Faculty of Physics
M.V.Lomonosov Moscow State University

## Investigation of a nonlinear-parametric divider with a fixed time duration of interaction

### L.V. Ваlakin, М.D. Каrasеv, V.I. Меdvеdеv

Moscow University Physics Bulletin 1981. 36. N 3. P. 1

An improved electromechanical frequency divider is experimentally and theoretically reviewed. In this divider, interaction between the electrical oscillations are the divided frequency and the low - frequency mechanical oscillatory system occurs during a short time interval τ≈T/2 (T=2π/ω) is the period of the divided frequency) near the equilibrium position. Truncated equations are obtained by means of the method of slowly varying amplitudes for the amplitudes and phases of this frequency divider, whose steady - state values are analyzed for two cases, one in which the interaction time is greater than half the period of the high - frequency oscillation (ωτ>π) and the second case in which it is less than it (ωτ<π). The amplitude responses of the divider for the divider bands thus obtained are compared to experimental data. Results of a coputation on the BESM - 4M of the steady - state amplitude and phase processes of an electromechanical frequency divider are presented for cases in which the external effect is approximated by one or two gaussian curves.

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## On the dynamic interaction of the crystals in rocks at the first type phase transitions

### M.V. Avdulоv

Moscow University Physics Bulletin 1981. 36. N 3. P. 8

Motion equations for rock crystals pulsating in a highly viscous liquid are considered. It is shown that attractive forces which cause the system to contract arise befween crystals pulsating in phase.

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## Admitance functions and thirdtime moments in nonlinear, nonequilibrium thermodynamics

### R.L. Stratonovich, A.V. Tоlstоpуatenко

Moscow University Physics Bulletin 1981. 36. N 3. P. 15

A method of finding admittance functions from nonlinear relaxational equations with external forces is set forth which does no require the introduction of a small parameter. The method is used to find the quadratic triple - subscript admittance functions in an arbitrary multi-component case. The resulting functions are substituted in a nonquantum version of the formula used to express the quadratic fluctuation-dissipation theorem. As a result, the triple - time moment of the equilibrium thermal fluctuations are computed in an arbitrary multi - component case. A comparison is made with the results of Markov nonlinear nonequilibrium thermodynamics. In particular, it is finally proved that a relaxational equation with external forces may be restored, in a quadratic- linear approximation, in terms of arelaxational equation without forces.

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## Single-circuit oscillator with additional unidirectional channel of delay feedback

### V.V. Abgarian, I.I. Minakova

Moscow University Physics Bulletin 1981. 36. N 3. P. 21

The stationary regime equations for a single-circuit feedback oscillator with additional unidirectional delay feedback channel are obtained by means of the harmonic balance method. Stability conditions of the different single-frequency oscillation conditions are analyzed and relations between the amplitude and frequency characteristics of the system and the system parameters are obtained by means of numerical methods. Theoretical results are confirmed in a highly qualitative manner by an experiment performed using an electro-acoustic feedback oscillator model with ultrasonic delay line.

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## The study of Vibrations of moving bodies by the coherent light scattered by them

### V.S. Anchutkin, V.I. Shmal'hauzen

Moscow University Physics Bulletin 1981. 36. N 3. P. 26

The penomenon of coherent emission by a moving coarse surface subjected to disturbances in the form of transverse vibrations is theoretically and experimentally investigated. Spectral patterns of the output signal from a photodetector are obtained for a model of an object in the form of a rotating duralumin disk that completes small angular wobbles. The technique and its equipment realization help in detecting the transverse vibrations of moving objects that diffusely scatter light, particularly the angular wobbles of moving parts. The experimental results are in good agreement with theoretical representations.

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## Interaction between a vortex line and uneven surface of type-II superconductor

### F.F. Ternovskii, L.N. Shehata

Moscow University Physics Bulletin 1981. 36. N 3. P. 30

The interaction between a cylindrical (with arbitrary profile) superconductor boundary and a vortex filament parallel to it is investigated. It is shown that a marked drop in the Bean - Livingston potential barrier may occur at definite points of the profile of an uneven bound-ary (due to a local increase in the surface current density). Even in those cases in which the characteristic scale of the distortions is small by comparison with the depth of penetration, the superheating field of the Meisner state may drop down to values on the order of $H_cϰ^{-1/2}$.

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## Gibbs's potential for a superconducting (type-II) quasi-closed system in the presence of a transport current

### F.F. Ternovskii

Moscow University Physics Bulletin 1981. 36. N 3. P. 37

An expression is found for the operation of a transport current source and a general definiti on of the Gibbs thermodynamic potential given for a superconductor of the second kind placed in an external magnetic field and carrying a transport current, based on successive application of the properties of the pairing potential phase.

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## Particles clouse packing influence on high dispersion $γ$-Fe$_2$O$_3$ magnetic properties

### L.V. Lasareva, A.V. Сheremushкina

Moscow University Physics Bulletin 1981. 36. N 3. P. 43

The influence of the particle packing density on the degree of magnetization, coercive force and interaction between particles in highly dispersed γ-$F_eO_3$ is experimentally studied. Measurements are conducted at packing densities p = 0.02-0.7 in magnetic fields which greatly exceed the saturation field. It was found that all the magnetic characteristics studied in such systems are functions of the packing density.

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## Subharmonice oscillations excitations process in a tank circuit with small nonlinearity

### A.N. Vachrameev

Moscow University Physics Bulletin 1981. 36. N 3. P. 49

The parametric nature of nonstationary processes that arise when subharmonic oscillations are excited in a circuit with a small nonlinearitу is explained.

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## Magnetostatic oscillations spectrum of an ellipsoid with domain structure

### S.A. Vyzulin, S.A. Kirov, N.E. Syr'ev

Moscow University Physics Bulletin 1981. 36. N 3. P. 53

A method is proposed for computing the magneto - static oscillation spectrum of an arbitrarily magnetized ferromagnetic ellipsoid both in the saturation region and the region of existence of the domain structure. The spectrum is computed for the case of a spheroidal sample of cubic ferrite monocrystal with negative first anisotropy constant magnetized perpendicular to the axis of rotation. In fields weaker than the saturation field, the computation is performed for the case of a two - phase plastic domain structure. An experimental study of the spectra of iron - yttrium garnet monocrystalline disks magnetized along [110] and cut in the plane (110) is performed in the range 400-2500 MHz. Good agreement is obtained over the entire range of field strengths studied, including in the domain structure, between the computed and experimental resonance oscillation frequencies in the (110), (220), (330), (440), (200), (210) arid (320) planes. However, a complete explanation of the low-frequency part of the experimental spectra could not be obtained, due to the inexactness of our approximation of the disk by a spheroid.

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## Investigation of radiation defects distribution in NaCl by transmission electron microscopy

### Yu.V. Bykov, V.G. Babaev, M.B. Guseva

Moscow University Physics Bulletin 1981. 36. N 3. P. 61

Data are presented on the study of the transverse slippage of argon ion- irradiated NaCI crystal (E-3 keV, current density 100 μA/$cm^{2}$, irradiated plane (100), slippage along (010) at a temperature of l80°C. Regions of defect localization in the slip plane are found by means of vacuum decoration radiation erosion of the profile of the near-surface layer of the crystal at different angles (40-90°) and different radiation doses ($10^{17}$-$10^{19}$ ion/$cm^{2}$). Based on the obtained data, it is concluded that the dimensions of the radiation - damaged regions found by means of the decoration method and the nature of the erosion of the ionirradiated near-surface layer are attributable to diffusion of radiation defects.

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## Electrical nonlinear-parametric high order frequency divider

### L.V. Balakin, M.D. Karasev, V.I. Medvedev

Moscow University Physics Bulletin 1981. 36. N 3. P. 66

An electrical version of ahigh - order nonlinear parametric frequency divider is proposed and realized for the first time to overcome defects found in electro - mechanical nonlinear parametric frequency dividers. The divider has as its basic section a high - quality electrical oscillatory low-frequency system resembling an underexcited RC oscillatory with Wien bridge operating under rigid constraints when half the voltage period of the divided frequency is fed to it. The division ratio, relation between amplitude of the distributed oscillations and the difference between the divided oscillations in the division band, and the relation between amplitude of distributed oscillations and the pumping voltage are all experimentally studied. The division circuit may be used to perform a division with ratio m ≤ 53 in a single cascade. An equivalent circuit of our frequency divider is presented in which truncated equations for the amplitude and phase are obtained by means of the slowly varying amplitude method. The stability of the nonzero solutions of the system of truncated equations is studied. Relations between the amplitudes of the distributed low-frequency oscillations and the (a) voltage misalignment of the divided frequency; (b) the pumpumping voltage; and (c) division ratio m are theoretically computed.

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## Study of tricritical point in triglycineselenate crystal by dynamical heat method at high pressure

### В.A. Strukov, Pоlandоv I.N., V.A.Chernenko, V.K. Novik

Moscow University Physics Bulletin 1981. 36. N 3. P. 71

The temperature dependences of the heat capacity of triglycineselenate crystal are experimentally studied over a broad range of temperatures and in direct proximity to the phase transition at different pressures up to 6.5 kbar. The dependences $(∆C)^{-2}=f(T)$ are approximated by straight lines only in the range $T_{c}$-T=0,2—1,5°С. The coefficient В in the Landau expansion of free energy is independent of pressure. Processing of the results in terms of critical indices showed there was a gradual variation in the index with pressure. At a pressure of 4 kbar, it was close to one half. The results are discussed under the assumption that defects influence the phase transition in triglycineselenate. It is concluded that at p = 1 bar, the phase transition in triglycineselenate is a phase transition of the first kind close to the tricritical point.

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## The structure of separated flow downstream from rough body

### E.P. Anisimоva, A.A. Speranskaya, S.G. Shaphaev

Moscow University Physics Bulletin 1981. 36. N 3. P. 78

Result s are presented of an experimental investigation of the structure of the velocity field in separated flow arising in the streamline of a semicylinder located on a smooth subjacent surface. The axis of the semicylinder is perpendicular to the incident flow, and the Reynolds number is equal to 2.1*10$^{5}$. The velocity field is studied by means of a two-component mechanotron - based anemometer. The existence of two separation zones is confirmed, with one located in front of and the other behind the semicylinder. In separated flow behind the semi-cylinder, a unique displacement layer is found; the vertical profiles of the longitudinal component of the mean velocity in the separated flow right up to the attachment zone are similar to the profile of the mean velocity in a plane turbulent displacement layer. The measured vertical profiles of the dispersion of the horizontal and vertical velocity components and the moment of correlation of the latter indicate significant spatial irregularity in the region of separated flow of the distribution of the integral characteristics of turbulence in the longitudinal direction. An analysis of the fluctuation autospectra of the velocity showed two statistically significant maxima which follow the semicylinder in the separation zone and corresponding Strouhal numbers from 0.013 to 0.018 and from 0.031 to 0,036.

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## Study of the stability of stationary regimes of many-circuite oscillator

### G.P. Minina

Moscow University Physics Bulletin 1981. 36. N 3. P. 83

An oscillator with slightly nonlinear active element characteristic bound to an arbitrary linear oscillatory system is considered in the article. Stability equations and equations for determining the stationary amplitude and frequency of the self - excited oscillations of sucha system are obtained. The equations are written in a form convient for computing the stability of the steady states of real multi - circuit self - excitedo scillatory systems. As an example, stability criteria for the self - excited oscillations in a three - circuit frequency stabilization system with a large regeneration reserve in the oscillatory circuit are obtained.

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## The spin-hamiltonian constant valuations with second order precision

### V.N. Lazukin, A.N. Terentjevskii, V.I. Danilenko

Moscow University Physics Bulletin 1981. 36. N 3. P. 89

Numerical solutions of the analytic expressions of different spin Hamiltonians are obtained by the method of perturbation theory. In addition, the general form of the spin Hamiltonian matrix is diagonalized by computer. A comparison of the computed estimates obtained by general methods may be used to numerically estimate the capabilities of methods from perturbation theory as a function of the electron spin resonance spectra thin - structure constant evaluation.

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## A method of studing of lock in oscillators with resonance coupling

### G.P. Minina

Moscow University Physics Bulletin 1981. 36. N 3. P. 93

A semigraphical method of treating lock in oscillators with a fractional - multiple ratio between the frequencies related by means of the resonance circuits is described. Domains of frequency synchronization, the system's frequency characteristics, and regions of in - phase and counter - phase regimes are obtained, and regions that remain stable with respect to a phase criterion are identified. The method proposed for considering mutual synchronization of oscillators may be used to obtain relatively simple analytic expressions by means of which it is possible to obtain a relation between the oscillator operation and various parameters.

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## Automized setup «Optical Doppler anemometer—computer ES-1010» for the study of slow hydrodynamic flows in real time scale

### M.V. Evdokimov, A.V. Priezzhev

Moscow University Physics Bulletin 1981. 36. N 3. P. 97

Experience gained in the use of the ES-1010 computer for processing the output signal of an optical Doppler anemometer in real time in study of slow stationary and fluctuating flows with velocities up to several mm/sec is described. Processing of the signals, which, in the general case, constitute nonstationary random processes, is performed by the BPF method. By means of a flexible software system, it is possible to implement information storage, processing, and output regimes in the interactive mode and to vary the regimes over broad ranges.

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## Efficiency of surface waves generation in beam-plasma systems

### V.К. Grishin, M.F. Кanevsкii

Moscow University Physics Bulletin 1981. 36. N 3. P. 100

The effectiveness of surface wave generation in the case of generation saturation is considered for the two most typical instances:(1) broad beam fanning of a plasma surface free of the magnetic field; (2) the beam fans a narrow plasma column (the beam and plasma are magnetized). The beam state is described by a nonlinear kinetic equation, and the plasma remains a linear dispersing medium. It is shown that the use of plasma fanning beams promotes marked increases in generation effective - ness.

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## Oxygen effects in the NMR experiments

### S.D. Varlamov, Yu.S. Konstantinov, A.M. Smirnov

Moscow University Physics Bulletin 1981. 36. N 3. P. 103

NMR experiments on light irradiation of liquids containing oxygen are described. The NMR frequency shifts when a small portion of the volume of the object is illuminated are measured. The shifts are attributed to local variation of the magnetic susceptibility that arises in the course of local variation of the concentration of dissolved oxygen and local variation of the temperature in the illuminated portion of the volume of the object. A study of the relation between the longitudinal relaxation time of chloroform protons and ultraviolet light irradiation time makes it possible to estimate the lifetime of particles that react with oxygen.

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## Nonlinear kinetic wave-beam equilibrium in damping systems

### Grishin V.K., Shaposhnikova E.N.

Moscow University Physics Bulletin 1981. 36. N 3. P. 106

The equilibrium state arising as a result of the development of beam instability in a damping system is studied by means of an exact solution of the nonlinear self-consistent kinetic equation for a purely harmonic wave. A number of basic system characteristics of a system in the equilibrium state, e.g., dispersion equation, efficiency of transf ormation of the beam's kinetic energy into field energy and the particle capture coefficient, are obtained.

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## The physical modelling of atmospheric vortices

### E.P. Anisimova, A.M. Gusev, A.A. Speranskaya, V.S. Shandin

Moscow University Physics Bulletin 1981. 36. N 3. P. 109

A description of an experimental unit that realizes a model of an atmospheric vortex system is presented. The model simultaneously reproduces the velocity, temperature, and air humidity fields. Thermal effects play the dominant role in this model of vortex systems.

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## Infrared GaAs crystal light modulator with 480 MGz modulation frequency

### M.I. Zusman, E.R. Moustel

Moscow University Physics Bulletin 1981. 36. N 3. P. 112

Modulation of infrared radiation with wavelength λ = 10.6 μm is experimentally observed. At a modulation frequency of f$_{m}$ = 480 MHz and modulation power of 16 W , the modulation intensity amounts to 37%.

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## Acceleration of electrons in classical cyclotron

### L.A. Sarkysian

Moscow University Physics Bulletin 1981. 36. N 3. P. 114

It is suggested that electrons as well as ions can be accelerated in a classical cyclotron. Such electron acceleration becomes possible when the cyclotron enters the microtron mode, The attainable energy of the electrons in cyclotrons with polar diameter from 1,2 to 1.5 m may amount to 30 to 50 MeV (the maximal energy of ions in existing microtrons amounts to 32 MeV). Electron acceleration in the quasi-continuous mode is possible.

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