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Thermodynamical considerations implying wall/particles scattering kernels
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References:
[1] |
K. Aoki and F. Golse, On the speed of approach to equilibrium for collisionless gas, Kinet. Relat. Models, 4 (2011), 87-107.
doi: 10.3934/krm.2011.4.87. |
[2] |
W. Arendt, Positive semigroups of Kernel operators, Positivity, 12 (2008), 25-44.
doi: 10.1007/s11117-007-2137-z. |
[3] |
L. Arkeryd and A. Nouri, Boltzmann asymptotics with diffuse reflection boundary conditions, Monatsh. Math., 123 (1997), 285-298.
doi: 10.1007/BF01326764. |
[4] |
V. Bagland, P. Degond and M. Lemou, Moment systems derived from relativistic kinetic equations, J. Stat. Phys., 125 (2006), 621-659.
doi: 10.1007/s10955-006-9173-0. |
[5] |
J. Banasiak and L. Arlotti, Perturbations of Positive Semigroups With Applications, Springer Monographs in Mathematics, Springer-Verlag London, Ltd., London, 2006. |
[6] |
C. Cercignani, Slow Rarefied Flows. Theory and Application to Micro-Electro-Mechanical Systems, Progress in Mathematical Physics, 41, Birkhäuser Verlag, Basel, 2006. |
[7] |
C. Cercignani, The Boltzmann Equation and its Application, Applied Mathematical Sciences, 67, Springer-Verlag, New York, 1988.
doi: 10.1007/978-1-4612-1039-9. |
[8] |
S. K. Diadze and J. G. Méolans, Temperature jump and slip velocity calculations from an anisotropic scattering kernel, Physica A, 358 (2005), 328-346.
doi: 10.1016/j.physa.2005.04.013. |
[9] |
V. Keicher, Convergence of Positive $C_0$-Semigroups to Rotation Groups, Ph.D thesis, Eberhard Karls Universität Tübingen, 2008. |
[10] |
I. Kuscer, Reciprocity in scattering of gas molecules by surfaces, Surface Science, 25 (1971), 225-237. |
[11] |
J. Lebowitz and P. G. Bergmann, Irreversible Gibsian ensembles, Ann. Physics, 1 (1957), 1-23.
doi: 10.1016/0003-4916(57)90002-7. |
[12] |
C. D. Levermore, Moment closure hierarchies for kinetic theories, J. Statist. Phys., 83 (1996), 1021-1065.
doi: 10.1007/BF02179552. |
[13] |
C. Mouhot, Quantitative linearized study of the Boltzmann collision operator and applications, Commun. Math. Sci., 2007, 73-86.
doi: 10.4310/CMS.2007.v5.n5.a6. |
[14] |
B.-S. Tam, A cone theoretic approach to the spectral theory of positive linear operators: The finite dimensional case, Tawainese J. Math., 5 (2001), 207-277. |
[15] |
H. Yamaguchi, K. Anazawa, Y. Matsuda, T. Niimi, A. Polikarpov and I. Graur, Investigation of heat transfer between two coaxial cylinders for measurement of thermal accomodation coefficient, Physics of Fluids, 24 (2012), 062002.
doi: 10.1063/1.4726059. |
show all references
References:
[1] |
K. Aoki and F. Golse, On the speed of approach to equilibrium for collisionless gas, Kinet. Relat. Models, 4 (2011), 87-107.
doi: 10.3934/krm.2011.4.87. |
[2] |
W. Arendt, Positive semigroups of Kernel operators, Positivity, 12 (2008), 25-44.
doi: 10.1007/s11117-007-2137-z. |
[3] |
L. Arkeryd and A. Nouri, Boltzmann asymptotics with diffuse reflection boundary conditions, Monatsh. Math., 123 (1997), 285-298.
doi: 10.1007/BF01326764. |
[4] |
V. Bagland, P. Degond and M. Lemou, Moment systems derived from relativistic kinetic equations, J. Stat. Phys., 125 (2006), 621-659.
doi: 10.1007/s10955-006-9173-0. |
[5] |
J. Banasiak and L. Arlotti, Perturbations of Positive Semigroups With Applications, Springer Monographs in Mathematics, Springer-Verlag London, Ltd., London, 2006. |
[6] |
C. Cercignani, Slow Rarefied Flows. Theory and Application to Micro-Electro-Mechanical Systems, Progress in Mathematical Physics, 41, Birkhäuser Verlag, Basel, 2006. |
[7] |
C. Cercignani, The Boltzmann Equation and its Application, Applied Mathematical Sciences, 67, Springer-Verlag, New York, 1988.
doi: 10.1007/978-1-4612-1039-9. |
[8] |
S. K. Diadze and J. G. Méolans, Temperature jump and slip velocity calculations from an anisotropic scattering kernel, Physica A, 358 (2005), 328-346.
doi: 10.1016/j.physa.2005.04.013. |
[9] |
V. Keicher, Convergence of Positive $C_0$-Semigroups to Rotation Groups, Ph.D thesis, Eberhard Karls Universität Tübingen, 2008. |
[10] |
I. Kuscer, Reciprocity in scattering of gas molecules by surfaces, Surface Science, 25 (1971), 225-237. |
[11] |
J. Lebowitz and P. G. Bergmann, Irreversible Gibsian ensembles, Ann. Physics, 1 (1957), 1-23.
doi: 10.1016/0003-4916(57)90002-7. |
[12] |
C. D. Levermore, Moment closure hierarchies for kinetic theories, J. Statist. Phys., 83 (1996), 1021-1065.
doi: 10.1007/BF02179552. |
[13] |
C. Mouhot, Quantitative linearized study of the Boltzmann collision operator and applications, Commun. Math. Sci., 2007, 73-86.
doi: 10.4310/CMS.2007.v5.n5.a6. |
[14] |
B.-S. Tam, A cone theoretic approach to the spectral theory of positive linear operators: The finite dimensional case, Tawainese J. Math., 5 (2001), 207-277. |
[15] |
H. Yamaguchi, K. Anazawa, Y. Matsuda, T. Niimi, A. Polikarpov and I. Graur, Investigation of heat transfer between two coaxial cylinders for measurement of thermal accomodation coefficient, Physics of Fluids, 24 (2012), 062002.
doi: 10.1063/1.4726059. |
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