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

## Problems of nonlinear dynamics: I. Chaos

### A.Yu. Loskutov

Moscow University Physics Bulletin 2001. 56. N 2. P. 1

This is the first part of a review devoted to some present-day problems of nonlinear dynamics, namely, the chaoticity of dynamical systems and the controllability of such systems. Basic bifurcation theory propositions, along with some results concerning the development of chaos in such systems, are presented. Some important properties of chaotic dynamical systems are discussed, methods to describe them are considered, and some ergodic theory propositions are elucidated.

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Theoretical and mathematical physics

## Examples of computations in the framework of a new perturbation theory with convergent series

### V.V. Belokurov, Yu.P. Solov'ev, E.T. Shavgulidze, I.L. Yudin

Moscow University Physics Bulletin 2001. 56. N 2. P. 23

Within the framework of a new perturbation theory with convergent series, certain quantities determined by finitely many terms of the expansion of the traditional perturbation theory are evaluated. The obtained results are compared with the known exact solutions.

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## Mixed boundary problem of magnetized semiconductor physics in an external domain

### A.O. Chikilev, P.A. Krutitskii

Moscow University Physics Bulletin 2001. 56. N 2. P. 31

The authors consider a mixed problem for the Laplace equation in an external multiply connected domain with a boundary composed of simple closed curves. The Dirichlet condition is preset on some curves and a condition with the skew derivative on the other curves. The problem is reduced to the uniquely solvable Fredholm equation of the second kind in the space of continuous functions. The existence and uniqueness of the solution are proved.

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Optics and spectroscopy

## Spectroscopic studies of the aggregation of biscyanine dyes in solutions

### K.G. Blinova, A.A. Ishchenko, l.L. Mushkalo, S.V. Patsaeva, A.V. Pekhota, V.I. Yuzhakov

Moscow University Physics Bulletin 2001. 56. N 2. P. 37

Spectral-luminescence properties of four biscyanine dyes that represent chemically combined dimers, as well as those of the corresponding monomeric dyes were studied. Electron absorption and luminescence spectra of aqueous and ethanol solutions of the dyes were measured. Processes of association of monomeric and dimeric dyes caused by solutions strengthtening were studied.

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## Measuring the optical characteristics of scattering media from the time profile of optical-acoustic signals

### P.S. Grashin, A.A. Karabutov, J.M. Pelivanov, N.B. Podymova

Moscow University Physics Bulletin 2001. 56. N 2. P. 44

To study the relationship between the position of the light intensity maximum in a scattering medium and the ratio between the light absorption and extinction coefficients at various scattering coefficients, an optical-acoustic method is used. Measurements are taken from the time profile of the pressure of an acoustic pulse excited in the medium in a thermal-optical fashion. A method for measuring the light absorption and reduced scattering coefficients of scattering media from the time profile of acoustic signals excited there is suggested.

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## Self-phase modulation and optical-harmonic generation in hollow fibers: simple recipes for a high efficiency

### A.N. Naumov, O.A. Kolevatova, A.M. Zheltikov

Moscow University Physics Bulletin 2001. 56. N 2. P. 50

Simple expressions for the estimation of the gas pressure allowing thirdharmonic generation in leaky modes of a hollow fiber to be phase matched and permitting optimal sizes of a hollow fiber for ultrashort-pulse generation to be chosen are derived. The enhancement of harmonic-generation efficiency in a hollow fiber relative to harmonics generation in a free gas is estimated.

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Solid state physics

## Crystal structure parameters of Pd$_{3}$Lu$_{2}$ intermetallide

### A.S. Ilyushin, N.A. Khatanova, E.A. Rykova, E.V. Silonova

Moscow University Physics Bulletin 2001. 56. N 2. P. 56

X-ray analysis was used to show that aging of Pd-44.5 at.% Lu and Pd-45.7 at.% Lu alloys at 500$^о$C resulted in the formation of the Pd$_3$Lu$_2$ intermetallide with a monoclinic lattice ($a=7.78$ Å, $b=8.90$ Å, $c=12.21$ Å, $\beta=117^о$). The crystallization of Pd$_3$Lu$_2$ is preceded by the formation of a metastable phase with a berthollide-type hexagonal lattice.

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Geophysics

## The role of the density structure of the near-water atmospheric layer in the atmosphere-ocean heat and mass exchange

### A.A. Budnikov$^1$, G.G. Khundzhua$^2$

Moscow University Physics Bulletin 2001. 56. N 2. P. 63

The stability of density stratification of the near-water atmospheric layer (NWAL} is analyzed. The relationship between the instability energy and the hydrometeorological parameters is evaluated. The role of the NWAL density and thermal structures in the atmosphere-ocean heat and mass exchange processes is demonstrated.

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Theoretical and mathematical physics

## The spectrum of the radial Schr$\stackrel{..}{o}$dinger equation with an arbitrary attractive potential

### O.S. Pavlova$^1$, A.R. Frenkin$^2$

Moscow University Physics Bulletin 2001. 56. N 2. P. 66

By a method based on examining the analytical properties of Laplace images of wave functions, the discrete spectrum of the radial Schr$\stackrel{..}{o}$dinger equation with an arbitrary attractive potential is determined. With the use of the new approach, the problem is reduced to approximately finding the roots of the characteristic equation corresponding to an infinite system of linear algebraic equations.

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## Gravitational search method for weakly luminous binary star systems

### V.I. Denisov

Moscow University Physics Bulletin 2001. 56. N 2. P. 69

It is shown that the effect of gravitational bending of light rays can be used to search for weakly luminous binary star systems.

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Atomic and nuclear physics

## Electron shell effect in coherent polarization bremsstrahlung of fast electrons on light element atoms

### V.K. Grishin, S.P. Likhachev, G.S. Nefedov

Moscow University Physics Bulletin 2001. 56. N 2. P. 72

It is shown that the spectrum of polarization bremsstrahlung of fast electrons on light element atoms with markedly pronounced electron shells have a specific structure split into high- and low-frequency components. The maximum coherence region is shifted toward frequencies lower than those predicted earlier. A carbon atom is considered to assess partial and full coherence regions of polarization bremsstrahlung.

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