules in aqueous solutions containing metal ions with different ionic radii ### G.P. Petrova$^1$, Y.M. Petrusevich$^2$, I.A. Perfil’eva$^1$, M.S. Ivanova$^1$, Chzhan Syaolei$^2\$

Moscow University Physics Bulletin 2008. 63. N 4. P. 296

The dynamic parameters of collagen molecules in aqueous solutions were assessed by the photon-correlation spectroscopy method. The dependences of translational diffusion coefficients as a function of pH in pure aqueous collagen solutions and in solutions containing salts of different metals such as Na, Ca, K, Pb were established. It has been reported that the size of a metal’s ionic radius affects intermolecular interactions and the mobility of collagen molecules in solution.

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