The interaction of the asymmetrical screw flows for the Bryan-Pidduck model |
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Author |
gordevskyy2006@gmail.com1, hukalov@ilt.kharkov.ua2
1) V.N. Karazin Kharkiv National University
Kharkiv, Ukraine; 2) B.Verkin Institute for Low Temperature Physics
and Engineering, Kharkiv, Ukraine
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Abstract |
Some approximate solutions of the Boltzmann equation for a model of rough spheres are
constructed. Several sufficient conditions which minimize the uniform-integral error between
parts of the Bryan-Pidduck equation are obtained.
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Keywords |
the Bryan-Pidduck equation; bimodal distribution; uniform-integral error
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DOI |
doi:10.15330/ms.50.2.173-188
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Reference |
1. S. Chapman, T.G. Cowling, The mathematical theory of non-uniform gases, Cambridge Univ. Press,
Cambridge, 1952.
2. G.H. Bryan, On the application of the determinantal relation to the kinetic theory of polyatomic gases, Rept. Brit. Assoc. Adv. Sci., 64 (1894), 102–106. 3. F.B. Pidduck, The kinetic theory of a special type of rigid molecule, Proc. Roy. Soc., A101 (1922), 101–110. 4. C. Cercignani, M. Lampis, On the kinetic theory of a dense gas of rough spheres, J. Statist. Phys., 53 (1988), 655–672. 5. V.D. Gordevskyy, Explicit approximate solutions of the Boltzmann equation for the model of rough spheres, Reports of the National Academy of Sciences of Ukraine, 4 (2000), 10–13. (in Ukrainian) 6. V.D. Gordevskyy, Approximate billow solutions of the kinetic Bryan-Pidduck equation, Math. Meth. Appl. Sci., 23 (2000), 1121–1137. 7. V.D. Gordevskii, A.A. Gukalov Interaction of locally Maxwellian flows in the model of rough spheres, Theor. Math. Phys, 176 (2013), ¹2, 322–336. (in Russian) 8. V.D. Gordevskyy, A.A. Gukalov, Interaction of the eddy flows in the Bryan–Pidduck model, Vysnik Kharkiv Univ., Ser. Mat. Prykl. Mat. Mech., 64 (2011), ¹2, 27–41. (in Russian) 9. V.D. Gordevskyy, A.A. Gukalov, Maxwell distributions in a model of rough spheres, Ukr. Mat. Zh., 63 (2011), ¹5, 629–639. (in Russian) 10. V.D. Gordevskyy, E.S. Sazonova Asymmetrical bimodal distributions with screw modes, Math. Phys., Anal., Geom., 3 (2011), V.7, 212–224. 11. C. Cercignani, Theory and Application of the Boltzmann Equation, Elsevier, New York, 1975. |
Pages |
173-188
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Volume |
50
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Issue |
2
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Year |
2018
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Journal |
Matematychni Studii
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Full text of paper | |
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