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Non-existence and non-uniqueness for multidimensional sticky particle systems
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), 53-85.
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), 304–-334, (electronic).
doi: 10.1137/S1540345902409931. |
[3] |
K. Aoki, P. Degond, S. Takata and H. Yoshida, Diffusion models for Knudsen compressors, Phys. Fluids, 19 (2007), 117103.
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), 026102.
doi: 10.1103/PhysRevLett.91.026102. |
[5] |
H. Babovsky, Derivation of stochastic reflection laws from specular reflection, Trans. Th. and Stat. Phys., 16 (1987), 113-126.
doi: 10.1080/00411458708204299. |
[6] |
J. J. M. Beenakker, Reduced Dimensionality in Gases in Nanopores, Phys. Low-Dim. Struct., (1995), 115-124. |
[7] |
J. J. M. Beenakker, V. D. Borman and S. Yu Krylov, Molecular Transport in the Nanometer Regime, Phys. Rev. Lett., 72 (1994), 514.
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), 379-382.
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), 4015.
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). |
[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). |
[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, Berlin, 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), 27-53. |
[15] |
C. Cercignani, Scattering kernels for gas-surface interaction, Proceedings of the Workshop on Hypersonic Flows for Reentry Problems, I (1990), 9-29, INRIA Antibes. |
[16] |
C. Cercignani, R. Illner and M. Pulvirenti, The Mathematical Theory of Dilute Gases, Springer: New York, 1994, 133-163. |
[17] |
C. Cercignani and M. Lampis, Kinetic models for gas-surface interactions, Transp. Th. and Stat. Phys., 1 (1971), 101-114.
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), 1319-1336.
doi: 10.1080/00411459508206026. |
[19] |
S. Chandrasekhar, Radiative Transfer, Dover Publications, Inc., New York, 1960 |
[20] |
P. Charrier and B. Dubroca, Asymptotic transport models for heat and mass transfer in reactive porous media, Multiscale Model. Simul., 2 (2003), 124–-157 (electronic).
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), 409–-435.
doi: 10.1002/cpa.3160410403. |
[22] |
P. Degond, Transport of trapped particles in a surface potential, in Nonlinear Partial Differential Equations and Their Applications, Collége de France Seminar, XIV (1997/1998), Stud. Math. Appl. 31, North Holland, Amsterdam, (2002), 273-296.
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), 589-636.
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), 364-392.
doi: 10.1137/050642897. |
[25] |
L. Falk, Existence of solutions to the stationary linear boltzmann equation, Transport Theory and Statistical Physics, 32 (2003), 37-62.
doi: 10.1081/TT-120018651. |
[26] |
F. Golse, Knudsen layers from a computational viewpoint, Transport Theory Statist. Phys., 21 (1992), 211-236.
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), 1033–-1061.
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), 2032-2050.
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), 735.
doi: 10.1063/1.1581616. |
[32] |
J. C. Maxwell, On stresses in rarefied gases arising from inequalities of temperature, Phil. Trans. Royal Soc., Appendix (1879), 231-256. |
[33] |
F. Poupaud, Diffusion approximation of the linear semiconductor Boltzmann equation: Analysis of boundary layers, Asymptotic Anal., 4 (1991), 293-317. |
[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), 112001.
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), 53-85.
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), 304–-334, (electronic).
doi: 10.1137/S1540345902409931. |
[3] |
K. Aoki, P. Degond, S. Takata and H. Yoshida, Diffusion models for Knudsen compressors, Phys. Fluids, 19 (2007), 117103.
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), 026102.
doi: 10.1103/PhysRevLett.91.026102. |
[5] |
H. Babovsky, Derivation of stochastic reflection laws from specular reflection, Trans. Th. and Stat. Phys., 16 (1987), 113-126.
doi: 10.1080/00411458708204299. |
[6] |
J. J. M. Beenakker, Reduced Dimensionality in Gases in Nanopores, Phys. Low-Dim. Struct., (1995), 115-124. |
[7] |
J. J. M. Beenakker, V. D. Borman and S. Yu Krylov, Molecular Transport in the Nanometer Regime, Phys. Rev. Lett., 72 (1994), 514.
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), 379-382.
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), 4015.
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). |
[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). |
[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, Berlin, 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), 27-53. |
[15] |
C. Cercignani, Scattering kernels for gas-surface interaction, Proceedings of the Workshop on Hypersonic Flows for Reentry Problems, I (1990), 9-29, INRIA Antibes. |
[16] |
C. Cercignani, R. Illner and M. Pulvirenti, The Mathematical Theory of Dilute Gases, Springer: New York, 1994, 133-163. |
[17] |
C. Cercignani and M. Lampis, Kinetic models for gas-surface interactions, Transp. Th. and Stat. Phys., 1 (1971), 101-114.
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), 1319-1336.
doi: 10.1080/00411459508206026. |
[19] |
S. Chandrasekhar, Radiative Transfer, Dover Publications, Inc., New York, 1960 |
[20] |
P. Charrier and B. Dubroca, Asymptotic transport models for heat and mass transfer in reactive porous media, Multiscale Model. Simul., 2 (2003), 124–-157 (electronic).
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), 409–-435.
doi: 10.1002/cpa.3160410403. |
[22] |
P. Degond, Transport of trapped particles in a surface potential, in Nonlinear Partial Differential Equations and Their Applications, Collége de France Seminar, XIV (1997/1998), Stud. Math. Appl. 31, North Holland, Amsterdam, (2002), 273-296.
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), 589-636.
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), 364-392.
doi: 10.1137/050642897. |
[25] |
L. Falk, Existence of solutions to the stationary linear boltzmann equation, Transport Theory and Statistical Physics, 32 (2003), 37-62.
doi: 10.1081/TT-120018651. |
[26] |
F. Golse, Knudsen layers from a computational viewpoint, Transport Theory Statist. Phys., 21 (1992), 211-236.
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), 1033–-1061.
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), 2032-2050.
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), 735.
doi: 10.1063/1.1581616. |
[32] |
J. C. Maxwell, On stresses in rarefied gases arising from inequalities of temperature, Phil. Trans. Royal Soc., Appendix (1879), 231-256. |
[33] |
F. Poupaud, Diffusion approximation of the linear semiconductor Boltzmann equation: Analysis of boundary layers, Asymptotic Anal., 4 (1991), 293-317. |
[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), 112001.
doi: 10.1063/1.4829907. |
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