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

## Asymptotic approximation of the moving spike-type contrast structure in reaction-diffusion equations

### N.N. Nefedov, U.V. Bozhevolnov, V.A. Pyrkin

Moscow University Physics Bulletin 2011. 66. N 5. P. 411

The asymptotic approximation of a moving spike-type contrast structure for the reaction-diffusion equation is constructed. The results were applied for an important case of cubic nonlinearity.

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## Accounting for the local surface geometry in the classical theory of spin waves

### A.K. Nukhov, G.M. Musaev, K.K. Kazbekov

Moscow University Physics Bulletin 2011. 66. N 5. P. 416

The effect of the surface energy on the formation of the spin spectrum is considered. Different aspects are examined of the effect of the surface on the energy spectrum of the system associated with structural features of the surface structure. The calculations are carried out for the spectrum of elementary excitations of a ferromagnetic system that is bounded by a surface. Calculations are conducted following the standard method of the Hamiltonian diagonalization. Relationships are obtained that completely determine the surface spectrum in the zero approximation in the spin-spin interaction.

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Optics and spectroscopy. Laser physics

## Peculiarities of light beam reflection from the boundary of a 1D-photonic crystal

### I.G. Zakharova, V.F. Marchenko, M.S. Nebero, A.P. Sukhorukov

Moscow University Physics Bulletin 2011. 66. N 5. P. 422

Typical cases of lateral shift and deformation of the profile of two-dimensional light beams reflected from the surface of a one-dimensional photonic crystal are considered. We use harmonic modulation of the spatial dependence of dielectric permeability of a crystal, which permits one to study reflectance profiles analytically. The results of numerical calculations that were performed are presented for the cases when the angular spectrum of the incident beam is split.

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Condensed matter physics

## Formation of polyelectrolyte microcapsules with chemically bound adsorbed molecules of fluorescein isotiocyanate and their destruction under laser action

### A.N. Baranov$^1$, T.V. Bukreeva$^2$, I.V. Marchenko$^2$, G.S. Plotnikov$^1$, A.M. Saletsky$^1$

Moscow University Physics Bulletin 2011. 66. N 5. P. 427

Polyelectrolyte capsules with molecules of fluorescein isotiocyanate included in the shell have been obtained. The inclusion of dye molecules in the shell of the capsule allows the photosensibilized destruction of its structure. The measurements of the fluorescence intensity of a dye that was present in the shell revealed effective dissipation of the energy of photoexcited molecules by the surrounding organic matrix. The capsule suspension was irradiated by a laser in the absorption band of fluorescein isotiocyanate molecules. By measuring the size distribution of the capsules before and after irradiation with a laser it was shown that the capsules are destroyed under the effect of laser radiation.

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## Cluster structure of condensed media

### G.A. Melnikov$^1$, V.N. Verveyko$^1$, V.G. Melnikov$^2$, D.V. Verveyko$^1$, A.Yu. Verisokin$^1$

Moscow University Physics Bulletin 2011. 66. N 5. P. 432

This paper presents the results of a theoretical study of cluster formation in condensed media for simple and multi-atomic liquids, as an example. A two-parameter function is proposed by the authors for the density of the probability distribution of clusters, which corresponds to a disordered condensed media, depending on the number of constituent particles. Using this function, the universal mean, most probable, and rms numbers of particles in clusters of noble gases, liquid metals, and some organic liquids were calculated. As well, the cluster component of total entropy for the substances under study was computed.

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## AFM observation of a retgersite crystal surface growing in a water-ethanol solution

### E.V. Petrova

Moscow University Physics Bulletin 2011. 66. N 5. P. 437

In situ investigation of the growth and dissolution of retgersite crystals $\alpha$-NiSO$_4\cdot6$H$_2$O in water-ethanol solutions (10–50 wt% of ethanol) was made by atomic force microscopy (AFM). The habit of crystals grown in aqueous and water-ethanol solutions, as well as the Raman scattering spectra, were identical. It is shown that the typical peak of sulphate ions at 981 cm$^{-1}$ does not change after the addition of ethanol. Absorption spectra of aqueous and water-ethanol solutions also have similar characteristic features. AFM images of hillocks on the (001) face of retgersite crystals were obtained directly in the process of their growth. Using a series of distorted AFM images obtained in situ, a geometrical calculation scheme is given, which allows one to recover the real direction of the growth steps. The kinetic coefficient of growth steps in aqueous and water-ethanol solutions of retgersite is estimated.

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Chemical physics, physical kinetics, and plasma physics

## Conservation laws for a vortex in a compressible nonequilibrium medium

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

Moscow University Physics Bulletin 2011. 66. N 5. P. 443

The problem of conservation of magnitudes is considered for a vortex in a relaxing compressible medium. Heat release due to the relaxation of a nonequilibrium medium leads to the propagation of compression waves, which remove material. Traditional integrals of motion are inapplicable in this case. We pro-pose the concept of integral quantity, which is conserved with an arbitrary degree of accuracy despite the fact that waves cross the boundary of the integration domain. Based on this concept, a broad class of conservation laws is derived for axisymmetric disturbances of columnar vortices, including conservation of the circulation and total angular momentum of the vortex. For nonaxisymmetric disturbances, it is shown that the total angular momentum and properly defined energy integral are conserved. Numerical verification of the derived conservation laws is performed and the perspectives for using these conservation laws in numerical simulations are discussed.

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Biophysics and medical physics

## Interaction of albumin and $\gamma$-globulin molecules with gold nanoparticles in water solutions

### V.V. Gibizova$^1$, I.A. Sergeeva$^1$, G.P. Petrova$^1$, A.V. Priezzhev$^2$, N.G. Khlebtsov$^3$

Moscow University Physics Bulletin 2011. 66. N 5. P. 449

The molecular mobility of scattering particles in water solutions of albumin and $\gamma$-globulin proteins with gold nanoparticles was investigated by the dynamic light scattering method. The dependences of translation diffusion coefficients of particles at various concentrations of the solution components have been obtained. It was revealed that in a wide range of concentrations of the solution components there is no interaction of gold nanoparticles with albumin, whereas gold nanoparticles form complexes with $\gamma$-globulin molecules.

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## The fluorescence characteristics and the molecular association of the Rose Bengal nanomarker in human serum albumin solutions

### I.M. Vlasova, A.A. Kuleshova, A.M. Saletsky

Moscow University Physics Bulletin 2011. 66. N 5. P. 453

The decrease in the degree of molecular association of the Rose Bengal nanomarker in solutions with the addition of human serum albumin (HSA) has been revealed. It has been observed that in solutions with the addition of HSA the fluorescence quenching and the shifting of the fluorescence spectrum peaks of Rose Bengal to the red take place. It has been shown that the dependence of the effective binding constant of binding Rose Bengal to HSA steadily decreases with an increase in the pH value. It has been established that the values of the molecular association degree of Rose Bengal and the values of the effective constant of its binding to HSA depend on the magnitude of the electronegativity of the atoms in its structural formula, as well as on the pK values of its ionizable groups.

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## Model for the calculation of the trajectories of electron movements in an aqueous environment placed in a magnetic field

### A.V. Belousov, A.S. Namestnikov, A.P. Chernyaev

Moscow University Physics Bulletin 2011. 66. N 5. P. 458

In this work the application of a rather simple half-analytic model for plotting and studying electron trajectories in an aqueous environment in a transverse magnetic field was considered. The energies of electrons used in medical electron accelerators, viz., those up to 30 Me, were considered and the induction value of the magnetic field was changed within limits up to 3 T. Our data are compared with those in the works of other authors, who used the Monte Carlo simulation method, as well as with experimental data.

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Astronomy, astrophysics, and cosmology

## On the stability of the solar chromosphere-corona transition region

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

Moscow University Physics Bulletin 2011. 66. N 5. P. 462

We prove the stability of a previously obtained temperature-versus-thickness distribution in the solar chromosphere-corona transition region. The temperature distribution has been obtained on the assumption that the plasma heating by classical heat flux is balanced by the energy loss due to radiation.

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## The kinetic description of the accelerated-electron flux in solar flares

### P.A. Gritsyk, B.V. Somov

Moscow University Physics Bulletin 2011. 66. N 5. P. 466

We propose an accurate quantitative model describing the propagation of flare-accelerated electrons in the solar atmosphere. This model is based on a kinetic equation considering Coulomb collisions of accelerated electrons with thermal electrons and protons in the plasma of the solar corona and chromosphere. Using a self-consistent approach, we find the distribution function of accelerated electrons and the electric field of the reverse current balancing the electric current carried by the accelerated-electron flux. We compare our two-dimensional (in the velocity space) model with the widely used classical one-dimensional model that overlooks the reverse-current effect.

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## Simulation of propagating EAS Cherenkov radiation over the ocean surface

### O.P. Shustova$^1$, N.N. Kalmykov$^2$, B.A. Khrenov$^2$

Moscow University Physics Bulletin 2011. 66. N 5. P. 473

We present computing results of the Cherenkov light propagation in the air and water from an extensive air shower (EAS) over the ocean. Limits on the zenith angles of the showers, for which the registration of the flash of reflected photons by the space-detector is possible, are analyzed with consideration for waves on the ocean surface.

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Physics of Earth, atmosphere, and hydrosphere

## Excitation of tornados by squall storms

### S.A. Arsenyev, N.K. Shelkovnikov

Moscow University Physics Bulletin 2011. 66. N 5. P. 480

The theory of tornado generation by squall storms has been constructed. The results of the theoretical calculations are confirmed by field observations and are in good agreement with measurements.

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## Ultralow-frequency variations of the magnetic field during the propagation of acoustic-gravitaty waves in the ionosphere

### V.E. Kunitsyn$^1$, S.L. Shalimov$^2$

Moscow University Physics Bulletin 2011. 66. N 5. P. 485

The effect of the generation of ULF variations of the magnetic field during the propagation of acoustic-gravitaty waves (AGW) in the ionosphere is analyzed within a simple model. It is shown that AGW-induced ionospheric irregularities can significantly contribute to the ground magnetic field variations. Some changes in ULF variations associated with seismic events are considered as application of this mechanism.

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Physics of nuclei and elementary particles

## A mathematical model of the evolution of free radical concentrations in a cell under ionizing radiation

### O.I. Vasilenko, G.V. Petrunkin

Moscow University Physics Bulletin 2011. 66. N 5. P. 489

A probabilistic mathematical model that describes the evolution of the free radical concentration in a cell under ionizing radiation is proposed. The model is of a stochastic character and allows one to describe the generation of free radicals in the process of radiolysis, as well as the interaction between the radicals of different types and between the radicals and the cell constituents (the latter is responsible for radiobiological effect). The possibility of the presence in the cell of a certain equilibrium quantity of radicals of nonradiative origin at the moment that the irradiation begins is taken into account. The results thus obtained show that under certain values of the model’s free parameters the total number of free radicals in a cell under radiation may decrease. This effect can explain the “positive” influence of small doses of ionizing radiation.

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Chemical physics, physical kinetics, and plasma physics

## Flash ignition of a carbon nanotube

### N.N. Sysoev$^1$, A.I. Osipov$^1$, A.V. Uvarov$^1$, O.A. Kosichkin$^2$

Moscow University Physics Bulletin 2011. 66. N 5. P. 492

A mechanism for the flash ignition of a carbon nanotube (CNT) is proposed. At the first stage (during flash ignition) oxidation of an ultradispersed impurity of metals in the CNT occurs. At the second stage, heating by chemical reactions occurs. The final stage is the initiation of the combustion wave. Qualitative descriptions of processes at each stage are given.

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