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

## Mathematical problems arising in the development of an "ecological policeman"

### N.A. Tikhonov, M.K. Trubetskov, G.N. Medvedev

Moscow University Physics Bulletin 2004. 59. N 4. P. 1

Based on numerical techniques, the potentialities of an integral-sorption method for monitoring the presence of contaminants in waste water are studied using an instrument called an "ecological policeman". The simplest linear model of the process and an ion-exchange sorption model that makes it possible to study the sorption dynamics in conditions close to the actual ones, where the dissolved components undergo sorption not independently, but while affecting one another, are considered.

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## Spectral properties of an electromagnetic waveguide with nonuniform filling

### A.N. Bogolyubov, M.D. Malykh, V.L. Ponomareva

Moscow University Physics Bulletin 2004. 59. N 4. P. 11

The instability of the eigenvalues of an electromagnetic waveguide with real filling with respect to small perturbations of its parameters is proved.

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## The Dirichlet-Neumann problem for the Helmholtz equation outside cuts in a plane

### P.A. Krutitskii, К.V. Prozorov

Moscow University Physics Bulletin 2004. 59. N 4. P. 16

For the Helmholtz equation outside cuts in a plane a boundary-value problem is studied. The Dirichlet condition is specified on one side of each cut and the Neumann condition, on its other side. The existence and uniqueness theorems for the solution of the boundary-value problem are proved. An integral representation for the solution is obtained in the form of potentials. From a uniquely solvable system of integral equations, the density in the potentials is determined.

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## Quantum corrections in $N=1$ supersymmetric electrodynamics regularized by higher derivatives

### A.A. Soloshenko, К.V. Stepanyants

Moscow University Physics Bulletin 2004. 59. N 4. P. 21

The structure of the effective action and renormgroup functions in $N=1$ supersymmetric electrodynamics regularized by higher derivatives is studied. The results are applied to solve the anomaly puzzle in the model under consideration.

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## Evolution of the spin of a charged particle in an electric field

### A.E. Lobanov

Moscow University Physics Bulletin 2004. 59. N 4. P. 26

Dynamics of the spin of a charged particle with anomalous magnetic moment in an arbitrary constant electric field is investigated. The fields, where a solution of the Bargmann-Michel-Telegdi equation can be represented in a complete form, are found. Rotation of a particle spin in scattering in the Coulomb field is studied.

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Atomic and nuclear physics

## Gamma sources with a wide-angle irradiation field

### V.K. Grishin, B.S. Ishkhanov, S.P. Likhachev, V.I. Shvedunov

Moscow University Physics Bulletin 2004. 59. N 4. P. 31

Systems providing for the production of a homogeneous photon field for the irradiation of objects of large angular dimensions Eire considered. It is demonstrated that such systems can be developed on the basis of bremsstrahlung of an electron beam with a certain angular distribution.

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## Studies of the distribution of the arrival times of extensive air showers from the data obtained with the eas msu setup using nonlinear analysis techniques

### M.Yu. Zotov, G.V. Kulikov, Yu.A. Fomin

Moscow University Physics Bulletin 2004. 59. N 4. P. 35

The results of nonlinear analysis of the times of registration of extensive air showers (EAS), obtained with the "Prototype EAS-1000" unit operating as part of the EAS MSU setup are presented. In particular, EAS clusters and also sets of showers showing signs of chaotic dynamics are detected. Possible mechanisms responsible for the emergence of these phenomena are discussed.

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## Effect of the longitudinal magnetic field on the radial electric field in a low-pressure discharge

### R.Z. Shaikhitdinov, V.M. Shibkov

Moscow University Physics Bulletin 2004. 59. N 4. P. 40

The measurement results of the radial behavior of the plasma potential of a low-pressure discharge in a cylindrical dielectric tube placed in a longitudinal magnetic field are presented. It is demonstrated that for the correct measurement of the radial electric field from the probe floating potential difference account should be taken of the plasma potential displacement caused by the inhomogeneous radial distribution of the electron concentration.

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Solid state physics

## Variation of the domain-wall relaxation frequency in an amorphous ferromagnet under adsorption of methanol molecules

### V.E. Zubov, A.D. Kudakov, N.L. Levshin, T.S. Fedulova

Moscow University Physics Bulletin 2004. 59. N 4. P. 44

Using a magnetooptical method, a reversible decrease in the relaxation frequency of a domain wall on the surface of an amorphous soft ferromagnet during adsorption of methanol molecules was observed. The detected effect is explained by the appearance of magnetic defects that form in the adsorption of methanol molecules on the ferromagnet's surface, a process in which hydrogen bonds are formed. The results of this research and the earlier data on the effect of reversible adsorption of water molecules on the dynamics of the domain walls in ferromagnets are compared.

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Geophysics

## Model of shear layer interaction and description of mass exchange in a density flow

### В.I. Samolyubov, A.V. Shil'nev

Moscow University Physics Bulletin 2004. 59. N 4. P. 48

The results of experimental and theoretical studies into the vertical heat and suspended matter transfer in a near-bottom stratified flow are presented. To calculate the distributions of water temperature and suspended particle concentration over the entire flow depth, a mathematical model verified against in-situ measurement data is suggested. The model is constructed on the basis of the hypothesis of interaction between the shear layers (the near-bottom layer and the mixing layer). The method developed is suitable for the theoretical description of the profiles of water temperature and suspended matter concentration differing in local curvature, as well as quasistepped profiles and those containing suspended matter concentration maxima. Time variations of the profiles are calculated under nonsteady-state boundary conditions. The effects of the density flow stratification and the suspended matter activity on the vertical mass exchange in the shear layers and in the flow core are taken into account.

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Theoretical and mathematical physics

## New aspects in the spectral problem of the radial Schrodinger equation with an arbitrary attracting potential

### O.S. Pavlova, A.R. Frenkin

Moscow University Physics Bulletin 2004. 59. N 4. P. 56

The operator method of integral transforms for finding the energy spectrum of the radial Schrodinger equation, which is used for attracting potentials, is further developed.

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## Ferromagnetic state of the $SU(2)$-vacuum

### V.Ch. Zhukovskii, О.V. Tarasov

Moscow University Physics Bulletin 2004. 59. N 4. P. 60

The conditions for the ferromagnetic state of the chromomagnetic vacuum to exist are considered. It is shown that tachyonic modes can condense into a spatially uniform state if the length of the chromomagnetic field is limited. The problem of the phase transition between the ferromagnetic and superconducting states is considered.

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## Effect of mach number on electric-discharge characteristics in supersonic airflow

### A.F. Alexandrov, A.P. Ershov, В.I. Timofeev, I.B. Timofeev

Moscow University Physics Bulletin 2004. N 4.

The results of measurements of the parameters of transverse electric discharges placed in supersonic airflows with Mach numbers M = 2 and M = 6 are compared. It is shown that the dependences of the electric field strength and the discharge-channel diameter on current for two Mach numbers are close.

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Optics and spectroscopy

## Effect of ultralow-frequency commutation of radiation direction in solid-state ring lasers in self-modulation modes of the second kind

### A.N. Shelaev

Moscow University Physics Bulletin 2004. 59. N 4. P. 68

It has been established both experimentally and theoretically that in YAG:Nd$^{3+}$ solid-state ring lasers (SRLs) with strong competition and nonlinear coupling of counter-running waves (CRW) there exists, due to CRW self-diffraction on induced inverted-population gratings, an unusual (for laser physics) effect of ultralow-frequency instability in both uni- and bidirectional lasing when the radiation-direction commutation frequency is lower than the lowest-frequency SRL parameter, the rate of inverted-population relaxation $1/T_1$, by a factor of $10^5$ or more (commutation period Tc longer than $T_k>10^2$ s).

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Solid state physics

## Investigation of dissipation in the torsion modes of thin fused silica fibers

### I.A. Bilenko, S.L. Lourie

Moscow University Physics Bulletin 2004. 59. N 4. P. 72

In highly sensitive experiments with test masses, the use of thin quartz fibers with small intrinsic losses as suspensions is planned. The results of measurements of losses in fibers with diameters ranging from 1.5 to 19 pm are presented. The results obtained suggest that the contribution of surface losses increases as the diameter decreases.

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