IKBFU's Vestnik

2009 Issue №04

The conservation laws in the Euler problem about two attractive centers and the integration of the dynamic equations

Abstract

The article establishes that Euler’s problem of two attractive centres contains another conservation law alongside with the energy conservation
one, which is also quadratic in velocities. These conservation laws and elliptic coordinates considerably simplify the procedure of trajectory equations generation.

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Filtrational flows in the area, restricted by the sides of a rectangle

Abstract

The article uses the method of spatial point reflection for the definition of complex potentials of filtrational flows in an area limited by
rectangle. The article considers possible conditions and generates solutions in the form of infinite series. For point source the series are presented by means of the Jacobi theta-function or the Weierstrass sigmafunction.

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The interaction between an anticyclone and barrier

Abstract

The article considers the interaction of a two-dimensional anticyclone with a barrier and generates and solves its motion equation. The
authors claim that an anticyclone accelerates at the approach of the edge of a barrier forming an intensive stream. The article also offers
the streamline pattern analysis.

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The application of effective Hamiltonian method for open quantum system

Abstract

The article shows that the Lindblad Master Equation for finitedimensional Hilbert space can be presented as a Schrödinger Equation on a Hilbert space of greater dimension. This equation can be considered as an equation of the evolution of an integrated system consisting of two subsystems: observational and auxiliary ones. This equation allows solutions in the form of entangled states.

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The ionosphere effects from Poincare waves in the atmosphere

Abstract

The article focuses on the possibilities of physical interpretation of global ionosphere agitations in the period of elevated geomagnetic activity.
The authors offer a physical interpretation of this phenomenon based on the assumption about the agitation of planetary Poincare waves in atmosphere. The analysis of the space-time structure of these waves gives a credible explanation of the ionospheric dynamics under  observation.

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The bottom gravitational stream on inclined bottom in Ecmann approximation

Abstract

The article examines the deduction and the scope of the equation describing the dynamics of a thin layer of liquid over inclined bottom
in the framework of Eckman’s approach and obtains exact solutions in the form of travelling waves. The author makes a conclusion this equation
is non-integrable on the basis of Painlevé analysis.

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