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

## On bifurcation of the amplitude of forced Alfven oscillations

### S.A. Markovskii

Moscow University Physics Bulletin 1997. 52. N 1. P. 1

Tl1e forced nonlinear Alfven oscillations in a system with a discrete spectrum are considered. In such a system, the discreteness of the spectrum or dissipation may cause stabilization of unstable processes of interaction between the initial Alfven wave and small perturbations. For this case, a correction to the natural frequency of small stationary oscillations has been found. The bifurcation of the oscillation amplitude was shown to occur under changes of the driving force frequency. This effect must be taken into account when describing plasma dynamics in MHD resonators, such as the earth's polar ionosphere and solar coronal loops.

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## Finslerian kinematic transformations between moving reference frames

### G.S. Asanov

Moscow University Physics Bulletin 1997. 52. N 1. P. 6

The Finslerian kinematic approach [1-9] is applied to the case when the kinematic transformations refer to two moving reference frames. The respective explicit form for the transformation coefficients has been found.

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## Theory of NMR correlation experiments with relayed coherence transfer

### V.S. Tumanov

Moscow University Physics Bulletin 1997. 52. N 1. P. 10

Using the method of projection operators, two-dimensional NMR spectra have been calculated for correlation spectroscopy with relayed coherence transfer. Arbitrary first-order spectra from systems with three groups of equivalent nuclei have been discussed. Some general rules of calculations by the projection operator method are formulated.

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## Neutrino oscillations in a magnetized neutron star with consideration for the realistic equation of state

### A.M. Egorov, G.G. Likhachev, A.I. Studenikin

Moscow University Physics Bulletin 1997. 52. N 1. P. 14

With consideration for the variation of the neutron star matter density described by the realistic equation of state we have considered in detail the "boundary effect" based upon neutrino oscillations in a magnetic field, i.e., the transition of half the active neutrinos under the influence of a magnetic field to the sterile state when leaving the neutron star. Basing upon the numerical calculations performed we have concluded that neutrino oscillations may become essential in the regions near the surface of the neutrino star and up to the distances of the order of 600 star radii.

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## Calculation of fundamental frequencies and radiative losses of open dielectric resonators

### A.A. Usankin

Moscow University Physics Bulletin 1997. 52. N 1. P. 21

A numerical algorithm for calculating radiative losses and fundamental frequencies of open dielectric resonators having the form of a body of revolution with an arbitrary generatrix has been developed. It is shown that this algorithm can be applied to the study of modes of the whispering gallery type for high values of the azimuth index.

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## Radiative decay of $b$-quark in a non-Abelian chromomagnetic field

### A.E. Grigoruk, V.Ch. Zhukovskii

Moscow University Physics Bulletin 1997. 52. N 1. P. 27

The spectrum and the width of the $b \to s+\gamma$ decay in an external non-Abelian chromomagnetic field simulating the vacuum gluon condensate have been evaluated. The obtained result is consistent with similar nonperturbative corrections calculated earlier by other methods. But the exact functional dependence of the probability of decay on the condensate field intensity disagrees with predictions of other authors who used unfounded approximations. It is shown that the effect of gluon condensate reduces to an increase in the quark mass and to the interaction of the chromatic magnetic moment with the chromomagnetic field.

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## Ray diffusion in anisotropic media

### V.D. Gusev, O.K. Vlasova

Moscow University Physics Bulletin 1997. 52. N 1. P. 33

Dynamic equations have been derived which describe ray diffusion in the weak-fluctuation approximation for any anisotropic medium. A technique for going from ray equations in an anisotropic medium with random inhomogeneities of the refraction index to Einstein-Fokker equations has been suggested. As an example, the problem of light scattering in a uniaxial crystal is solved. The formula derived for the transition probability of the beam state indicates anisotropic scattering even for an isotropic correlation function of scattering inhomogeneities.

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## Excess noise in suspensions of torsion pendulums

### A.Yu. Ageev, V.P. Mitrofanov

Moscow University Physics Bulletin 1997. 52. N 1. P. 43

The equilibrium angular orientation of a torsion pendulum suspended by a thin tungsten wire changes with time. Examining the statistics of such changes over the period of oscillations showed that for low stresses in the wire (less than 60-70% of the breaking stress), the distribution of these values is close to the Gaussian distribution. For high stresses, this distribution differs from a Gaussian one by the presence of rare comparatively large jumps of the rotation angle. They can be considered as a manifestation of strain jumps in solids caused by the dislocation motion. In mechanical systems, strain jumps cause an excess noise, which can make a substantial contribution to fluctuations in the arrangement of test masses of laser gravitational antennas.

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Optics and spectroscopy

## Intermittence of structural states of laser beams on near-the-ground paths

### T.I. Arsenyan, L.S. Kornienko, P.V. Korolenko, E.A. Kulyagina, G.V. Petrova, N.N. Fedotov

Moscow University Physics Bulletin 1997. 52. N 1. P. 38

This paper is concerned with the phenomenon of the intermittence of structural states of laser beams-quasiperiodic discontinuous transitions between two structural states of the beam (a dislocationless and a stochastic state). The authors have studied the conditions of appearance and the specific features of manifestation of structural intermittence on near-the-ground slant and horizontal paths. The relationship between the optical effects studied and the changes of the turbulent properties of the atmosphere are discussed.

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Solid state physics

## Phase stability in the Ginzburg-Devonshire model

### G.V. Belokopytov

Moscow University Physics Bulletin 1997. 52. N 1. P. 49

The thermodynamic potential in the form traditional for the theory of ferroelectric phase transitions in barium titanate has been considered. It has been proved that the potential admits the existence of a monoclinic phase. The physical reasons for its absence in $BaTiO_3$ have been found out. The conditions under which the polarization jump on the equilibrium surface of polar phases in phase transitions is negligibly small have been determined.

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## Manifestation of structural features in the cation sublattice of the 2212-type single crystals in Raman scattering

### L.I. Leonyuk$^1$, G.-Yu. Babonas$^2$

Moscow University Physics Bulletin 1997. 52. N 1. P. 56

A series of 2212-type single crystals grown by the method of cooling a nonstoichiometric melt has been examined. For specimens with controlled chemical and phase compositions, the dependence of the fine structure of their Raman spectra on the alloying effects and the presence of isostructural phases has been determined. The results can be used for optical diagnostics.

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Geophysics

## Water basin heat losses under the conditions of free convection

### Ya.L. Aleksandrov, E.P. Anisimova, S.N. Dikarev, A.A. Speranskaya, O.A. Speranskaya

Moscow University Physics Bulletin 1997. 52. N 1. P. 68

An integral numerical model is discussed which allows one to determine the density of the heat flux from water to air under the conditions of free convection in a nonaerated water mass. The primary external model parameters include the water and air temperatures and the air humidity and do not include the temperature of the underlying water surface. The calculated heat losses from a basin are compared with experimental data.

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## Correlation between the Earth's global magnetic and gravity fields

### N.A. Chuikova, N.V. Alakhverdova

Moscow University Physics Bulletin 1997. 52. N 1. P. 72

The correlation between the anomalies of the gravity ( G) and magnetic (M) fields which have common sources of uniform magnetization is studied. Formulas for the G- and M-potentials of such sources are obtained. The following cases are analyzed theoretically and calculated for actual models of the Earth's G- and M-fields: (1) the G- and M-potentials are created by a uniformly magnetized body with different directions of magnetization; (2) the G- and M-potentials are created by sources with different orientations of their magnetic moments, located on a spherical surface.

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Astronomy

## Motion of poles of the Earth's principal axes of inertia due to Earth's rotational deformation

### Yu.V. Barkin

Moscow University Physics Bulletin 1997. 52. N 1. P. 80

The variations in the coefficients of the second harmonic of the geopotential that are caused by periodic motions of the pole and by the irregularities of the diurnal rotation of the Earth were determined for an Earth model with an elastic mantle. Periodic perturbations in the motion of the poles of the Earth's polar and equatorial axes of inertia were found which are caused by perturbations of the components of the Earth's angular velocity.

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## Effect of gyroscope plane inclination on the accuracy of determination of the Earth's rotation parameters

### V.E. Zharov, S.N. Markova, M.V. Sazhin

Moscow University Physics Bulletin 1997. 52. N 1. P. 86

A laser gyroscope has been developed in the Sternberg State Institute of Astronomy for the determination of the Earth's rotation parameters. This work is concerned with the effect of the relative inclination of mirrors on the accuracy of determination of these parameters.

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## Hierarchical star clusters with maximum population

### V.G. Surdin

Moscow University Physics Bulletin 1997. 52. N 1. P. 90

It is shown that hierarchical stellar systems containing tens of components may exist in the Galaxy. They can be sought by cosmic astrometric instruments, and if the results are positive, this will provide very valuable data for stellar cosmogony.

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Theoretical and mathematical physics

## Application of Lanczos-type methods to compute the waveguide modes

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

Moscow University Physics Bulletin 1997. 52. N 1. P. 96

Lanczos-type methods are applied for solving the generalized algebraic eigenvalue problem which occurs in the finite-element waveguide mode analysis. The line of approach is suggested, which stabilizes the calculation of smaller eigen- values in the presence of a high-multiplicity zero eigenvalue. Computational features of the problem are discussed.

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## Radiation-induced shift of the ground-state energy of an electron in a static magnetic field in (2+1)-dimensional quantum electrodynamics

### I.M. Ternov, A.V. Borisov, K.V. Zhukovskii

Moscow University Physics Bulletin 1997. 52. N 1. P. 99

The one-loop radiation-induced shift of the ground state energy of an electron in a magnetic field has been calculated within the framework of (2+1)-dirnensional quantum electrodynamics whose Lagrangian includes a Chern-Simons term of a topological nature. The asymptotic behavior of energy shift as a function of field intensity and topological mass parameter has been examined. A comparison with the known results of (3+1)-dimensional electrodynamics has been made.

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Optics and spectroscopy

## Structure of highly anisotropic laser speckle patterns

### Yu.V. Vasiliev, E.F. Kuritsyna, A.E. Lukyanov

Moscow University Physics Bulletin 1997. 52. N 1. P. 102

The paper describes an experiment on the generation of laser speckle patterns with high value of transverse anisotropy. An express-method of visual photometry is proposed for the qualitative analysis of the structure of highly anisotropic laser speckle patterns.

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