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

## Nonstationary contrasting structures for the generalized Kolmogorov-Petrovskiy-Piskunov equation

### A.A. Bykov, A.S. Sharlo

Moscow University Physics Bulletin 2012. 67. N 2. P. 147

The solution to the generalized Kolmogorov-Petrovskiy-Piskunov (GKPP) equation is shown to have a contrasting structure. Contrasting structures (CSs) are characterized by the existence of wide areas with a small field gradient separated by narrow internal transition layers (ITLs) with a large field gradient. The ITLs in an inhomogeneous medium are shown to drift and the drift velocity is determined. The CS drift velocity for the GKPP equation is compared with a simpler model of the reaction-advection-diffusion equation.

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## A class of models with spontaneous compactification of the Freund-Rubin type and a nontrivial solution for the vector field

### E.R. Rakhmetov, S.I. Keizerov

Moscow University Physics Bulletin 2012. 67. N 2. P. 154

A theory of interacting gravity, vector, and antisymmetric third-rank tensor fields with self-consistent spontaneous compactification solutions of the Freund-Rubin type in seven-dimensional space-time is considered. A class of models is studied, which allow the same type of compactification and possess nontrivial solutions for the vector field. A subclass of the models is separated in which the four-dimensional Lorentz invariance is either unbroken or weakly broken.

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## Dimensional reduction of fermions in the Gross-Neveu model under the conditions of violated Lorentz invariance

### N.V. Gubina, V.Ch. Zhukovsky, S.G. Kurbanov

Moscow University Physics Bulletin 2012. 67. N 2. P. 159

The Gross-Neveu model with violated Lorentz invariance is analyzed. The effective potential for the 3D and 2D cases is calculated. The gap equation is obtained and the symmetry features of the model are considered. Dimensional reduction allows the establishment of the concordance between the results for a different number of measurements.

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## The possibility of the classification of infrasonic signals using methods for checking statistical hypotheses

### A.I. Chulichkov$^1$, N.D. Tsybulskaya$^1$, S.N. Kulichkov$^2$

Moscow University Physics Bulletin 2012. 67. N 2. P. 166

This work is devoted to the possibility of the classification of signals using methods for checking statistical hypotheses. On the basis of analysis of the typical peculiarities of signals that belong to the same class we performed an empirical derivation of the shape of the class. The mechanism of the definition of the separability of signals of each class, as well as the level of criterion for defining critical domain were suggested. A classification algorithm was obtained on the basis of the research. The efficiency of the suggested methodology was tested on the problem of separability of infrasonic signals recorded in the atmosphere.

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## The calculation of the quadrupole exchange interaction parameter in a system of disordered magnetic moments

### M.K. Bakhnyan, A.M. Savchenko, B.I. Sadovnikov

Moscow University Physics Bulletin 2012. 67. N 2. P. 169

The parameters of quadrupole exchange and electron-phonon interaction are calculated within the limits of the exchange interaction model. It is shown that a magnetically disordered system forms an effective exchange interaction between electrons.

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## Features of the calibration of vector acoustic units in the inhomogenous field of a vertically oscillating liquid column

### V.A. Gordienko, B.I. Goncharenko, S.S. Zadorozhnyi, M.V. Starkova

Moscow University Physics Bulletin 2012. 67. N 2. P. 175

The features of the calibration of finite-sized vector acoustic units in the field of a plane standing wave and the possibility of taking the frequency-dependent errors that occur at the same time into account, which allows extension of the frequency range of existing facilities in the region of higher frequencies without the loss of precision of horn calibration, are discussed.

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Optics and spectroscopy. Laser physics

## A locally optimal algorithm for detecting weak geophysical signals at the output of laser gravitational antennas

### A.V. Gusev, I.S. Yudin

Moscow University Physics Bulletin 2012. 67. N 2. P. 182

A locally optimal algorithm for detecting weak low-frequency geophysical signals by the use of long-baseline laser interferometric gravitational antennas that operate in the free spectral range mode is considered. The likelihood ratio is derived using the estimate-correlation online processing of signals. The main element of the optimal detector in the Gaussian approximation is the realizable Wiener filter. A calculation formula for the signal-to-noise ratio is presented.

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Condensed matter physics

## A structural study of biocompatible magnetic nanofluid with synchrotron radiation-based X-ray scattering techniques

### A.V. Shulenina$^1$, M.V. Avdeev$^2$, V.L. Aksenov$^1$, A.A. Veligzhanin$^3$, Ya.V. Zubavichus$^2$, A.Hajdu$^4$, E. Trombacz$^5$

Moscow University Physics Bulletin 2012. 67. N 2. P. 186

In this paper, water colloidal solutions of nanoparticles of magnetite (magnetic nanofluids, (MNFs)) are investigated by synchrotron X-ray diffraction (XRD) and small-angle scattering (SAXS). To prevent aggregation, nanoparticles are coated with polyacrylic acid (PAA) in a single solution and citric (CA) in the other solutions. In both cases, the maxima of the particle size distribution from SAXS (9–10 nm) correspond to the sizes of the magnetite crystallites that were estimated from the broadening of the diffraction lines. In addition, the SAXS data indicate the presence of a significant proportion of aggregates (up to 60 nm in diameter) in both colloidal solutions, although fundamental differences in the structures of aggregates between the MNFs stabilized by PAA and CA were not observed. In this study determination of the structural characteristics of MNFs were carried out in order to obtain stable dispersive non-aggregating nanoparticles of magnetite for use as contrast agents in magnetic resonance tomography, drug carriers, and other biomedical applications.

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## An investigation of the infrared spectra of melt water at room temperature

### A.V. Khakhalin, V.T. Shalabaeva, Ya.N. Shirshov

Moscow University Physics Bulletin 2012. 67. N 2. P. 192

It was shown experimentally that the infrared spectra of melted and never-frozen distilled water differed at frequencies of 1640 and 2130 cm$^{-1}$. This is explained by the long relaxation of water molecules structures to an equilibrium state in melt water. It was suggested that near the frequency 2130 cm$^{-1}$ there was a bigger influence of dissolved gas relaxation on the value of the transmitted intensity of infrared radiation than near the 1640 cm$^{-1}$ line.

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## X-ray circular dichroism under reflection from antiferromagnetically coupled multilayers

### M.A. Andreeva, E.E. Odintsova

Moscow University Physics Bulletin 2012. 67. N 2. P. 196

The fluorescence yield under the Bragg reflection of right and left circular polarized radiation with a wavelength in the vicinity of the Fe$L_{2,3}$ absorption edges from the periodic multilayer [Fe(1.5 nm)/V(1.5 nm)]$_{10}$ that is characterized by the antiferromagnetic interlayer exchange coupling has been theoretically analyzed in L-MOKE geometry. It has been shown that the largest polarization asymmetry of reflectivity takes place at the “magnetic” Bragg reflection, which appears due to the doubling of the magnetic period. The expected occurrence of the dichronic signal in the fluorescence yield by its selective excitation in the layers with the same magnetization direction was confirmed, but the effect is suppressed by the specific behaviour of the standing waves in the strongly absorbing multilayers where the standing wave antinodes are situated in layers with low absorption.

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## The features of nonlinear absorption during resonance one- and two-photon excitation of the basic exciton transition in colloidal CdSe/ZnS quantum dots

### V.S. Dneprovskii$^1$, E.A. Zhukov$^1$, M.V. Kozlova$^1$, A.M. Smirnov$^1$, T. Wumaier$^2$

Moscow University Physics Bulletin 2012. 67. N 2. P. 201

The features of the nonlinear absorption of CdSe/ZnS quantum dots (colloidal solution) in the case of resonant one- and two-photon excitation of the basic exciton transition by powerful ultra-short laser pulses were determined. In one-photon excitation, with an increasing intensity of impulses, a decrease in absorption (bleaching) is relayed by an increase in absorption, which is associated with the process of the filling of the states (saturation) of a two-level system with the lifetime of the excited state depending on the light intensity. The arising Fresnel or Fraunhofer diffraction of the laser ray that pass through a colloidal solution with a high concentration of quantum dots is associated with the formation of the transparency channel and self-diffraction of laser ray on an induced diaphragm. In two-photon excitation, the features of the nonlinear absorption and luminescence tracks (the dependence of luminescence intensity on distance) were explained by the influence, in addition to the two-photon absorption, of the processes that are responsible for the slower growth of nonlinear absorption and luminescence quenching at high intensities of laser pulses.

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Biophysics and medical physics

## Determination of the binding constants of nanomarkers of the fluorescein family to human serum albumin

### I.M. Vlasova, Ju.A. Gordeeva, A.A. Vlasov, A.M. Saletsky

Moscow University Physics Bulletin 2012. 67. N 2. P. 208

Using three models, the constant of quenching of fluorescence of nanomarkers of the fluorescein family and the actual constants of its binding to human serum albumin (HSA) at different values of pH are determined. The presence of two mechanisms of binding of nanomarkers of the fluorescein family to HSA and anti-cooperativity are shown. The dependence of the constants of the quenching fluorescence of nanomarkers on pH was found: for fluorescein this was nonlinear, for its halogen derivatives (erythsosine, eosin, and Rose Bengal) it was monotonous and decreased with an increase of pH. It is shown that the electronegativity of the atoms in the structural formulas of nanomarkers of the fluorescein family influences the values of the constants of binding of nanomarkers to HSA.

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## Self-organization as the driving force for the evolution of the biosphere

### A.E. Sidorova, V.A. Tverdislov

Moscow University Physics Bulletin 2012. 67. N 2. P. 213

Synergic parallels between the mechanisms of the spatio-temporal evolution of physic-chemical and biological systems are considered. The evolution of the biosphere is treated as self-organization in the hierarchy of the active media, which is its driving force. The superposition of selection, vertical and horizontal gene transfer, as well as the processes of divergence and convergence of species, constitutes the synergetic out-line of biological evolution.

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Astronomy, astrophysics, and cosmology

## Anomalies of density, stresses, and the gravitational field in the interior of mars

### N.A. Chuikova, L.P. Nasonova, T.G. Maksimova

Moscow University Physics Bulletin 2012. 67. N 2. P. 218

We determined the possible compensation depths for relief harmonics of different degrees and orders. The relief is shown to be completely compensated within the depth range of 0 to 1400 km. The lateral distributions of compensation masses are determined at these depths and the maps are constructed. The possible nonisostatic vertical stresses in the crust and mantle of Mars are estimated to be 64 MPa in compression and 20 MPa in tension. The relief anomalies of the Tharsis volcanic plateau and symmetric feature in the eastern hemisphere could have arisen and been maintained dynamically due to two plumes in the mantle sub-stance that are enriched with fluids. The plumes that originate at the core of Mars can arise and be maintained by the anomalies of the inner gravitational field achieving +800 mGal in the region of plume formation, −1200 mGal above the lower mantle-core transition layer, and −1400 mGal at the crust.

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## Rigidity dependence of cosmic-ray escape length obtained from a comparison of proton and iron spectra in the energy range 3–3000 GeV

### O.N. Strelnikova$^1$, L.G. Sveshnikova$^2$

Moscow University Physics Bulletin 2012. 67. N 2. P. 226

A simple leaky-box model of cosmic-ray propagation in the Galaxy is quite suitable for analysis of cosmic-ray nuclei energy spectra and composition at energies under 1 GeV [1, 2]. Within this model the full information about the cosmic-ray propagation in the Galaxy is compressed into a single parameter, viz., escape length, $X_e$, which characterizes the mean grams of matter that are passed by cosmic-rays from sources to the Earth. In this paper we analyze the worldwide data on proton and iron cosmic-ray spectra that have been collected in experiments and obtain the rigidity dependence of the escape length from the measured rigidity dependence of the proton/iron ratio. This agrees well with the one estimated by a standard manner from the secondary/primary nuclei ratio. However, at ${R>300}$ GV the behavior of $X_e(R)$ distinctly changes, which can point to a change of the proton/iron ratio in cosmic-ray sources.

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Condensed matter physics

## The influence of surface-active substances on the crystallization process and magnetic properties of goethite nanoparticles

### A.N. Antonov$^1$, A.A. Novakova$^{1,2}$, T.S. Gendler$^3$

Moscow University Physics Bulletin 2012. 67. N 2. P. 230

To prevent the process of aggregation and growth of α-FeOOH nanoparticles, during chemical syntheses various surface-active substances (SASs) with a concentration of 3 g/dm$^3$ were added into the solution. The applied SASs were: cetylpyridinium chloride (CPC), sodium dodecyl sulphate (SDS), and complexone EDTA. Using various methods it was found that SAS molecules have a dual effect on the obtained nanoparticles: on one hand SAS application increases the number of small α-FeOOH nanoparticles with sizes of 2–5 nm. On the other hand, SAS molecules react with surface atoms of the nanoparticles and form additional compounds.

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