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

## Stability and particle number fluctuations in a supercritical domain

### P.N. Nikolaev

Moscow University Physics Bulletin 2012. 67. N 5. P. 413

The supercritical domain of the phase diagram of a substance is investigated. The dependence of the line of the stability minima and of the line of the particle number fluctuation maxima on the isotherms on the type of equations of state is determined. The connection between the fluctuation value near the critical point and the value of the compressibility at the critical point is found. This analysis showed that the Van Laar type of equation is the most effective among three-parameter equations of state for the description of the supercritical domain.

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## Nonlinear-electrodynamic effects in the electromagnetic field of a rotating pulsar

### M.I. Vasil’ev$^1$, V.A. Sokolov$^2$

Moscow University Physics Bulletin 2012. 67. N 5. P. 418

This paper is concerned with the calculation of nonlinear-electrodynamic effects in the field of a rapidly rotating pulsar. For an electromagnetic wave, exact and asymptotic equations of electrodynamic rays and the law thereof are proposed. The time for the nonlinear-electrodynamic delay is shown to be 3.5 times greater than that for rapidly rotating pulsars or pulsars at rest and the angle of nonlinear-electrodynamic bending of rays is shown to be higher by almost 1.7 times.

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## A fractional order diffusion-wave equation for time-dispersion media

### A.N. Bogolubov, A.A. Koblikov, D.D. Smirnova, N.E. Shapkina

Moscow University Physics Bulletin 2012. 67. N 5. P. 423

Electromagnetic fields in time-dispersion media with a power-law dependence on time are analyzed. It is shown that these media are fractal and their fractal dimension is determined. Equations for scalar and vector potentials are derived using analogues of Maxwell’s equations for these types of media with the use of Caputo fractional derivatives. Electromagnetic fields in a bounded domain are numerically calculated for arbitrary functions of charge and current.

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Physics of nuclei and elementary particles

## Nonperturbative effects caused by the radiative component of the electron magnetic moment in hydrogen-like atoms

### K.A. Sveshnikov, D.I. Khomovskii

Moscow University Physics Bulletin 2012. 67. N 5. P. 429

The lower levels of the discrete spectrum of a hydrogen-like atom are calculated within the point-like nucleus approximation with nonperturbative consideration for the Schwinger interaction of the radiative component of the magnetic moment of a free electron with the Coulomb field of a nucleus. The behavior of the 1s $1s_{1/2}$, $2s_{1/2}$, $2p_{1/2}$ and $2p_{3/2}$ levels is investigated depending on the nuclear charge values, including the range of ${Z>137}$, where the Dirac Hamiltonian continues to be self adjoint in the presence of the Schwinger term. It is shown that the Schwinger interaction for large $Z$ causes significant changes in the properties of the discrete spectrum; in particular, the first level that reaches the threshold of a negative continuum is $2p_{1/2}$ and this occurs at ${Z=147}$. The behavior of the $g$-factor of an electron for the $1s_{1/2}$ and $2p_{1/2}$ states as a function of $Z$ is considered as well and it is shown that for extremely large charges the correction to the $g$-factor due to the Schwinger term becomes a very significant effect.

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## Compensation for chromatic aberrations in acousto-optic systems used in spectral analysis of images

### V.B. Voloshinov$^1$, K.B. Yushkov$^2$, T.V. Yukhnevich$^1$

Moscow University Physics Bulletin 2012. 67. N 5. P. 437

This paper considers novel optical schemes that are related to acousto-optic systems for the spectral analysis of images. The systems are characterized by a low level of transverse and longitudinal chromatic aberrations. Mathematical expressions that describe the magnitudes of the transverse aberration in various configurations of acousto-optic filters are derived. A decrease in longitudinal chromatic aberrations is examined in an optical scheme that is based on a single objective lens and an additional negative lens. A similar analysis is carried out for a confocal system that is formed of two objective lenses. The experimental investigations carried out in the visible range of the spectrum demonstrated a decrease in the longitudinal shifts of images by a factor of 2.5 and by as much as two orders of magnitude or more in the transverse image shifts.

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Condensed matter physics

## The special features of the frequency dependence of phononless hopping conduction

### M.A. Ormont

Moscow University Physics Bulletin 2012. 67. N 5. P. 443

Within the framework of perturbation theory the imaginary part of the phononless conduction of a lightly doped compensated semiconductor is calculated. It is shown that when the basis of localized atomic-like functions is used, the superlinear frequency dependence of the real part of the conduction corresponds to the approximately linear frequency dependence of the imaginary part of the conductivity. It has been found that at frequencies below the transition (crossover) frequency $\omega_{\rm cr}$ from the linear to quadratic frequency dependence of the real part of conductivity, the dielectric loss tangent depends weakly on the frequency and it is determined by the relationship of $\hbar\omega_{\rm cr}$ to the width of the impurity band. It is shown that measurements of the dielectric loss tangent can provide information on the localization radius of impurity states.

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## Updating a software package for the simulation of diffraction patterns and the computation of the parameters of the twinning and self-accommodation of martensite crystals

### A.G. Khundzhua, E.A. Brovkina, M.M. Melnikov

Moscow University Physics Bulletin 2012. 67. N 5. P. 448

An updated software package for the simulation of point diffraction pictures and the computation of several crystallographic characteristics of martensite crystals in alloys with the shape-memory effect is presented. Optimization was carried out for the procedure of the analysis of the orientation relationships between the lattices of austenite and martensite from the viewpoint of the possibility of the formation of self-accommodation complexes.

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Biophysics and medical physics

## Using the dynamic light-scattering method for the analysis of a blood-serum model solution

### I.M. Papok, G.P. Petrova, K.A. Anenkova, E.A. Papish

Moscow University Physics Bulletin 2012. 67. N 5. P. 452

We used photon correlation spectroscopy to investigate various dynamic processes that occur in samples of a blood-serum solution. These processes were induced by directional changes of the surface charges of macromolecules and the concentration of the solution. We suggest that the obtained associations between the translational diffusion coefficient value ($D_t$) and the medium pH value, as well as the protein concentration value, indicate the possibility of using the dynamic light scattering method for the effective diagnosis of common diseases, including cardiovascular lesions and cancers.

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Physics of Earth, atmosphere, and hydrosphere

## The potential and vortex traces of a tsunamigenic earthquake in the ocean

### M.A. Nosov, G.N. Nurislamova

Moscow University Physics Bulletin 2012. 67. N 5. P. 457

An equation system that describes the potential and vortex residual hydrodynamical fields that emerge in the rotating ocean during tsunami generation by co-seismic deformations of the bottom was obtained in terms of linear long-wave theory. For the model case of a cylindrically symmetrical deformation of the bottom, a completely analytical solution was found. On the basis of this solution, the structure of residual fields was analyzed and estimates of the residual horizontal displacements of water particles, of the speed of the vortex current, and of the energy of a geostrophic vortex were obtained under typical tsunami source conditions.

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Theoretical and mathematical physics

## Modeling a waveguide with a nonlinear insert with a quadratic nonlinearity

### A.N. Bogolyubov, M.D. Malykh, A.A. Belov

Moscow University Physics Bulletin 2012. 67. N 5. P. 462

The scalar problem of the scattering of a wave from a nonlinear insertion lying in the interior of a waveguide is reduced by the incomplete Galerkin method to the boundary value problem for a Hamiltonian system. The cases in which this problem admits a solution in finite terms are indicated. Examples are given to illustrate specific phenomena due to the nonlinearity of the problem.

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Astronomy, astrophysics, and cosmology

## A numerical analysis of the physical characteristics of a compact star with a moderate concentration of matter

### A.S. Rokhmanenkov

Moscow University Physics Bulletin 2012. 67. N 5. P. 466

We find numerical solutions for a system of gravitational equations (these equations were proposed by Yu.M. Loskutov after modification of the Hilbert-Einstein equations) for the internal and external physical characteristics of compact stars with a moderate concentration of matter when their gravitational fields are not too strong. The evolution of solutions with an increase of the mass of an object is simulated. The corresponding graphs are constructed.

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## Global wolf numbers

### I.F. Nikulin

Moscow University Physics Bulletin 2012. 67. N 5. P. 471

A new (global) series of Wolf numbers (W G ), which takes all the sunspots on the Sun’s surface, including the spots that are invisible from the Earth, into account, is proposed for consideration with the aim of obtaining a more complete characteristic of solar activity. The optimum configuration of spacecraft for this purpose is examined.

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