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

## Applying the method of potentials to problem of interaction between spherical gravitational wave and constant electromagnetic field

### V.I. Grigoryev, I.P. Denisova

Moscow University Physics Bulletin 2000. 55. N 1. P. 1

The problem of interaction between a spherical gravitational wave and a constant electromagnetic field has been solved. The expressions have been found for the strengths of an electric and a magnetic field, angular distribution and the total intensity of electromagnetic radiation that originates in this interaction.

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## Gottfried's integral and valence quarks contribution

### E.N. Bukina$^1$, V.M. Dubovik$^1$, V.S. Zamiralov$^2$

Moscow University Physics Bulletin 2000. 55. N 1. P. 4

The experimental value of Gottfried's integral is shown to be equal to the value of a modified valence quarks distribution. BjOrken 's sum rule is valid in the valence quark approximation, while the contributions of sea quarks violate it. Based on the available experimental data, the polarization distributions of quarks and antiquarks in the proton have been obtained.

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## Some new properties of strongly nonlinear ion sound

### l.M. Aleshin, D.V. Peregudov

Moscow University Physics Bulletin 2000. 55. N 1. P. 9

The solution of the Vlasov-Poisson equations that describe a stationary ionacoustic soliton has been analyzed. It is shown that for certain ratios of the number of flying-to-trapped electrons, a significant change in the solitary wave properties is possible.

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## Asymptotic behavior of effective action in supersymmetric theories

### K.V. Stepan'yants, V.B. Fokin

Moscow University Physics Bulletin 2000. 55. N 1. P. 14

Using a program written with the help of the MAPPLE analytical calculation program, asymptotic expansions of exact effective action for $N=1$ and $N=2$ supersymmetric models have been obtained within strong and weak coupling.

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## On a manifold of the Laughlin problem unique solutions

### B.A. Lysov, 0.F. Dorofeev

Moscow University Physics Bulletin 2000. 55. N 1. P. 21

The present paper has revealed that there exist exact solutions in the form of elementary functions (unique Laughlin's states) for certain relationships between the magnetic field induction and the value of the electron charge in the problem of correlated motion of two electrons in a constant and uniform magnetic field. The authors ha~e suggested a number of considerations that allow an understanding of the physical idea of these remarkable attributes of the magnetic field. The interest in this problem is associated with a new experimentally discovered state of the substance.

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## Ion energy distribution function for gas discharge positive column in pure gases

### S.A. Dvinin, V.A. Dovzhenko, A.A. Kuzovnikov

Moscow University Physics Bulletin 2000. 55. N 1. P. 27

The ion energy distribution function at an arbitrary point of a low-pressure discharge positive column has been calculated with regard to ions recharging. The calculations were performed for arbitrary relationships between the free path of ions,. the Debye radius, and the plasma size. The results can be used in designing technological plasma chambers for ionic etching and thin film deposition.

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## A possibility of selective excitation of characteristic waves at doubly reflected ionospheric radio transmission path

### V.V. Balinov, Yu.V. Berezin, O.Yu. Volkov

Moscow University Physics Bulletin 2000. 55. N 1. P. 32

The possibilities of improving the quality of information transmission in doubly reflected ionospheric radio transmission paths are discussed. It is shown that a combination of the method of selective excitation of characteristic waves in the ionosphere and that of polarization filtration of a multipath signal with a definite signal-to-noise ratio can improve the quality of information transmission in the doubly reflected radio transmission path more than by an order of magnitude.

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Acoustics and molecular physics

## Numerical simulation of nonlinear waves with "discontinuity" and "derivative discontinuity" singularities

### A.A. Slavnov, V.A. Khokhlova

Moscow University Physics Bulletin 2000. 55. N 1. P. 36

An asymptotical spectral method has been developed for the description of nonlinear acoustical waves containing "discontinuity" and "derivative discontinuity" singularities. The method allows one to model the propagation of discontinuous perturbations using a small number of harmonics {20-50). A closed system of connected nonlinear equations has been obtained for a finite number of complex harmonic amplitudes. The system approximates the equation of simple waves in the spectral representation.

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Solid state physics

## Hall effect in frustrated ferrimagnetic alloys $eps'$-Mn$_3$Ga

### V.N. Prudnikov, M.V. Prudnikova

Moscow University Physics Bulletin 2000. 55. N 1. P. 42

Electrical resistance, transverse magnetoresistance and the Hall effect have been studied in alloys $eps'$-Mn$_3$Ga in a frustrated ferrimagnetic state. For a paramagnetic state, the normal Hall coefficient $R_0$ is about $\sim10^{-13}$ Ом$\cdot$см$\cdot$Гс$^{-1}$ typical of metals. Magnetic ordering causes a pronounced change in $R_0$ and the reversal of its sign. The anomalous Hall coefficient reverses its sign at the same time as $R_0$ and is not functionally related to electrical resistance. The magnitude and the sign of the Hall effect depend on the presence of two subsystems, one of which is connected with short-range magnetic order domains, and the other with frustrated spins at the boundaries of these domains.

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## Tunneling transparence of intentionally disordered superlattices in electric field

### A.V. Dmitriev, 0.V. Pupysheva

Moscow University Physics Bulletin 2000. 55. N 1. P. 48

Vertical electron transport in intentionally disordered semiconductor superlattices in the electric field has been studied theoretically. Numerical values of the coefficients for electron tunneling through thin-layer superlattices with different types of disorder in a finite field have been obtained.

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## Mechanisms of surface energy dissipation in moving domain wall in iron single crystals

### V.E. Zubov, A.D. Kudakov, N.L. Levshin, P.A. Polyakov

Moscow University Physics Bulletin 2000. 55. N 1. P. 53

The anomalously high effect of physical adsorption on the mobility of a 180-deg domain wall in the near-the-surface region observed in filamentary single crystals of iron has been accounted for by increased coercivity due to the formation of adsorption defects and also due to nonstationary random motion of the nearthe-surface portion of the domain wall.

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Geophysics

## Eddy instability and origination of whirlwinds and tornadoes

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

Moscow University Physics Bulletin 2000. 55. N 1. P. 57

The process of origination of strong whirlwind or tornado in the atmosphere was demonstrated to have the form of an exponential growth (explosive instability) of air flow vorticity. The conditions for eddy instability realization have been clarified and formulas for theoretical estimates have been derived.

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Astronomy

## Compatible analysis of variations in ion fluxes and spectra in geomagnetic trap during storms

### A.S. Kovtyukh

Moscow University Physics Bulletin 2000. 55. N 1. P. 62

New methods have been proposed for analyzing the adiabatic component of variations in ion fluxes and spectra for radiation belts and ring current using satellite data during storms.

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Theoretical and mathematical physics

## Explicit solutions of completely integrable classical three-particle system in an external field

### D.V. Meshcheryakov, V.B. Tverskoi

Moscow University Physics Bulletin 2000. 55. N 1. P. 66

Explicit solutions of one completely integrable three-particle system in an external field have been found. An equation integrating the initial conditions, the coupling constant, and the time of two particles "fall" into the singularity of the interaction potential has been obtained.

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## Spectral problem for the Schr$\stackrel{..}{o}$dinger radial equation

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

Moscow University Physics Bulletin 2000. 55. N 1. P. 69

A method for determining the spectrum of the Schrodinger radial equation with some retaining and attractive potentials has been suggested. The method is related to a study of Laplace images of wave functions. The problem reduces to solving an infinite system of linear algebraic equations. Power potentials and their combinations with the Coulomb potential and the Yukawa potential have been studied extensively.

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## A waveguide in wave nonexcitation mode

### A.N. Bogolyubov, A.L. Delitsyn, A.G. Sveshnikov

Moscow University Physics Bulletin 2000. 55. N 1. P. 73

The problem of electromagnetic wave radiation in a waveguide is the concern of the present paper. It is found that there exist currents that do not radiate running waves. The considered phenomenon is in good agreement with the known Weinstein scheme. The existing methods do not yet allow us to isolate a similar class of solutions.

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## Однопетлевые поправки в $d=2+1$ калибровочной теории

### V.Ch. Zhukovsky, N.A. Peskov

Moscow University Physics Bulletin 2000. 55. N 1. P. 76

One-loop boson contribution to the gauge field effective potential has been calculated. Exact constant solutions of the Yang-Mills field equations in the classical nonabelian SU(2) field theory with the Chern-Simons topological mass in the 2+1-dimensional space-time have been considered as a background. Quark and gluon propagators in this field have been obtained. One-loop fermion mass operator and the energy correction have been calculated for the case of the fermion mass equal to $m=\theta/4$.

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