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Bulletin of the MRSU / Section "Physics and mathematics" / 2013 № 3.

 

E.A. Bedrikova, A.V. Latyshev

[THE KRAMERS PROBLEM FOR QUANTUM BOSE-GASES WITH CONSTANT COLLISION FREQUENCY AND SPECULAR-DIFFUSIVE BOUNDARY CONDITIONS] In: Bulletin of the Moscow Regional State University (electronic journal) [Bulletin of the Moscow Regional State University (electronic journal)], 2013, no. 3.


UDC Index: 533.72:517.958

Date of publication: 01.08.2013

The full text of the article

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Abstract


The Kramers problem for quantum Bose-gases with specular-diffuse boundary conditions of the kinetic theory is considered. The Kramers problem is the problem of finding a distribution function of the mass velocity and the sliding velocity of a rarefied gas moving along a flat, solid surface in case when the gas moves along some axis and there is a given gradient of its mass velocity. The solution is received for the semi-spatial Kramers problem about the isothermal sliding of a monoatomic gas having constant collision frequency and specular-diffusive boundary conditions. The new method of solution of the boundary problems from the kinetic theory is developed. The method allows to receive the solution with any degree of accuracy. At the basis of the method lays the idea of representation of a boundary condition on the distribution function in the form of a source in the kinetic equation. The solution is received in the form of Neumann series.

Key words


quantum Bose-gas, Kramers problem, specular-diffusive boundary conditions, Neumann series

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