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

## A study of the propagation of electromagnetic pulses through photonic crystal structures

### A.N. Bogolyubov, I.A. Butkarev, Yu.S. Dement’eva

Moscow University Physics Bulletin 2010. 65. N 6. P. 425

A mathematical model for the study of two- and three-dimensional photonic crystals and of waveguide systems based on them was designed and applied. The numerical algorithm for the construction of the solution was built using such numerical methods as the method of finite differences in the time domain (FDTD), the TS/SF method, and the method of a perfectly matched layer (PML), which makes it possible to apply the algorithm under consideration to the study of other waveguide systems as well. The results of the simulation of particular waveguide systems are presented.

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## The properties of a dynamo wave in the case of intense meridional circulation

### E.P. Popova

Moscow University Physics Bulletin 2010. 65. N 6. P. 432

The solution of a Parker dynamo was constructed for the case of intensive meridional circulation using a method similar to WKB. We show how to build a solution in the transition from the traveling-wave regime to the regime of stationary magnetic field configuration. A solution of the Hamilton-Jacobi equations was discovered for the problem of a dynamo containing a triple point in the complex plane wave vector.

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## The construction of exact solutions of the model problem on rotating fluid in domains with angular points

### S.D. Troitskaya

Moscow University Physics Bulletin 2010. 65. N 6. P. 438

A new method has been developed for the construction of a two-dimensional model problem on the oscillations of rotating ideal fluid in some domains containing angular points. It is proved that these solutions correspond to the absolutely continuous component of the spectrum of the linear operator connected with the problem.

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## Solution properties of a model problem on oscillations of a rotating fluid in domains with angular points

### S.D. Troitskaya

Moscow University Physics Bulletin 2010. 65. N 6. P. 446

The behavior of a two-dimensional model problem on the oscillations of a rotating ideal fluid in some domains containing angular points has been studied under $t\to\infty$. The existence is proved of solutions for which the entire energy of the initial state with time is almost completely concentrated in arbitrarily small neighborhoods of the angular points.

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## Improvement of the Oberbeck-Boussinesq approximation for solving unstationary convection problems in a closed cavity

### N.A. Vinnichenko, A.V. Uvarov

Moscow University Physics Bulletin 2010. 65. N 6. P. 454

The validity of using simplified models of compressible fluids for calculations of unstationary convection flows inside closed cavities is tested for the problem of hot gas cooling in a rectangular cavity with cold walls. The Oberbeck-Boussinesq approximation and other simplified models are shown to yield incorrect values of pressure, density, and temperature if average pressure change is not negligible. Modification of the numerical method is proposed, which allows one to describe the temporal dependence of pressure correctly without loss of computational efficiency. The results obtained by using a modified Oberbeck-Boussinesq approximation and the complete equations for a fully compressible fluid are compared.

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## Study of a low-frequency oscillation phenomena associated with a diffusion process via a hollow-fiber membrane

### N.A. Tikhonov, M.G. Tokmachev

Moscow University Physics Bulletin 2010. 65. N 6. P. 460

Experimental data related to low-frequency oscillations of substance concentration are under consideration. The phenomenon has been mathematically modeled for stationary external conditions. The model developed here considers the dependence of local membrane conductivity on solution concentration. The calculation results fit the experimental data well. A theoretical explanation of the phenomenon is presented. It has been demonstrated that a positive feedback between changes in flows and concentrations in a membrane occurs in the process that determines the appearance of oscillations in the process of diffusion of the substance.

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## Maslov symbol for the density matrix in the case of quantization of pairs

### D.S. Golikov

Moscow University Physics Bulletin 2010. 65. N 6. P. 466

Ultrasecondary quantization methods are applied to the equation for a density matrix. The identity for an ultrasecondary quantized hamiltonian was obtained, which allows us to define the true symbol of the equation for a density matrix by quantization by pairs. The investigation of the corresponding system of variation equations shows that this quantum system has a Maslov superfluidity model spectrum.

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Physics of nuclei and elementary particles

## Photodisintegration of Hg isotopes

### B.S. Ishkhanov$^{1,2}$, V.N. Orlin$^1$, S.Yu. Troischiev$^2$

Moscow University Physics Bulletin 2010. 65. N 6. P. 471

Yields of photonuclear reactions of several Hg isotopes are measured on a bremsstrahlung photon beam with a maximal energy of 19.5 MeV using a gamma-activation analysis. Cross sections of photonuclear reactions on stable Hg isotopes are calculated within bonds of the collective model taking isospin splitting of giant dipole resonance into account. The experimental results are compared with the results of theoretical calculations and earlier experimental studies.

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## Diffraction of an electromagnetic wave on the finite lattice of carbon nanotubes-vibrators located at dielectric interfaces

### A.M. Lerer, G.P. Sinyavsky

Moscow University Physics Bulletin 2010. 65. N 6. P. 477

A solution of the boundary problem on electromagnetic wave diffraction on a lattice of carbon nanotubes-vibrators is reduced to the solution of a set of integrodifferential equations, whose kernels are represented as a Fourier integral. Such representation of kernels makes it possible to easily overcome solution problems related to their singularities and reduce the computation time by one order of magnitude. Integrodifferential equations are solved using the Galerkin method with a Chebyshev basis. The effect of a substrate on amplitude-frequency characteristics and the scattering pattern of carbon nanotube antennas is studied. Both the resonance frequency and the amplitude of a scattered field are shown to increase in the case of approaching nanovibrators. The amplitude dependence on the number of vibrators is nonlinear.

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## The dependence of the regularity of an output pulse signal of a neural model on the frequency ratio of input oscillations

### Yu.V. Ushakov, A.A. Dubkov

Moscow University Physics Bulletin 2010. 65. N 6. P. 483

A model of a neural system generating a train of delta pulses under the effect of noises and sinusoidal signals with commensurable frequencies is considered. The dependence of the regularity of the above pulse train on the ratio of input oscillation frequencies is obtained using the theory of the hidden Markov chain.

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## Research activities on a double-gap output section of a multiple-beam klystron

### D.N. Echin, Y.A. Trofimov, K.A. Zaitsev, N.A. Sukhareva, V.M. Pikunov

Moscow University Physics Bulletin 2010. 65. N 6. P. 487

In this article the double-gap output section of a multiple-beam klystron is studied using modern measurement equipment and computer simulation methods. Well-known techniques of cold two-terminal measurements are adapted to equipment capabilities. A comparison between the measured characteristic and computer simulation results is discussed.

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Optics and spectroscopy. Laser physics

## Frequency modulation spectroscopy of coherent dark resonances of multi-level atoms in a magnetic field

### Yu.V. Vladimirova$^{1,2}$, V.N. Zadkov$^{1,2}$

Moscow University Physics Bulletin 2010. 65. N 6. P. 493

The resonances of coherent population trapping (CPT) excited by a frequency-modulated (FM) field at the Zeeman sublevels during the transition $F_g=2\rightarrow F_e=1$ $D_1$ of the $^{87}$Rb $D_1$-absorption line were studied theoretically. The influence of the nonlinear Zeeman effect on the structure of the observed resonances was considered. The spectra of CPT resonances were calculated for different values of magnetic field induction and compared with the experimental data.

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Condensed matter physics

## On the contrast of the terrace conductivity of graphite

### V.V. Shvets$^1$, O.V. Sinitsyna$^{2,3}$, G.B. Meshkov$^{1,2,3}$, I.V. Yaminsky$^{1,2,3}$

Moscow University Physics Bulletin 2010. 65. N 6. P. 501

The recently developed technique of scanning resistance microscopy (SRM) has recommended itself as a high-precision tool for the investigation of surface conductive properties. It is different from conventional atomic-force microscopy in its ability to obtain simultaneous data about both the topography and contact resistance of a probe and sample. This method was used for investigation of the conductive properties of highly oriented pyrolytic graphite (HOPG). A series of experimental facts testifies that the field of application of SRM during the performance of nanoobject research on graphite substrate is restricted by the surface of atomic plateau. This is connected with the fact that during crossing of atomic steps the state of contact of the probe and sample changes, which has a great influence on its conducting properties.

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## On the pyroelectricity of DKDP single crystals and PZT-40 ceramics at 1.5–30 K

### N.D. Gavrilova, V.K. Novik

Moscow University Physics Bulletin 2010. 65. N 6. P. 506

Following the results of the analysis of experimental data in article are defined lowest modes responsible for pyroelectricity in single crystal DKDP (87,3 and 201,6 cm-1) and ferroelectric ceramic PZT-40 (20,7, 54,75 and 171,3 cm-1). Set of the physical mechanisms which are present in real polar dielectrics, active in the pyroelectricity at an interval 0–30 K, and the methods of its identification, separation and single quantitative response definition for each of spontaneous polarization components is discussed.

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Chemical physics, physical kinetics, and plasma physics

## Laboratory simulation of the interaction of water molecules with carbonaceous aerosols in the atmosphere

### E.D. Kireeva$^1$, O.B. Popovicheva$^1$, T.D. Khokhlova$^2$, N.K. Shoniya$^2$

Moscow University Physics Bulletin 2010. 65. N 6. P. 510

A number of samples that simulate the chemical composition of carbonaceous aerosols emitted by transport into the atmosphere have been synthesized using the method of deposition of organic compounds and sulfuric acid, which are identified in the particulate coverage of diesel and aircraft engine soot particles, onto the surface of elemental carbon. The analysis of water adsorption isotherms allows one to estimate the influence of the surface chemistry of particles on the degree of their hygroscopicity. Water adsorption measurements show that modification of a particle surface by nonpolar organics (aliphatic and aromatic hydrocarbons) leads to the hydrophobization of a soot surface. The impact of polar oxygen-containing organic compounds (ethers, ketones, aromatic, and aliphatic acids) on adsorption capacity with respect to the water of samples that they modify substantially depends on the nature and composition of the hydrophobic part of the molecules. Among the ionic compounds organic acid salts have the most hydrophilization effect, which is comparable with the adsorption capacity of soot with sulfuric acid deposited on its surface. This observation allows one to quantitatively define how the nature of chemical compounds on soot surface influences water adsorption and to estimate the interaction of water molecules with fossil fuel combustion particles in a humid atmosphere.

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Astronomy, astrophysics, and cosmology

## The coronal streamer belt and the last two minima of activity of the sun

### G.A. Porfir’eva, G.V. Yakunina, A.B. Delone

Moscow University Physics Bulletin 2010. 65. N 6. P. 516

The structure of the streamer belt and the dynamics of mass ejections during the last two minima of solar activity in 1996–1997 and 2008–2009 are analyzed based on observations from the Solar and Heliospheric Observatory (SOHO) and the Solar Terrestrial Relations Observatory (STEREO). Certain features are revealed in the characteristics of the streamer belt in the last minimum between cycles 23 and 24 compared with the previous minimum between cycles 22 and 23 of solar activity. The connection is considered between the photospheric activity and sector structure of the global solar magnetic field with the topology and dynamics of the streamer belt. Models are briefly discussed that explain the observed phenomena. Data published in scientific journals and on the Internet are used.

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## Methods of complex analysis in model calculations of the magnetospheres of relativistic stars

### I.V. Oreshina, B.V. Somov

Moscow University Physics Bulletin 2010. 65. N 6. P. 521

In this paper the two-dimensional problem is solved for the magnetosphere of a relativistic compact star. The direct and reverse currents in the magnetotail are calculated, as well as the force exerted by the magnetic field on the edge of the current layer. The dependence of the solution on the parameters of the model is investigated.

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## On the classic heat conduction in the chromosphere-corona transition region of the solar atmosphere

### O.V. Ptitsyna, B.V. Somov

Moscow University Physics Bulletin 2010. 65. N 6. P. 527

The distribution of the temperature versus the thickness in the chromosphere-corona transition region of the solar atmosphere on the assumption that the plasma heating by classical heat flux is balanced by the energy loss by radiation. It is shown that the transition region between the corona and chromosphere is a thin layer, to which, however, a simple collision approximation may be applied.

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Physics of Earth, atmosphere, and hydrosphere

## Paleointensity of the geomagnetic field in the last half-million years in regions of the Red Sea and south of the Mid-Atlantic Ridge

### V.I. Maksimochkin$^1$, J.R. Mbele$^1$, V.I. Trukhin$^1$, A.A. Schreider$^2$

Moscow University Physics Bulletin 2010. 65. N 6. P. 531

The paleointensity of a geomagnetic field is determined on the basis of the standard Thellier’s method using the remanent magnetization ($H_a$) of basalts of the rift zone of the Red Sea (with an age of 0.5 million years) and south of the Mid-Atlantic Ridge (with an age of 0.1–0.3 million years). Samples were selected whose natural remanent magnetization (NRM) was mainly one-component and the measured Curie temperatures of the titanium-magnetite fraction ($T_C=205$-250$^0$C) were close to the calculated values. Samples with $T_C\approx580$$^0$C were also used. It was shown that NRM of basalts with both high and low $T_C$ values have a thermoremanent nature. The studies have revealed that the law of independence and additivity of partial thermoremanent magnetizations (PTRMs) is satisfied for the collected samples with an error of no more than 6% and the error of determination of the field of TRM creation using the Arai-Nagata diagram is no more than 10%. The value $H_a=32$ A/m determined from NRM of basalts south of the Mid-Atlantic Ridge appears to be approximately equal to the contemporary intensity of the geomagnetic field ($H_E$) in this region. In the Red Sea region, $H_a=77.5$ A/m, which is 2.5 times higher than the current value. It is suggested that during formation of the basalts of the Red Sea rift zone the geomagnetic pole was located in that region and the virtual dipole moment was 35% higher than its contemporary value.

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Theoretical and mathematical physics

## Density waves in quark matter within the Nambu-Jona-Lasinio model in an external magnetic field

### V.Ch. Zhukovsky$^1$, K.G. Klimenko$^2$, I.E. Frolov$^1$

Moscow University Physics Bulletin 2010. 65. N 6. P. 539

The possibility of forming static dual scalar and pseudo-scalar density wave condensates in dense quark matter is considered for the Nambu-Jona-Lasinio model in an external magnetic field. Within a mean-field approximation, the effective potential of the theory is obtained and its extrema are numerically studied and a phase diagram of the system is constructed. It is shown that the presence of a magnetic field favors the formation of spatially inhomogeneous condensate configurations at low temperatures.

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## Calculation of the phase transition characteristics of a magnetically ordered system by the renormalization group method

### O.G. Karchev, A.M. Savchenko

Moscow University Physics Bulletin 2010. 65. N 6. P. 543

The phase transition “collapse” of magnetic moments of sublattices in segnetoantiferromagnetics in a strong magnetic field is considered. It is shown that spin fluctuations play an essential role and determine the characteristics of the phase transition. Consecutive accounting for the spin fluctuations by the renormalization group method and ɛ-expansion results in a phase transition in segnetoantiferromagnetics in a strong magnetic field that occurs at a first-order phase transition, which is close to second order for a nonzero relativistic constant of the magnetoelectric bond and any inductive capacity.

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## A new definition of regularity for representation of canonical commutation relations algebras

### Yu.S. Vernov$^{1,3}$, M.N. Mnatsakanova$^2$, S.G. Salinsky$^3$

Moscow University Physics Bulletin 2010. 65. N 6. P. 547

A new criterion of regularity for the representation of canonical commutation relations algebras is given on the basis of the concept of an analytical vector.

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Physics of Earth, atmosphere, and hydrosphere

## The capture of large bottom particles by eddies in a dam break flow

### O.N. Mel’nikova, V.N. Semenyuk

Moscow University Physics Bulletin 2010. 65. N 6. P. 550

On the base of an experimental study of the boundary layer of the head of a dam break flow it is shown that the thickness of a viscous layer exceeds the bottom particle diameter $d_p$, increases with $d_p$, and decreases with the flow velocity (for ${d_p<1.2}$ cm). Bottom particles are captured by satellite eddies, which originate from main eddies near the bottom. Main eddies periodically appear in the viscous layer if the flow decelerates downstream. If ${d_p>0.045}$ cm the satellite diameter is smaller than $d_p$. Satellites close in and run into one eddy, which can contain the bottom particles if the flow velocity achieves a critical value $U_{\rm dip}$. Particles can be captured when the flow velocity has a higher value${U_{\rm cr}>U_{\rm dip}}$. It is possible under this condition that a particle starts to rotate in the satellite without slippage.

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