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

## Analysis and synthesis of fractal antenna radiation patterns

### A.N. Bogolyubov, A.A. Koblikov, N.E. Shapkina

Moscow University Physics Bulletin 2009. 64. N 6. P. 561

A problem of fractal antenna radiation pattern synthesis is considered. The problem of synthesis of fractal antenna radiation patterns is solved for two kinds of antennas (discrete and linear) in one- and two- dimensional cases. With the use of the theory of fractal synthesis, new modes with new properties are obtained in fractal electrodynamics. Fractal radiation pattern synthesis was conducted by means of the Weierstrass function.

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## Study of laser beam propagation in a rotating reference frame

### M.M. Denisov$^1$, A.A. Zubrilo$^2$

Moscow University Physics Bulletin 2009. 64. N 6. P. 569

Curvature and torsion are calculated for a laser beam in a rotating reference frame. We show that for the problem of laser location of high-apogee artificial satellites one should take into account the difference between the corotating and coordinate distances between two given points of the beam.

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## Oscillations appearing during sorption of amino acids on ion-exchanger grains on the basis of mathematical simulation

### N.A. Tikhonov, M.S. Shchepanskiy

Moscow University Physics Bulletin 2009. 64. N 6. P. 573

Oscillations in concentration and grain size could occur in the process of amino acid sorption on ion-exchanger grains. This phenomenon has been observed in several experimental works. The theoretical explanation of the phenomenon was given earlier by means of an elementary model. In this work the process was studied using a physically more sophisticated model represented by partial differential equations as the result of mathematical simulation. The structure of oscillations inside the grain could not be determined experimentally and also is studied in this work.

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## Peculiarities of two-photon impurity absorption spectra in a quantum molecule with a tunnel-transparent potential barrier

### V.Ch. Zhukovskii$^1$, V.D. Krevchik$^2$, M.B. Semenov$^2$, Yu.G. Smirnov$^2$, P.V. Krevchik$^2$, S.A. Gubina$^2$

Moscow University Physics Bulletin 2009. 64. N 6. P. 579

The effect of dissipative tunneling parameters on the spectral dependence of the probability of two-photon impurity absorption in a quantum molecule is theoretically investigated. The effect of the tunnel barrier transparency on two-photon impurity absorption in a quantum molecule is shown to manifest itself as a change in the width of energy levels of the virtual and final states due to variations in such parameters of dissipative tunneling as temperature, photon-mode frequency, and the constant of interaction with a heat bath.

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## A resonator with a chiral filling

### Yu.V. Mukhartova

Moscow University Physics Bulletin 2009. 64. N 6. P. 585

In this paper the theory of electromagnetic shielded resonators with a uniform chiral filling is considered. An algorithm for determining the parameters of such systems is proposed. As an example, a spherical chiroresonator is investigated, for which the dispersive equation and the eigenfields are obtained. It is shown that only hybrid eigenfields may exist in such a resonator, and pure E- and H-oscillations are not supported.

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## Numerical simulation of gas flows on the basis of quasi-hydrodynamic equations

### T.G. Elizarova$^1$, O.V. Bulatov$^2$

Moscow University Physics Bulletin 2009. 64. N 6. P. 589

Based on seven well-known test problems, reflecting the outstanding characteristics of nonstationary flows of an inviscid gas, the possibilities of using a quasi-hydrodynamic algorithm for the numerical solution of Euler equations are investigated.

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Physics of nuclei and elementary particles

## Simulation of tau neutrino interaction in an emulsion track detector

### A.M. Anokhina$^1$, V.I. Galkin$^1$, T.A. Dzhatdoev$^1$, V.V. Nikitina$^2$, T.M. Roganova$^2$

Moscow University Physics Bulletin 2009. 64. N 6. P. 594

Simulation of the interactions between tau neutrinos ντ and the material of the emulsion track detector using Geant4 software is described. The purpose of the work is to generate artificial events and to estimate, on their basis, the reconstruction accuracy for the geometric parameters (vertex coordinates, impact parameters, and track kink angles) and distributions of these parameters used in the selection criteria of the OPERA experiment.

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Optics and spectroscopy. Laser physics

## Raman spectroscopy of the components of 18th-century icon painting

### N.N. Brandt$^1$, N.L. Rebrikova$^2$, A.Yu. Chikishev$^3$

Moscow University Physics Bulletin 2009. 64. N 6. P. 600

The method of Raman spectroscopy is employed in the analysis of lead-containing pigments in ancient Russian painting, transformed pigments, chalk, and drying oil. The Raman spectra of white lead and the mixture of yellow lead oxide, red lead, and lead dioxide are measured, and the test Raman measurements of various fragments of the paint layer of the 18th-century Russian icon Evangelist Mark from the Kirillo-Belozerski State Historical Architectural Art Museum-Reserve are performed. The destructive action of laser radiation on various pigments is evaluated when measuring their Raman spectra.

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## Mathematical simulation of self-oscillations in a fiber optic laser with a microresonator reflector

### F.A. Egorov$^1$, V.T. Potapov$^1$, A.P. Neugodnikov$^2$, V.V. Nikitin$^3$

Moscow University Physics Bulletin 2009. 64. N 6. P. 605

In this paper we obtain approximate equations that describe the dynamics of a fiber optic laser with an external reflector, constructed on the basis of microresonance structures under inhomogeneous pumping conditions. The results demonstrate the possibility of the existence of selfmodulation modes with frequencies equal to the frequency of natural vibrations of the microresonator structure. The parameter ranges in which self-oscillations are possible are calculated.

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## Information analysis of quantum nondemolition measurement of a photon in a resonator

### D.N. Yanyshev, B.A. Grishanin, V.N. Zadkov.

Moscow University Physics Bulletin 2009. 64. N 6. P. 611

The concept of entangled quantum measurement was demonstrated by the example of the fundamental value of the experiment on quantum nondemolition measurement of a photon in a resonator with the use of a probe atom [1]. The quantum-information analysis of this experiment was performed. A mechanism of information transmission in the nondemolition measurement scheme in the case of the classical and quantum formalism was demonstrated. The results were shown to coincide in both cases. This is the result of copying the classical part of the initial quantum information attributed to a set of quantum object states.

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Condensed matter physics

## Glass transition of Langmuir-Blodgett polymer films

### K.A. Verkhovskaya$^1$, A.A. Plakseev$^1$, N.D. Gavrilova$^2$, A.M. Lotonov$^2$, S.G. Yudin$^1$

Moscow University Physics Bulletin 2009. 64. N 6. P. 617

The dielectric dispersion of vinylidene fluoride-trifluoroethylene copolymer P(VDF/TrFE) (70/30) films obtained by the Langmuir-Blodgett technique was investigated in the low-temperature range from 20 to −100°C. The thickness of the explored films was 40 nm. A glass-transition range from −25 to −40°C was detected; this indicates the presence of an amorphous phase in the LB films.

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## Critical properties of binary liquid mixtures at different temperature modes

### S.G. Il’ina, K.A. Keivsar, A.V. Nikulin

Moscow University Physics Bulletin 2009. 64. N 6. P. 621

The coexistence curves (CC) of two binary mixtures, methanol-heptane (M-H) and perfluorodekaline-heptan (PFD-H), are measured for two temperature modes, namely heating and cooling. Distinctions in the behavior of the two systems in different temperature modes are revealed. For the M-H system this is likely to be attributed to the effects of surface processes and for the PFD-H systems, to the formation of colloidal structures. An additional signal related to the contribution of a meniscal layer is found and measured.

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Biophysics and medical physics

## A theoretical study of a relationship between the photosystem II fluorescence and the redox state of the electron transport chain of higher plants

### D.V. Kirzhanov$^1$, A.K. Kukushkin$^2$

Moscow University Physics Bulletin 2009. 64. N 6. P. 627

A method for analyzing processes of less than 1 μs duration in the model, which was introduced earlier for studying the regulation of photosynthesis, is created. This method makes possible consideration of the initial stages of transitional modes. The obtained theoretical kinetics of the induction of photosystem II fluorescence and photosystem I EPR signal qualitatively conform those observed in experiments. The model demonstrates a complicated nonlinear relationship between the fluorescence of the photosystem II and the redox state of the electron transport chain of chloroplast.

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Astronomy, astrophysics, and cosmology

## On the angular distribution of extensive air showers

### M.Yu. Zotov, N.N. Kalmykov, G.V. Kulikov, V.P. Sulakov

Moscow University Physics Bulletin 2009. 64. N 6. P. 632

Angular distributions of extensive air showers with different number of charged particles in the range ${2.5\cdot10^5}$-${4\cdot10^7}$ are derived using the experimental data obtained with the EAS MSU array. Possible approximations of the obtained distributions with different empiric functions available in literature, are analyzed. It is shown that the exponential function provides the best approximation of the angular distributions in the sense of the $\chi^2$ criterion.

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## Optimal interconnection of resonant gravitational antennas

### A.V. Gusev, V.N. Rudenko

Moscow University Physics Bulletin 2009. 64. N 6. P. 635

A new scheme for interconnecting resonant gravitational antennas is considered. This algorithm is based on the theory of combined detection and estimation of a vectorial signal on a pseudo-gravitational impulse background. The used minimax approach takes into account the beats between gravitational and pseudo-gravitational signals.

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Physics of Earth, atmosphere, and hydrosphere

## Interaction of Kelvin waves and inertial oscillations with the lithosphere in an oceanic shelf region

### S.A. Arsen’ev, N.K. Shelkovnikov

Moscow University Physics Bulletin 2009. 64. N 6. P. 638

In this paper, the theory of interaction of Kelvin waves with the lithosphere at a sloping shelf is developed.

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## Magnetooptical visualization of stray magnetic fields of sample rocks using magnetouniaxial garnet ferrite film

### V.V. Randoshkin$^1$, N.V. Vasil’eva$^2$, Yu.A. Durasova$^2$, N.N. Sysoev$^{1,2}$, P.N. Sysoev$^2$, V.M. Ladygin$^3$

Moscow University Physics Bulletin 2009. 64. N 6. P. 642

The stray magnetic fields of rock samples with inclusions of the magnetic grains and magnetic crystals were observed using epitaxial ((Bi,Lu)$_3$(Fe,Ga)$_5$O$_{12}$ films with uniaxial magnetic anisotropy. Basalt rocks with inclusions of titano-magnetite and native elsen but also crystals of titano-magnetite and pyrrhotin were investigated. Stray magnetic fields were visualized with the Faraday Effect.

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## Influence of mechanic stresses on remanent magnetization of oceanic basalts

### V.I. Maksimochkin, V.I. Trukhin

Moscow University Physics Bulletin 2009. 64. N 6. P. 648

We studied the change of remanent saturation magnetization of ocean basalts exposed to different types of compression: uniaxial, quasihydrostatic, and hydrostatic. It is found that the character of remanent magnetization changes depends on the compression type and magnetization direction in the space. The stability of the remanent magnetization grows both with the increase of coercive force of ferrimagnetic grains and in passing from titanomagnetite to magnetite. It is shown that from the change of the remanent magnetization during laboratory specimen compression one can judge the in situ tectonic impacts suffered by rocks.

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Theoretical and mathematical physics

## Energy distribution in strongly perturbed chaotic system

Moscow University Physics Bulletin 2009. 64. N 6. P. 655

The analytical expression for the energy distribution for the Duffing oscillator that moves chaotically under the strong harmonic perturbation is obtained as a function of the perturbation amplitude and frequency.

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Optics and spectroscopy. Laser physics

## Reconstruction of dielectric permittivity profile of a plate with strong frequency dispersion

### A.A. Golubkov$^1$, V.A. Makarov$^2$

Moscow University Physics Bulletin 2009. 64. N 6. P. 658

We demonstrate the possibility and propose the algorithm of unique reconstruction of the dielectric permittivity profile of a plate with a one-dimensional inhomogeneity (possibly, a plate with absorption), provided that the reflection and transmission coefficients of the plate for $s$-polarized plane waves are known in a certain range of incidence angles.

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Condensed matter physics

## Temperature spin transition in new iron complexes with benzimidazole derivatives

### L.V. Khenkin$^1$, A.A. Novakova$^1$, T.Yu. Kiseleva$^1$, V.V. Sotsky$^2$, N.V. Usol'tseva$^2$

Moscow University Physics Bulletin 2009. N 6.

Study of a valence and spin state of iron ions in complexes of Fe (II) with benzimidazole derivatives have been performed by Mossbauer spectroscopy. It was established that depending on anion type and the length of alkyl radical there were variations of the temperature spin transition range, and also a valency condition of iron ions.

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Physics of Earth, atmosphere, and hydrosphere

## Transcontinental radio tomographic chain: First results of ionospheric imaging

### V.E. Kunitsyn$^1$, E.D. Tereshchenko$^2$, E.S. Andreeva$^1$, V.F. Grigor’ev$^2$, N.Yu. Romanova$^2$, M.O. Nazarenko$^1$, Yu.M. Vapirov$^3$, I.I. Ivanov$^4$

Moscow University Physics Bulletin 2009. 64. N 6. P. 661

The results of studying the structure of the ionospheric plasma distribution from data obtained at the transcontinental Russian radio tomographic chain, which is the world’s longest, are presented. The 4000 km long tomographic chain extends from the Svalbard Archipelago to Sochi. The unique feature of this upgraded radio tomographic system is that for the first time observations cover a wide sector of the ionosphere from high latitudes (polar cap and auroral region) to low latitudes. This allows us to study the transfer of perturbations in the system auroral-subauroral-midlatitude-low latitude ionosphere, and to analyze ionospheric electron density distributions in different latitudinal regions as a function of different external factors and solar-geophysical conditions. The first recent results speak for a complex structure of the ionospheric plasma, even in quiet geophysical conditions (${K_p<2}$)

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