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

## Space-time topology as a consequence of the dynamics of closed boson strings. II. The second approximation

### N.F. Nelipa, M.Yu. Pekar

Moscow University Physics Bulletin 1992. 47. N 1. P. 4

The possibility of constructing a theory where the space-time topology would be determined by the dynamics of closed boson strings is analyzed. The analysis has the form of an expansion into a series with respect to the coupling constant. The second-order expansion is considered. Some new constraints on the admissible space-time topology are found in addition to those in the first-order approximation.

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## The inverse problem for a one-dimensional singular oscillator

### V.B. Gostev, A.R. Frenkin

Moscow University Physics Bulletin 1992. 47. N 1. P. 8

The inverse problem for the one-dimensional Schr$\stackrel{..}{o}$dinger equation with a singular potential is solved using an oscillator with perturbation $\lambda x^{-2}$ as an example. The corrections to the potential were found to possess a weaker singularity as compared to the seed potential.

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## Solution asymptotics for nonlinear dissipative equations at large $x$ aud $t$

### P.I. Naumkin

Moscow University Physics Bulletin 1992. 47. N 1. P. 12

An asymptotic representation is obtained at large $x$ and $t$ for the solution to Cauchy's problem for the following nonlinear dissipative equations: the Korteweg-de Vries-Burgers equation, the Kolmogorov-Petrovskii-Piskunov equation. the Ott-Sudan-Ostrovskii equation and the Burgers equation with linear damping.

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## Renormalization in terms of the observables

### D.A. Slavnov

Moscow University Physics Bulletin 1992. 47. N 1. P. 16

A procedure is described that makes it possible to express uniquely all observable quantities in terms of several base quantities. The result does not depend on the applied renormalization scheme.

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## On the uniqueness in one of the coefficient problems relating to technological processes

Moscow University Physics Bulletin 1992. 47. N 1. P. 20

Consideration is given to a problem relating to technological treatment of a blank whose structure is nonhomogeneous in the transverse direction, which manifests itself in the dependence of the diffusion (or thermal conductivity) coefficient on the transverse coordinate. The uniqueness of the determination of this coefficient from the given concentration (or temperature) profile at an instant close to the end of the process is proved.

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## Accumulation of a photosensitizer in cells with allowance for the passage of its charged forms across the membrane

### L.V. Zhorina, N.V. Stepanova

Moscow University Physics Bulletin 1992. 47. N 1. P. 24

A mathematical model has been constructed and studied of the penetration of hematoporphyrin (HP) ions into cells and their accumulation there. HP is a photosensitizer most frequently used in the photodynamic therapy of tumors. It is shown that the selectivity of HP accumulation in tumors depends on the following factors: {a) the lowered acidity inside malignant cells and in the surrounding medium and {b) the higher concentration in tumor cells of lipids, to which the HP molecules bind.

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Atomic and nuclear physics

## On the role of double collisions in $(е, 2е)$ processes

### Yu.V. Popov, N.M. Kuz'mina

Moscow University Physics Bulletin 1992. 47. N 1. P. 30

The region of efficiency of the second Born approximation (SBA) in the theory of ionization of atoms by fast electrons is considered. A model (ASBA) is constructed for approximate calculations of the SBA contribution to the differential cross section $d^3\sigma$. The calculations are compared with a large array of experimental values of $d^3\sigma$ in the reaction $Н(е,2е)Н^+$.

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## Nonlinear waves in a laminar Brillouin electron beam propagating in a strip-line

### 0.I. Vasilenko

Moscow University Physics Bulletin 1992. 47. N 1. P. 37

The multiscaling method of the perturbation theory was used to examine the nonlinear waves propagating in the Brillouin electron beam in vacuo between two plane parallel electrodes. A dispersion correlation was obtained, and the amplitude of the waves was shown to be described by the Korteweg-de Vries equation that admits soliton solutions. The equation coefficients were determined as a function of parameters of the equillibrium unperturbed beam. A kind of one-soliton solution is presented.

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## Acoustooptic filtering of electromagnetic radiation using two Bragg diffraction modes

### V.B. Voloshinov, A.N. Uskov

Moscow University Physics Bulletin 1992. 47. N 1. P. 43

The results are given of a theoretical study of the feasibility of spectral filtering of uncollimated optical beams by means of acoustooptic filters based on a paratellurite crystal. The parameters of a sophisticated filter with two piezo-electric transducers are calculated. The device can operate in various diffraction modes with different selectivity of interaction of light and sound.

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## Heat energy balance in a low-pressure SHF surfatron

### P.S. Bulkin, A.P. Ershov, G.S. Solntsev, M.M. Rakhman, L.I. Tsvetkova

Moscow University Physics Bulletin 1992. 47. N 1. P. 50

Analysis is presented of the results of experimental studies of a radial heat flow $Q_T (z)$ along the plasma column of an SHF surfatron in Xe at a pressure of 0.5-1.2 Torr. Energy loss caused by the energy transfer to the walls by positive ions accelerated by the ambipolar diffusion field and the potential gradient near the discharge tube wall was found to play an important part. This channel of energy loss is most effective in heavy gases. In the experimental conditions of this study. the properties of the discharge along its total length can be described by means of a single kinetic plasma model.

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Optics and spectroscopy

## Trigonal germanium dioxide: its preparation and optical parameters

### T.M. Glushkova$^1$, D.F. Kiselev$^1$, I.B. Makhina$^2$, M.M. Firsova$^1$, A.P. Shtyrkova$^1$

Moscow University Physics Bulletin 1992. 47. N 1. P. 55

The following physical properties of trigonal germanium dioxide grown by the hydrothermal method at 185°C were studied: density, the refractive and optical specific rotatory dispersions in the visible spectral range, and the spectra of optical transmission over the 0.2-10 μm range. The data obtained were compared with the same parameters for $\alpha$-quartz, which is a structural analog of trigonal germanium dioxide.

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## Changes in the mechanical and electric parameters of bilayer lipid membranes in their interaction with hematoporphyrin

### T. Hianik$^1$, D. Masarikova$^1$, L.V. Zhorina$^2$, M.Yu. Poroshina$^2$, E.B. Chernyaeva$^2$

Moscow University Physics Bulletin 1992. 47. N 1. P. 59

The interaction of hematoporphyrin IX (HP) with artificial bilayer lipid membranes (BLMs) has been studied. It has been found that after dark incubation of BLMs in a HP solution (at concentrations from $10^{-6}$ to $3 \cdot 10^{-5}$ M) the conductance of the BLMs does not change very much, the elasticity modulus ( $E_{\perp}$ ) and the dynamic viscosity coefficient $\eta$ diminish by 21.9-31.3%, while the membrane potential $U_1$ becomes negative (-50 mV). Irradiation of a modified BLM by a He-Ne laser leads to an increase of the parameters $E_{\perp}$ aud $\eta$ by 40.7 to 66.2%, to a decrease of $U_1$ to -20 mV, and also to irreversible changes in the mechanical properties of the membrane. Binding of HP with BLM proceeds noncooperatively with the constant $К = 10^{5}$ $М^{-1}$.

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## Dynamics of stimulated Raman backscattering: numerical experiment

### I.N. Zhmakin, S.Yu. Nikitin, D.A. Sivashov

Moscow University Physics Bulletin 1992. 47. N 1. P. 65

The dynamics of Raman backscattering was studied under conditions when the duration of the pumping pulse was greater than the dephasing time for molecular vibrations and the time of light travel through the medium. Three basic regimes were found to be possible: quasistatic, spiking, and transient. Realization conditions and specific features of these regimes were established.

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### I.N. Sisakyan, A.V. Tikhonravov, A.B. Shvartsburg, A.V. Shepelev, V.G. Yakushkina

Moscow University Physics Bulletin 1992. 47. N 1. P. 73

Quantitative calculation of optimization coatings based on the analysis of the field-dependent optical properties of semiconductor materials in the far-infrared region has been made. The amplitude-phase characteristics of the adaptive radio-optical devices were computed. It has been shown that optimization interference coatings make it possible to increase the dynamic ranges of amplitude modulation systems by a factor of 3 to 4.

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Astronomy

## Gravitational waves and baryosynthesis

### M.V. Sazhin, Ya.A. Chechina

Moscow University Physics Bulletin 1992. 47. N 1. P. 78

Manifestations of the dust-dominated stages, which might take place in the early Universe, are analyzed. One of possible causes of such stages is baryosynthesis at temperatures T = 1015 GeV. Distortions in the spectrum of the gravitational wave background, brought about by the stage of baryosynthesis, are calculated.

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## Calculation of an optical system for a laser-controlled gyroscop

### V.E. Zharov, S.N. Markova, M.V. Sazhin, E.N. Fedoseev

Moscow University Physics Bulletin 1992. 47. N 1. P. 86

A passive square-shaped resonator is proposed to be used in the laser gyroscope system being developed at the Time Service Department of the Sternberg Astronomical Institute for measuring the Earth's rotation variations. The resonator has an arm l of 3.10 m and consists of two spherical mirrors of equal radius of curvature ($R_m$ = 10 m) and two flat mirrors, one of which is an input element and the other the output element.

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Solid state physics

## Conduction anisotropy induced by the electric field in narrow-gap Bi-Sb semiconductors

### E.V. Bogdanov, T.G. Kustova

Moscow University Physics Bulletin 1992. 47. N 1. P. 91

Heating of charge carriers in specimens of $n$- and $p$-type Bi-Sb semiconductor alloys whose axes are noncoincident with the crystallographic axes, gives rise to a transverse electric field. The specific features of this phenomenon were qualitatively explained in term of the theory of the Sasaki-Shibuya effect and the well-known concepts of the energy spectrum of these narrow-gap semiconductors.

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## Elcctricral properties of crystals of the formate and urea groups

### N.D. Gavrilova, N.P. Zaitseva, G. L. Slabkaya, L.V. Soboleva, S.V. Bogatyreva

Moscow University Physics Bulletin 1992. 47. N 1. P. 96

The temperature dependence of electrical conduction was studied and the activation energy was calculated for crystals with long hydrogen bonds, viz., lithium, yttrium, holmium, and erbium formates, urea and thiourea. A weak pyroelectric effect was revealed in the urea crystal at a temperature below room temperature. At temperatures below the phase transition temperature ($Т_С$ = 169 K) in weak electric fields, the thiourea crystal showed anomalies associated with a change in the behavior of protons on hydrogen bonds.

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## The matgnetic properties of $Gd_xCe_{1-x}MnSi$ compounds

### S.A. Nikitin, 0.V. Nekrasova, T.I. Ivanova, Yu.F. Popov

Moscow University Physics Bulletin 1992. 47. N 1. P. 101

The magnetic properties of the $Gd_xCe_{1-x}MnSi$ system of rare-earth compounds were studied. The Neel temperatures $T_N$ were determined for alloys with a Gd concentration in the range $0\le x\le 0,4$ and the Curie temperature $Т_С$ of alloys with a Gd concentration $x\ge 0,5$. The magnetic moments per formula unit were calculated. The curves of specific magnetization $\sigma$ versus magnetic field have showed, in the $0,2 < x < 0,6$ range of Gd concentration, sections corresponding to the threshold fields $В_{th}$, where $\sigma$ starts to grow sharply. A magnetic phase diagram was plotted and regions of existence of ferri-, antiferro-, and paramagnetic states were deterinined. A model was proposed to explain the magnetic properties of the compound, which assumes that there exists an antiferromagnetic exchange interaction between the Mn layers and a ferrimagnetic ordering of the Mn magnetic monents and rare-earth ions.

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Acoustics and molecular physics

### P.V. Elyutin

Moscow University Physics Bulletin 1992. 47. N 1. P. 107

An automodel solution of the soliton type, which, in propagating, conserves its shape though changes its parameters, has been obtained for the Corteweg-de Fries equation with an additional term that takes into account the nonlinear dissipation.

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Geophysics

## Generation of tsunami by oscillations of a sea floor section

### M.A. Nosov

Moscow University Physics Bulletin 1992. 47. N 1. P. 110

The problem of generation of surface waves in a layer of homogeneous heavy liquid by steady-state harmonic oscillations of a sea floor section is treated on the basis of the linear potential theory.

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