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Gas-surface interaction and boundary conditions for the Boltzmann equation
1. | Institut de Mathématiques de Bordeaux, ENSEIRB-MATMECA, IPB, Université de Bordeaux, F-33405 Talence cedex, France, France |
2. | Institut de Mathméatiques de Bordeaux, ENSEIRB-MATMECA, IPB, Université de Bordeaux, F-33405 Talence cedex |
References:
[1] |
K. Aoki, P. Charrier and P. Degond, A hierarchy of models related to nanoflows and surface diffusion,, Kinetic and Related Models, 4 (2011), 53.
doi: 10.3934/krm.2011.4.53. |
[2] |
K. Aoki and P. Degond, Homogenization of a flow in a periodic channel of small section,, Multiscale Model. Simul., 1 (2003).
doi: 10.1137/S1540345902409931. |
[3] |
K. Aoki, P. Degond, S. Takata and H. Yoshida, Diffusion models for Knudsen compressors,, Phys. Fluids, 19 (2007).
doi: 10.1063/1.2798748. |
[4] |
G. Arya, H.-C. Chang and E. Magin, Knudsen Diffusivity of a Hard Sphere in a Rough Slit Pore,, Phys. Rev. Lett., 91 (2003).
doi: 10.1103/PhysRevLett.91.026102. |
[5] |
H. Babovsky, Derivation of stochastic reflection laws from specular reflection,, Trans. Th. and Stat. Phys., 16 (1987), 113.
doi: 10.1080/00411458708204299. |
[6] |
J. J. M. Beenakker, Reduced Dimensionality in Gases in Nanopores,, Phys. Low-Dim. Struct., (1995), 115. Google Scholar |
[7] |
J. J. M. Beenakker, V. D. Borman and S. Yu Krylov, Molecular Transport in the Nanometer Regime,, Phys. Rev. Lett., 72 (1994).
doi: 10.1103/PhysRevLett.72.514. |
[8] |
J. J. M. Beenakker, V. D. Borman and S. Yu. Krylov1, Molecular transport in subnanometer pores: Zero-point energy, reduced dimensionality and quantum sieving,, Chem. Phys. Letters, 232 (1995), 379.
doi: 10.1016/0009-2614(94)01372-3. |
[9] |
J. J. M. Beenakker and S. Yu. Krylov, One-dimensional surface diffusion: Density dependence in a smooth potential,, J. Chem. Phys., 107 (1997).
doi: 10.1063/1.474757. |
[10] |
V. D. Borman, S. Yu. Krylov and A. V. Prosyanov, Theory of nonequilibrium phenomena at a gas-solid interface,, Sov. Phys. JETP, 67 (1988). Google Scholar |
[11] |
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). Google Scholar |
[12] |
F. Celestini and F. Mortessagne, The cosine law at the atomic scale: Toward realistic simulations of Knudsen diffusion,, Phys.Rev. E, 77 (2008).
doi: 10.1103/PhysRevE.77.021202. |
[13] |
C. Cercignani, The Boltzman Equation and Its Applications,, Springer, (1988).
doi: 10.1007/978-1-4612-1039-9. |
[14] |
C. Cercignani, Scattering kernels for gas-surface interactions,, Transp. Th. and Stat. Phys., 2 (1972), 27. Google Scholar |
[15] |
C. Cercignani, Scattering kernels for gas-surface interaction,, Proceedings of the Workshop on Hypersonic Flows for Reentry Problems, I (1990), 9. Google Scholar |
[16] |
C. Cercignani, R. Illner and M. Pulvirenti, The Mathematical Theory of Dilute Gases,, Springer: New York, (1994), 133.
|
[17] |
C. Cercignani and M. Lampis, Kinetic models for gas-surface interactions,, Transp. Th. and Stat. Phys., 1 (1971), 101.
doi: 10.1080/00411457108231440. |
[18] |
C. Cercignani, M. Lampis and A. Lentati, A new scattering kernel in kinetic theory of gases,, Trans. Theory Statist. Phys., 24 (1995), 1319.
doi: 10.1080/00411459508206026. |
[19] |
S. Chandrasekhar, Radiative Transfer,, Dover Publications, (1960).
|
[20] |
P. Charrier and B. Dubroca, Asymptotic transport models for heat and mass transfer in reactive porous media,, Multiscale Model. Simul., 2 (2003).
doi: 10.1137/S1540345902411736. |
[21] |
F. Coron, F. Golse and C. Sulem, A classification of well-posed kinetic layer problems,, Commun. Pure Appl. Math., 41 (1988).
doi: 10.1002/cpa.3160410403. |
[22] |
P. Degond, Transport of trapped particles in a surface potential,, in Nonlinear Partial Differential Equations and Their Applications, XIV (2002), 273.
doi: 10.1016/S0168-2024(02)80014-5. |
[23] |
P. Degond and S. Mas-Gallic, Existence of solutions and diffusion approximation for a model Fokker-Planck equation,, Transport Theory Statist. Phys., 16 (1987), 589.
doi: 10.1080/00411458708204307. |
[24] |
P. Degond, C. Parzani and M.-H. Vignal, A Boltzmann Model for Trapped Particles in a Surface Potential,, SIAM J. Multiscale model. Simul., 5 (2006), 364.
doi: 10.1137/050642897. |
[25] |
L. Falk, Existence of solutions to the stationary linear boltzmann equation,, Transport Theory and Statistical Physics, 32 (2003), 37.
doi: 10.1081/TT-120018651. |
[26] |
F. Golse, Knudsen layers from a computational viewpoint,, Transport Theory Statist. Phys., 21 (1992), 211.
doi: 10.1080/00411459208203921. |
[27] |
F. Golse and A. Klar, A numerical method for computing asymptotic states and outgoing distributions for kinetic linear Half-Space problems,, J. of Sta. Physics, 80 (1995).
doi: 10.1007/BF02179863. |
[28] |
G. Karniadakis, A. Beskok and N. Aluru, Microflows and Nanoflows,, Springer, (2005).
|
[29] |
A. Klar, Asymptotic-induced domain decomposition methods for kinetic and drift-diffusion equations,, SIAM J. Sci. Comput., 19 (1998), 2032.
doi: 10.1137/S1064827595286177. |
[30] |
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).
doi: 10.1063/1.474937. |
[31] |
S. Yu Krylov, Molecular transport in Sub-Nano-Scale systems,, RGD, 663 (2003).
doi: 10.1063/1.1581616. |
[32] |
J. C. Maxwell, On stresses in rarefied gases arising from inequalities of temperature,, Phil. Trans. Royal Soc., (1879), 231. Google Scholar |
[33] |
F. Poupaud, Diffusion approximation of the linear semiconductor Boltzmann equation: Analysis of boundary layers,, Asymptotic Anal., 4 (1991), 293.
|
[34] |
Y. Sone, Kinetic Theory and Fluid Dynamics,, Birkäuser, (2002).
doi: 10.1007/978-1-4612-0061-1. |
[35] |
Y. Sone, Molecular Gas Dynamics,, Birkäuser, (2007).
doi: 10.1007/978-0-8176-4573-1. |
[36] |
H. Struchtrup, Maxwell boundary condition and velocity dependent accommodation coefficients,, Phys. Fluids, 25 (2013).
doi: 10.1063/1.4829907. |
show all references
References:
[1] |
K. Aoki, P. Charrier and P. Degond, A hierarchy of models related to nanoflows and surface diffusion,, Kinetic and Related Models, 4 (2011), 53.
doi: 10.3934/krm.2011.4.53. |
[2] |
K. Aoki and P. Degond, Homogenization of a flow in a periodic channel of small section,, Multiscale Model. Simul., 1 (2003).
doi: 10.1137/S1540345902409931. |
[3] |
K. Aoki, P. Degond, S. Takata and H. Yoshida, Diffusion models for Knudsen compressors,, Phys. Fluids, 19 (2007).
doi: 10.1063/1.2798748. |
[4] |
G. Arya, H.-C. Chang and E. Magin, Knudsen Diffusivity of a Hard Sphere in a Rough Slit Pore,, Phys. Rev. Lett., 91 (2003).
doi: 10.1103/PhysRevLett.91.026102. |
[5] |
H. Babovsky, Derivation of stochastic reflection laws from specular reflection,, Trans. Th. and Stat. Phys., 16 (1987), 113.
doi: 10.1080/00411458708204299. |
[6] |
J. J. M. Beenakker, Reduced Dimensionality in Gases in Nanopores,, Phys. Low-Dim. Struct., (1995), 115. Google Scholar |
[7] |
J. J. M. Beenakker, V. D. Borman and S. Yu Krylov, Molecular Transport in the Nanometer Regime,, Phys. Rev. Lett., 72 (1994).
doi: 10.1103/PhysRevLett.72.514. |
[8] |
J. J. M. Beenakker, V. D. Borman and S. Yu. Krylov1, Molecular transport in subnanometer pores: Zero-point energy, reduced dimensionality and quantum sieving,, Chem. Phys. Letters, 232 (1995), 379.
doi: 10.1016/0009-2614(94)01372-3. |
[9] |
J. J. M. Beenakker and S. Yu. Krylov, One-dimensional surface diffusion: Density dependence in a smooth potential,, J. Chem. Phys., 107 (1997).
doi: 10.1063/1.474757. |
[10] |
V. D. Borman, S. Yu. Krylov and A. V. Prosyanov, Theory of nonequilibrium phenomena at a gas-solid interface,, Sov. Phys. JETP, 67 (1988). Google Scholar |
[11] |
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). Google Scholar |
[12] |
F. Celestini and F. Mortessagne, The cosine law at the atomic scale: Toward realistic simulations of Knudsen diffusion,, Phys.Rev. E, 77 (2008).
doi: 10.1103/PhysRevE.77.021202. |
[13] |
C. Cercignani, The Boltzman Equation and Its Applications,, Springer, (1988).
doi: 10.1007/978-1-4612-1039-9. |
[14] |
C. Cercignani, Scattering kernels for gas-surface interactions,, Transp. Th. and Stat. Phys., 2 (1972), 27. Google Scholar |
[15] |
C. Cercignani, Scattering kernels for gas-surface interaction,, Proceedings of the Workshop on Hypersonic Flows for Reentry Problems, I (1990), 9. Google Scholar |
[16] |
C. Cercignani, R. Illner and M. Pulvirenti, The Mathematical Theory of Dilute Gases,, Springer: New York, (1994), 133.
|
[17] |
C. Cercignani and M. Lampis, Kinetic models for gas-surface interactions,, Transp. Th. and Stat. Phys., 1 (1971), 101.
doi: 10.1080/00411457108231440. |
[18] |
C. Cercignani, M. Lampis and A. Lentati, A new scattering kernel in kinetic theory of gases,, Trans. Theory Statist. Phys., 24 (1995), 1319.
doi: 10.1080/00411459508206026. |
[19] |
S. Chandrasekhar, Radiative Transfer,, Dover Publications, (1960).
|
[20] |
P. Charrier and B. Dubroca, Asymptotic transport models for heat and mass transfer in reactive porous media,, Multiscale Model. Simul., 2 (2003).
doi: 10.1137/S1540345902411736. |
[21] |
F. Coron, F. Golse and C. Sulem, A classification of well-posed kinetic layer problems,, Commun. Pure Appl. Math., 41 (1988).
doi: 10.1002/cpa.3160410403. |
[22] |
P. Degond, Transport of trapped particles in a surface potential,, in Nonlinear Partial Differential Equations and Their Applications, XIV (2002), 273.
doi: 10.1016/S0168-2024(02)80014-5. |
[23] |
P. Degond and S. Mas-Gallic, Existence of solutions and diffusion approximation for a model Fokker-Planck equation,, Transport Theory Statist. Phys., 16 (1987), 589.
doi: 10.1080/00411458708204307. |
[24] |
P. Degond, C. Parzani and M.-H. Vignal, A Boltzmann Model for Trapped Particles in a Surface Potential,, SIAM J. Multiscale model. Simul., 5 (2006), 364.
doi: 10.1137/050642897. |
[25] |
L. Falk, Existence of solutions to the stationary linear boltzmann equation,, Transport Theory and Statistical Physics, 32 (2003), 37.
doi: 10.1081/TT-120018651. |
[26] |
F. Golse, Knudsen layers from a computational viewpoint,, Transport Theory Statist. Phys., 21 (1992), 211.
doi: 10.1080/00411459208203921. |
[27] |
F. Golse and A. Klar, A numerical method for computing asymptotic states and outgoing distributions for kinetic linear Half-Space problems,, J. of Sta. Physics, 80 (1995).
doi: 10.1007/BF02179863. |
[28] |
G. Karniadakis, A. Beskok and N. Aluru, Microflows and Nanoflows,, Springer, (2005).
|
[29] |
A. Klar, Asymptotic-induced domain decomposition methods for kinetic and drift-diffusion equations,, SIAM J. Sci. Comput., 19 (1998), 2032.
doi: 10.1137/S1064827595286177. |
[30] |
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).
doi: 10.1063/1.474937. |
[31] |
S. Yu Krylov, Molecular transport in Sub-Nano-Scale systems,, RGD, 663 (2003).
doi: 10.1063/1.1581616. |
[32] |
J. C. Maxwell, On stresses in rarefied gases arising from inequalities of temperature,, Phil. Trans. Royal Soc., (1879), 231. Google Scholar |
[33] |
F. Poupaud, Diffusion approximation of the linear semiconductor Boltzmann equation: Analysis of boundary layers,, Asymptotic Anal., 4 (1991), 293.
|
[34] |
Y. Sone, Kinetic Theory and Fluid Dynamics,, Birkäuser, (2002).
doi: 10.1007/978-1-4612-0061-1. |
[35] |
Y. Sone, Molecular Gas Dynamics,, Birkäuser, (2007).
doi: 10.1007/978-0-8176-4573-1. |
[36] |
H. Struchtrup, Maxwell boundary condition and velocity dependent accommodation coefficients,, Phys. Fluids, 25 (2013).
doi: 10.1063/1.4829907. |
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