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

## Problems of nonlinear dynamics: II. Suppression of chaos and control of dynamical systems

### A.Yu. Loskutov

Moscow University Physics Bulletin 2001. 56. N 3. P. 1

The second part of the paper (The first part entitled "Problems of Nonlinear Dynamics: I. Chaos" is published in Moscow University Phys. Bull., no. 2, p. 1, 2001) concerned with the newest problems of nonlinear dynamics is a survey of recent results on the theory of control of nonlinear (in particular, chaotic) dynamical systems and suppression of chaos. Modern approaches to stabilizing the unstable behavior of deterministic systems and methods for bringing dynamical systems into a given mode of motion best suited for applications have been described.

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Theoretical and mathematical physics

## Passive scalar transfer in stochastic steady flow

### S.V. Novikov, D.D. Sokolov

Moscow University Physics Bulletin 2001. 56. N 3. P. 24

Passive scalar behavior in a turbulent flow is compared with that in a steady flow of liquid with stochastic trajectories. Mixing of the admixture distribution with speed determined by turbulent diffusion is replaced, in a steady flow, by a phase of catastrophically fast leveling of admixture gradients.

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## Threshold reactions in crossed constant electromagnetic field with nonzero invariant $E^2-H^2$

### V.N. Rodionov, A.M. Mandel

Moscow University Physics Bulletin 2001. 56. N 3. P. 28

Influence of an external static electromagnetic field of special configuration (a superposition of a crossed ($E=H$) and a magnetic field) on certain processes of quantum electrodynamics, nonlinear phenomena in atomic physics and on a number of processes in semiconductor physics has been considered. A fundamental difference in influence produced by the crossed and the magnetic field on the probability of the reactions in question has been. demonstrated. A simple algorithm has been described that allows us to pass from the results valid for nonrelativistic limit in a crossed constant field to the case of the field with nonzero invariant $E^2-H^2\ne0$.

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## Calculating zeros of spherical Bessel functions and their derivatives

### V.P. Modenov

Moscow University Physics Bulletin 2001. 56. N 3. P. 34

A recurrent way of finding zeros of Bessel functions and their derivatives by way of reduction to the Cauchy problem for a differential equation with a parameter derivative and an algebraic right-hand side has been given.

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## Magnetic fields with nontrivial helicity and fermion zero modes

### V.Ch. Zhukovsky, I.V. Mamsurov

Moscow University Physics Bulletin 2001. 56. N 3. P. 38

The definition of a magnetic field with finite helicity and its correspondence to the topological Chern-Simons (CS) charge of the initial non-Abelian pure gauge field configuration has been considered. Zero-mode solutions of the Dirac equation have been obtained. Their properties have been investigated.

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Atomic and nuclear physics

## Resonance profile in electron-atomic scattering via negative ion formation

### V.V. Balashov

Moscow University Physics Bulletin 2001. 56. N 3. P. 43

Method of calculation and parametrization of basic characteristics of resonance scattering of electrons by atoms via the formation of autoionization states of a negative ion has been developed in a diagonalized approximation on the basis of the Fano method in the atomic collision theory and in the unified Feshbach nuclear reaction theory.

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## Detection of stochastic gravitational background in non-Gaussian additive noises

### A.V. Gusev, V.N. Rudenko

Moscow University Physics Bulletin 2001. 56. N 3. P. 50

A locally optimal algorithm has been developed for resonant gravitational antennas for detecting weak stochastic gravitational background in diversity reception under the conditions of minimal a priori information on stochastic properties of non-Gaussian additive noises.

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Optics and spectroscopy

## Modulation method of generating classical squeezed states

### Yu.E. D'yakov

Moscow University Physics Bulletin 2001. 56. N 3. P. 54

A new method of realization of transformations of the type "unsqueezed state <--> squeezed state" has been suggested and analyzed, in which a simple linear system with a modulator (an M-system) is used. It has been shown that the M-system is phase sensitive for a harmonic signal, namely, in this case the amplitude of the output signal can essentially depend on the phase of the input signal.

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## Aperture effects in laser beams propagating through atmospheric channels with intermittent turbulence

### T.I. Arsenyan, A.M. Zotov, P.V. Korolenko, M.S. Maganova, A.V. Mesnyankin

Moscow University Physics Bulletin 2001. 56. N 3. P. 58

The influence of aperture of collimated laser beams propagating through atmospheric channels under the conditions of intermittent turbulence on the transformation of their space-time structure has been experimentally investigated. It has been found that there exists a critical value of beam exit aperture approximating the size of the first Fresnel zone of the channel, the excess of which results in stochastic radiation. The change of statistical characteristics of radiation for the near-critical aperture has been considered.

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Acoustics and molecular physics

## Dynamics of gas flows in long microchannels

### K.V. Zhukovskii

Moscow University Physics Bulletin 2001. 56. N 3. P. 64

Steady flow of three-dimensional compressible isothermal flows in long microchannels has been considered with due regard for molecular effects. Using the expansions of the Navier-Stokes equation in terms of a small parameter (channel height-to-length ratio), the solutions for streamlined velocity, pressure distribution and mass flow have been obtained. The influence of compressibility and rarefaction effects on gas flow dynamics as well as the influence of the flow slipping on the tracer scale along the channel walls on pressure, velocity profiles, and mass transfer have been studied.

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Solid state physics

## Relationship between exchange and relativistic energies defining linear magnetoelectric effect in Cr$_2$O$_3$ antiferromagnet

### S.S. Krotov, A.V. Lisnyak

Moscow University Physics Bulletin 2001. 56. N 3. P. 70

The linear magnetoelectric effect in $\mathrm{Cr_2O_3}$ 3 within the framework of a phenomenological approach has been considered. The longitudinal (an external field is parallel to the three-fold axis) and the transverse part of the effect in $\mathrm{Cr_2O_3}$ are shown to be dictated by the exchange and relativistic interactions, respectively. This explains the change in the magnetoelectric effect tensor $\alpha_{ij}$ under the spin-flop transition and determines the toroidal moment $\textbf{T}$ vector components which are other than zero in the $\mathrm{Cr_2O_3}$ spin-Hop phase.

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## Special features of dielectric response of triglycineselenate crystals near the Curie point

### N.D. Gavrilova, A.A. Zheleznyak, A.M. Lotonov, V.K. Novik

Moscow University Physics Bulletin 2001. 56. N 3. P. 74

A smooth transition from one dielectric response mechanism to another caused by frequency and temperature variations and the fulfillment of the universal fractal-power law for the $\lg\epsilon'(\lg\omega)$ and $\lg\epsilon''(\lg\omega)$ dependences have been demonstrated by the example of low-frequency dielectric dispersion of triglycineselenate single crystals near the Curie point.

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## Concentration of EL2 centers in GaAs single crystals grown from melts of various compositions

### V.A. Morozova$^1$, O.G. Koshelev$^1$, E.P. Veretenkin$^2$, V.N. Gavrin$^2$, Yu.P. Kozlova$^2$, A.V. Markov$^3$, A.Ya. Polyakov$^3$

Moscow University Physics Bulletin 2001. 56. N 3. P. 81

The concentration of EL2 centers in unalloyed high-resistance GaAs grown from a melt enriched in Ga was shown to reduce by 50 percent as the atomic fraction of arsenic decreased from 0.5 to 0.454. Thermal annealing increased the concentration of centers 1.6 times.

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Theoretical and mathematical physics

## Spectral properties of the problem of an irregular waveguide

### A.L. Delitsyn

Moscow University Physics Bulletin 2001. 56. N 3. P. 87

Spectral problem of a waveguide with insertion in the form of a permeable scatterer is considered. It is established that the discrete spectrum contains infinitely many points immersed in the continnous spectrum for scatterers of a certain kind.

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