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Gain of integrability for the Boltzmann collisional operator
A hierarchy of models related to nanoflows and surface diffusion
1. | Department of Mechanical Engineering and Science, Graduate School of Engineering, Kyoto University, Kyoto 606-8501 |
2. | Institut de Mathméatiques de Bordeaux, ENSEIRB-MATMECA, IPB, Université de Bordeaux, F-33405 Talence cedex, France |
3. | 1-Université de Toulouse; UPS, INSA, UT1, UTM, Institut de Mathématiques de Toulouse, F-31062 Toulouse, France |
References:
[1] |
K. Aoki and P. Degond, Homogenization of a flow in a periodic channel of small section, Multiscale Model. Simul., 1 (2003), 304-334.
doi: 10.1137/S1540345902409931. |
[2] |
K. Aoki, P. Degond, S. Takata and H. Yoshida, Diffusion models for Knudsen compressors, Phys. Fluids, 19 (2007), 117103: 1-20. |
[3] |
J. J. M. Beenakker, Reduced dimensionality in gases in nanopores, Phys. Low-Dim. Struct., 10/11 (1995), 115-124. |
[4] |
J. J. M. Beenakker and S. Yu. Krylov, One-dimensional surface diffusion: density dependence in a smooth potential, J. Chem. Phys., 107 (1997), 4015-4023.
doi: 10.1063/1.474757. |
[5] |
J. J. M. Beenakker, V. D. Borman and S. Yu. Krylov, Molecular transport in the nanometer regime, Phys. Rev. Lett., 72 (1994), 514-517.
doi: 10.1103/PhysRevLett.72.514. |
[6] |
J. J. M. Beenakker, V. D. Borman and S. U. Krylov, Molecular transport in subnanometer pores: Zero-point energy, reduced dimensionality and quantum sieving, Chem. Phys. Letters, 232 (1995), 379-382.
doi: 10.1016/0009-2614(94)01372-3. |
[7] |
V. D. Borman, S. Yu. Krylov and A. V. Prosyanov, Theory of nonequilibrium phenomena at a gas-solid interface, Sov. Phys. JETP, 67 (1988), 2110-2121. |
[8] |
V. D. Borman, S. Yu. Krylov and A. V. Prosyanov, Fundamental role of unbound surface particles in transport phenomena along a gas-solid interface, Sov. Phys. JETP, 70 (1990), 1013-1022. |
[9] |
P. Charrier and B. Dubroca, Asymptotic transport models for heat and mass transfer in reactive porous media, Multiscale Model. Simul., 2 (2003), 124-157.
doi: 10.1137/S1540345902411736. |
[10] |
P. Degond, Transport of trapped particles in a surface potential, in "Nonlinear Partial Differential Equations and Their Applications," Collège de France Seminar, North Holland, XIV (2002), 273-296. |
[11] |
P. Degond, C. Parzani and M.-H. Vignal, A Boltzmann model for trapped particles in a surface potential, Multiscale Model. Simul., 5 (2006), 364-392.
doi: 10.1137/050642897. |
[12] |
E. Frenod and K. Hamdache, Homogenisation of transport kinetic equations with oscillating potentials, Proceedings of the Royal Society of Edinburgh A, 126 (1996), 1247-1275. |
[13] |
J. K. Holt, H. G. Park, Y. Wang, M. Stadermann, A. B. Artyukhin, C. P. Grigoropoulos, A. Noy and O. Bakajin, Fast mass transport sub-2-nanometer carbon nanotubes, Science, 312 (2006), 1034-1037.
doi: 10.1126/science.1126298. |
[14] |
G. Karniadakis, A. Beskok and N. Aluru, "Microflows and Nanoflows," Springer-Verlag, 2005. |
[15] |
S. Yu. Krylov, A. V. Prosyanov and J. J. M. Beenakker, One dimensional surface diffusion. II. Density dependence in a corrugated potential, J. Chem. Phys., 107 (1997), 6970-6979.
doi: 10.1063/1.474937. |
[16] |
S. Yu. Krylov, Molecular transport in sub-nano-scale systems, in "Rarefied Gas Dynamics,'' A. D. Ketsdever and E. P. Muntz (eds.), Am. Inst. Phys., (2002). |
[17] |
Y. Sone, "Kinetic Theory and Fluid Dynamics," Birkäuser, 2002. |
[18] |
Y. Sone, "Molecular Gas Dynamics: Theory, Techniques, and Applications," Birkäuser, 2007. |
show all references
References:
[1] |
K. Aoki and P. Degond, Homogenization of a flow in a periodic channel of small section, Multiscale Model. Simul., 1 (2003), 304-334.
doi: 10.1137/S1540345902409931. |
[2] |
K. Aoki, P. Degond, S. Takata and H. Yoshida, Diffusion models for Knudsen compressors, Phys. Fluids, 19 (2007), 117103: 1-20. |
[3] |
J. J. M. Beenakker, Reduced dimensionality in gases in nanopores, Phys. Low-Dim. Struct., 10/11 (1995), 115-124. |
[4] |
J. J. M. Beenakker and S. Yu. Krylov, One-dimensional surface diffusion: density dependence in a smooth potential, J. Chem. Phys., 107 (1997), 4015-4023.
doi: 10.1063/1.474757. |
[5] |
J. J. M. Beenakker, V. D. Borman and S. Yu. Krylov, Molecular transport in the nanometer regime, Phys. Rev. Lett., 72 (1994), 514-517.
doi: 10.1103/PhysRevLett.72.514. |
[6] |
J. J. M. Beenakker, V. D. Borman and S. U. Krylov, Molecular transport in subnanometer pores: Zero-point energy, reduced dimensionality and quantum sieving, Chem. Phys. Letters, 232 (1995), 379-382.
doi: 10.1016/0009-2614(94)01372-3. |
[7] |
V. D. Borman, S. Yu. Krylov and A. V. Prosyanov, Theory of nonequilibrium phenomena at a gas-solid interface, Sov. Phys. JETP, 67 (1988), 2110-2121. |
[8] |
V. D. Borman, S. Yu. Krylov and A. V. Prosyanov, Fundamental role of unbound surface particles in transport phenomena along a gas-solid interface, Sov. Phys. JETP, 70 (1990), 1013-1022. |
[9] |
P. Charrier and B. Dubroca, Asymptotic transport models for heat and mass transfer in reactive porous media, Multiscale Model. Simul., 2 (2003), 124-157.
doi: 10.1137/S1540345902411736. |
[10] |
P. Degond, Transport of trapped particles in a surface potential, in "Nonlinear Partial Differential Equations and Their Applications," Collège de France Seminar, North Holland, XIV (2002), 273-296. |
[11] |
P. Degond, C. Parzani and M.-H. Vignal, A Boltzmann model for trapped particles in a surface potential, Multiscale Model. Simul., 5 (2006), 364-392.
doi: 10.1137/050642897. |
[12] |
E. Frenod and K. Hamdache, Homogenisation of transport kinetic equations with oscillating potentials, Proceedings of the Royal Society of Edinburgh A, 126 (1996), 1247-1275. |
[13] |
J. K. Holt, H. G. Park, Y. Wang, M. Stadermann, A. B. Artyukhin, C. P. Grigoropoulos, A. Noy and O. Bakajin, Fast mass transport sub-2-nanometer carbon nanotubes, Science, 312 (2006), 1034-1037.
doi: 10.1126/science.1126298. |
[14] |
G. Karniadakis, A. Beskok and N. Aluru, "Microflows and Nanoflows," Springer-Verlag, 2005. |
[15] |
S. Yu. Krylov, A. V. Prosyanov and J. J. M. Beenakker, One dimensional surface diffusion. II. Density dependence in a corrugated potential, J. Chem. Phys., 107 (1997), 6970-6979.
doi: 10.1063/1.474937. |
[16] |
S. Yu. Krylov, Molecular transport in sub-nano-scale systems, in "Rarefied Gas Dynamics,'' A. D. Ketsdever and E. P. Muntz (eds.), Am. Inst. Phys., (2002). |
[17] |
Y. Sone, "Kinetic Theory and Fluid Dynamics," Birkäuser, 2002. |
[18] |
Y. Sone, "Molecular Gas Dynamics: Theory, Techniques, and Applications," Birkäuser, 2007. |
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