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

## Radiation conditions for an impedance waveguide

### A.N. Bogolyubov, M.D. Malykh, and Yu.V. Mukhartova

Moscow University Physics Bulletin 2006. N 1. P. 1

А proЫem of excitation of oscillations bу current in а regular cylindrical wave-guide Ω with the Shchukin-Leontovich boundary conditions is considered. It is demonstrated that the requirement of existence of а generalized Fourier transformation (Fr-transformation) is а fairly correct radiation condition that singles out а solution in the form of а superposition of waves outgoing from the source.

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## Elliptic transformation of field equations in an implicit nonradiative plasma model

### L.V. Borodachev

Moscow University Physics Bulletin 2006. N 1. P. 7

А method of constructing а staЫe numerical solution of self-consistent field equations in the Vlasov-Darwin discrete model with an implicit calculation scheme of charged-particle dynamics is discussed.

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## Neutron decay in strong magnetic field with consideration for interaction of fermion anomalous magnetic moments with an external field

### Н. Goudarzi and I.V. Mamsurov

Moscow University Physics Bulletin 2006. N 1. P. 12

Total probabllity of neutron, $\beta$-decay in external magnetic field with consideration for interaction of the particle magnetic moments with the field is obtained. The cases of weak and strong magnetic field are considered. In the case of а weak field, comparison with the results obtained earlier is carried out.

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## Quasigasdynamic equations and an approximation formula for volume viscosity

### T.G. Elizarova and V.V. Seregin

Moscow University Physics Bulletin 2006. N 1. P. 18

The form of quasigasdynamic (QGD) equations oЬtained Ьу the momentary averaging of the model kinetic equation is presented. Based on the representation of the QGD equations in the form of differential conservation laws and the separation of the dissipative terms in the Navier-Stokes form, an estimation formula for the volume viscosity coefficient is oЬtained. The formula derived is similar to the known volume viscosity expression associated with the rotational nonequilibrium.

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## An algorithm for solving the Helmholtz equation in а cylindrical region with impedance boundary conditions

### V.P. Modenov and S.A. Ivanov

Moscow University Physics Bulletin 2006. N 1. P. 24

А scheme for а partial Galerkin method for studies of the propagation of axisymmetric electromagnetic waves in а cylindrical region with third-kind boundary conditions with а complex impedance that is small in absolute value is developed and mathematically substantiated.

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## Upper and lower energy estimates for few-body nuclear and Coulomb systems

### A.G. Donchev, S.A. Kalachev, N.N. Kolesnikov, and V.I. Tarasov

Moscow University Physics Bulletin 2006. N 1. P. 28

In the framework of the variational method with trial functions of the exponential and Gauss types, upper and lower estimates of energy for nuclear type systems and for the Coulomb systems of three, four and five particles have been found. The douЫe-ended estimates of energy not only allow one to find the exact energy range, but also provide an extra possibllity of extrapolation to the exact energy value. In this way, within the same accuracy, smaller volume of calculations can Ье performed using а lesser number of trial functions.

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## Asymptotic eigenvalues of the mode\ Hamiltonian for interacting bosons

### D.S. Golikov

Moscow University Physics Bulletin 2006. N 1. P. 35

An asymptotic of the eigenvalues of the Hamiltonian for а system of interacting bosons is constructed. The results are demonstrated to correspond to the corollaries of the Bogolyubov variational principle.

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## Tensor-index representation and difference approximation for а quasigasdynamic system

### D.V. Tikhomirov

Moscow University Physics Bulletin 2006. N 1. P. 41

Исследована квазигазодинамическая система (КГД-система) на сложных расчетных областях. Построен общий вид КГД-системы в тензорно-индексном представлении в произвольных координатах, а также разностная аппроксимация полученных уравнений в потоковой форме в виде законов сохранения.

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## А mathematical model of inha\ation of toxic substances Ьу the human body during emergencies at nuclear facilities

### S.P. Babenko and A.V. Bad'in

Moscow University Physics Bulletin 2006. N 1. P. 48

А situation in which uranium hexafluoride (UF$_6$) is discharged bу accident into the atmosphere of the working areas at nuclear facilities is examined. А mathematical model describing the formation of aerosol particles of UO$_2$F$_2$ and HF in the atmosphere of the working areas is developed. The model takes into account the drift of aerosol particles under the forces of gravity and viscous drag. The doses of toxic substances, uranium and fluorine, absorbed bу the human body in the course of breathing are estimated.

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## Calibration of pressure gradient detectors in air in the near-zone field in unequipped areas

### B.I. Goncharenko and V.A. Gordienko

Moscow University Physics Bulletin 2006. N 1. P. 53

The possiЬility of calibrating sound detectors in the near-zone field within real areas is shown. On the basis of experimental data it is demonstrated that the conditions needed for the spherical decrease of the field in real laboratory areas are met within the operating frequency range over horizontal distance up to 60-80 cm. Comparison of the data on calibration of а PGD channel in the near-zone field with similar data oЬtained for other controlled environments showed good agreement.

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## Effect of side lobes in the receiving antenna pattern on the superresolution performance in passive radio imaging systems

### Yu.A. Pirogov and A.L. Timanovskii

Moscow University Physics Bulletin 2006. N 1. P. 59

The effect of side lobes of the instrument function of а passive radio imaging system on the superresolution algorithms (SRA)is considered. The effects are studied Ьу doing computer simulations of the reconstruction of test images. It is shown that the most common SRA cannot Ье used if the side-lobe level exceeds -10 dB.

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## Dissociation rate constants of diatomic molecules in а vibrationally nonequilibrium gas

### А.I. Osipov and S.L. Shelepin

Moscow University Physics Bulletin 2006. N 1. P. 81

А method for calculating level-dependent dissociation cross sections, based on the solution of an ill-posed inverse problem, is outlined. The dissociation rate constants of the 0_2 and N_2 molecules over а wide temperature range and also under two-temperature conditions are calculated.

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Optics and spectroscopy

## Studying the features of Со ions sorption in aqueous serum albumin solutions

### Yu.M. Petrusevich, G.P. Petrova, А.М. Makurenkov, and A.V. Boiko

Moscow University Physics Bulletin 2006. N 1. P. 64

The sorption of cobalt ions on the surface of albumin macromolecules in aqueous solutions is studied Ьу the nuclear magnetic resonance relaxation method. The number of the sorption centers is determined and the adsorption energy is estimated. The dynamic light scattering method is used to measure the diffusion coefficients of the macromolecular albumin clusters formed in the presence of cobalt ions.

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## Charge-transfer luminescence in ytterЬiuim-doped sesquioxides

### D.N. Krasikov, N.V. Gerasimova, I.A. Kamenskikh, V.V. Mikhailin, and S.N. Shcherbinin

Moscow University Physics Bulletin 2006. N 1. P. 69

The charge-transfer luminescence spectra and kinetics and also the IR luminescence spectra of the Lu$_2$O$_3$-2%Yb, Y$_2$O$_3$-3%Yb, Sc$_2$O$_3$-0.7%Yb ytterblumdoped and Yb$_2$O$_3$ sesquioxides exposed to UV and VUV radiation were measured at 10-300 К, and the charge-transfer luminescence excitation spectra were measured in the energy range 4-25 eV. The charge-transfer luminescence spectra studied are shown to contain two luminescence components differing in temporal and spectral characteristics due to the Yb$^{3+}$ ions in two different crystallographic positions.

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## Self-modulation in 786-nm saturaЬ!e-absorber mode-locking injection lasers

### А.А. Anashkov, G.V. Belokopytov, and A.S. Lar'kin

Moscow University Physics Bulletin 2006. N 1. P. 76

Electron-optical chronography is used to study self-modulation in saturableabsorber mode-locking injection lasers emitting light at а wavelength of 786 nm. In the laser samples studied, the excitation of radiation pulses occurred in а single mode, and the near-field radiation structure suffered no changes during pulse generation. When the pumping current was increased within the range 20-32 mA, the repetition frequency of the light pulses generated approximated а logarithmic function of the pumping current and was varied between 1 and 2.6 GHz.

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Geophysics

## Yu.G. Smirnova, А.В. Nelepo, and G.G. Khundzhua

### Phytoplankton in heat- and mass-exchange processes in the El Niiio zone

Moscow University Physics Bulletin 2006. N 1. P. 88

Recent ecological disasters and cataclysms, such as drought, fires, heavy rains and spring fioods-induced inundation in different regions of the Earth are more and more often attributed to the unpredictable and little-studied El Niňo phenomenon. Although the processes involved in the El Niňo phenomenon are regional, their effects are nevertheless global.

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## Equations of elastic waves in porous media

### S.A. Arsen'ev, V.N. Nikolaevskii, and N.K. Shelkovnikov

Moscow University Physics Bulletin 2006. N 1. P. 91

Nonlinear equations that describe propagation of elastic waves in moving porous media saturated with flowing liquid or gas are derived.

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Solid state physics

## Measurement reduction method in the proЫem of detecting the paramagnetism- induced superparamagnetism phase transition

### V.I. Nikolaev and О.Р. Тretyakova

Moscow University Physics Bulletin 2006. N 1. P. 96

The potentialities offered bу the measurement reduction method in the problem of detecting the paramagnetism-induced superparamagnetism phase transition exemplified Ьу а system of nanoparticles with а log-normal size distribution have bееn studied. It is shown that the method makes it possiЪle to transform initial experimental data to а form which would correspond to the improvement of the actual experimental conditions (in the first place, а significantly smaller size scatter of particles). Аll basic features of the method application "technology" are illustrated on а concrete example of the temperature-field dependence of magnetic susceptibllity for an ensemЪle of nanoparticles in the Curie point region.

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## New smooth nonlocal model potential of base metals

### O.V. Kris'ko, V.M. Silonov, T.V. Skorobogatova, and D.P. Bokarev

Moscow University Physics Bulletin 2006. N 1. P. 100

А new smooth nonlocal model potential of base metals the form factor of which is free of nonphysical oscillations is proposed.

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