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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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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

List of references

1. Case K.M. Elementary solutions of the transport equations and their applications Ann. Phys. 1960. V.9. No. 1.
2. Cercignani C. Elementary solutions of the linearized gas dynamics Boltzmann equation and their applications to the slip flow problem Ann. Phys. (USA). 1962. V. 20. No. 2.
3. Cercignani C. Mathematical Methods in Kinetic Theory. New York: Plenum Press, 1969.
4. Cercignani C. The method of elementary solutions for kinetic models with velocitydependent collision frequency Ann. Phys. 1966. V. 40.
5. Cercignani C. The Kramers problem for a not completely diffusing wall J. Math. Phys. Appl. 1965. V.10.
6. Cercignani C., Foresti P., Sernagiotto F. Dependence of the slip coefficient on the form of the collision frequency. Part 2 Nuovo Cimento. 1968. V. LV11. B. No. 2.
7. Cercignani C., Lampis M. Kinetic model for gas surface ineraction Transport Theory and Statist. Physics. 1971. V.1.
8. Ferziger J.H. and Kaper H.G. Mathematical Theory of Transport Processes in Gases. Amsterdam: NorthHolland Publishing Company, 1972.
9. 32
10. Gritsienko N.V., Latyshev A.V., Yushkanov A.A. Plasma Waves Reflection from a Boundary with Specular Accomodative Conditions Comp. Maths. and Math. Phys. 2010. V. l. 50. No. 8.
11. Latyshev A.V., Yushkanov A.A. Isothermal slip of a Fermi gas with specular diffuse reflection from the boundary Russian Physics Journal. 2009. V. 52. Is. 12.
12. Latyshev A.V., Yushkanov A.A. Skin effect with arbitrary specularity in Maxwellian Plasma J. of Math. Phys. 2010. V. 51.
13. Latyshev A.V., Yushkanov A.A. Smolukhowski problem for degenerate Bose gases Theor. Mathem. Phys. Springer New York. 2008. V. 155. No. 3.
14. Latyshev A.V., Yushkanov A.A. Smoluchowski problem for metals with mirror diffusive boundary conditions Theor. and Mathem. Physics. 2009. No. 161(1).
15. Latyshev A.V., Yushkanov A.A. Solution of the Skin Effect Problem with Arbitrary Coefficient of Specular Reflection Comp. Mathem. and Mathem. Physics. 2009. V. 49. No. 1.
16. Latyshev A.V., Yushkanov A.A. Structure of the Electric Field im the Skin Effect Problem Physics of Solid State. 2009. V. 51. No. 4.
17. Latyshev A.V., Yushkanov A.A. Temperature jump in degenerate quantum gases in the presence of a BoseEinstein condensate Theor. and Mathem. Phys. 2010. V. 162(1)..
18. Latyshev A.V., Yushkanov A.A. Temperature jump in degenerate quantum gases with the Bogoliubov exictation energy and in the presence of the Bose—Einstein condensate Theor. and Mathem. Physics. 2010. V. 165(1).
19. Latyshev A.V., YUshkanov A.A. Granichnye zadachi dlya kvantovogo fermi gaza Teor. i matem. fizika. 2001. T. 129. No. 3.
20. Latyshev A.V., YUshkanov A.A. Novyi metod resheniya granichnykh zadach kineticheskoi teorii ZH. vychisl. matem. i matem. fiziki. 2012. T. 52. No. 3.

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