# zbMATH — the first resource for mathematics

## Aoki, Kazuo

Compute Distance To:
 Author ID: aoki.kazuo Published as: Aoki, K.; Aoki, Kazuo
 Documents Indexed: 87 Publications since 1977, including 2 Books
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#### Co-Authors

 3 single-authored 26 Takata, Shigeru 25 Sone, Yoshio 8 Degond, Pierre 8 Kosuge, Shingo 7 Golse, François 7 Sugimoto, Hiroshi 6 Ohwada, Taku 6 Taguchi, Satoshi 5 Yoshida, Hiroaki 4 Bardos, Claude Williams 4 Tsuji, Tetsuro 4 Yasuda, Shugo 3 Cercignani, Carlo 3 Mieussens, Luc 2 Funagane, Hitoshi 2 Markowich, Peter Alexander 2 Nishino, Kenji 2 Pulvirenti, Mario 2 Waniguchi, Yorifumi 2 Yang, Tong 1 Abe, Yoshiaki 1 Aikawa, Hidefumi 1 Andries, Pierre 1 Baranger, Céline 1 Bi, Lifu 1 Bobylev, Alexandre Vasiljévitch 1 Cavallaro, Guido 1 Charrier, Pierre 1 Chi, Yaojun 1 Dogbé, Christian 1 Doi, Toshiyuki 1 Fan, Chun 1 Groppi, Maria 1 Hadjiconstantinou, Nicolas G. 1 Hatano, Masatake 1 Hattori, Masanari 1 Huang, Guowei 1 Hui, Tian 1 Illner, Reinhard 1 Inamuro, Takaji 1 Jüngel, Ansgar 1 Kagaya, Ryo 1 Kataoka, Takeshi 1 Kogan, Michail N. 1 Kono, Akihiro 1 Kugimoto, Ko 1 Kuo, Hung-Wen 1 Laneryd, Carl-Johan Tor 1 Latocha, Vladimir 1 Lin, Yu-Chu 1 Marchioro, Carlo 1 Martalò, Giorgio 1 Masukawa, Noboru 1 Mathiaud, Julien 1 Misumi, Junichi 1 Motohashi, Hideto 1 Onishi, Yoshimoto 1 Perthame, Benoît 1 Radtke, Gregg A. 1 Shibata, Takumi 1 Simonella, Sergio 1 Spiga, Giampiero 1 Sun, Juan 1 Tatsumi, Eri 1 Tomota, Tatsunori 1 Tritsch, V. 1 Wu, Kung-Chien 1 Yamada, Tatsuo 1 Yamashita, Ichiro 1 Yano, Takeru
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#### Serials

 20 Physics of Fluids 8 Journal of Statistical Physics 8 Physics of Fluids, A 7 Kinetic and Related Models 3 Journal of Fluid Mechanics 3 Transport Theory and Statistical Physics 3 Bulletin of the Institute of Mathematics. Academia Sinica. New Series 2 ZAMP. Zeitschrift für angewandte Mathematik und Physik 2 European Journal of Mechanics. B. Fluids 2 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 2 RIMS Kokyuroku 2 European Journal of Mechanics. B. Fluids 2 Multiscale Modeling & Simulation 1 Computers & Mathematics with Applications 1 Journal of Computational Physics 1 Physics of Fluids 1 Fluid Dynamics Research 1 Journal of Differential Equations 1 Journal de Mécanique Théorique et Appliquée 1 Journal of Applied Statistics 1 Journal of the Physical Society of Japan 1 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 1 Communications in Computational Physics 1 Bollettino dell’Unione Matematica Italiana. Series IX 1 Rivista di Matematica della Università di Parma. Serie 8 1 Séminaire Laurent Schwartz. EDP et Applications
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#### Fields

 74 Fluid mechanics (76-XX) 43 Statistical mechanics, structure of matter (82-XX) 12 Partial differential equations (35-XX) 8 Classical thermodynamics, heat transfer (80-XX) 5 Numerical analysis (65-XX) 4 General and overarching topics; collections (00-XX) 4 Integral equations (45-XX) 2 History and biography (01-XX) 1 Approximations and expansions (41-XX) 1 Functional analysis (46-XX) 1 Statistics (62-XX) 1 Mechanics of deformable solids (74-XX) 1 Quantum theory (81-XX) 1 Astronomy and astrophysics (85-XX)

#### Citations contained in zbMATH

69 Publications have been cited 884 times in 458 Documents Cited by Year
Numerical analysis of the Poiseuille and thermal transpiration flows between two parallel plates on the basis of the Boltzmann equation for hard-sphere molecules. Zbl 0696.76092
Ohwada, Taku; Sone, Yoshio; Aoki, Kazuo
1989
Numerical analysis of the shear and thermal creep flows of a rarefied gas over a plane wall on the basis of the linearized Boltzmann equation for hard-sphere molecules. Zbl 0695.76032
Ohwada, Taku; Sone, Yoshio; Aoki, Kazuo
1989
Temperature jump and Knudsen layer in a rarefied gas over a plane wall: Numerical analysis of the linearized Boltzmann equation for hard-sphere molecules. Zbl 0661.76082
Sone, Yoshio; Ohwada, Taku; Aoki, Kazuo
1989
A consistent BGK-type model for gas mixtures. Zbl 1001.82093
Andries, Pierre; Aoki, Kazuo; Perthame, Benoit
2002
Numerical analysis of a uniform flow of a rarefied gas past a sphere on the basis of the Boltzmann equation for hard-sphere molecules. Zbl 0806.76081
Takata, Shigeru; Sone, Yoshio; Aoki, Kazuo
1993
Numerical analysis of gas flows condensing on its plane condensed phase on the basis of kinetic theory. Zbl 0721.76085
Aoki, Kazuo; Sone, Yoshio; Yamada, Tatsuo
1990
Numerical analysis of steady flows of a gas condensing on or evaporating from its plane condensed phase on the basis of kinetic theory: Effect of gas motion along the condensed phase. Zbl 0825.76718
Aoki, Kazuo; Nishino, Kenji; Sone, Yoshio; Sugimoto, Hiroshi
1991
Inappropriateness of the heat-conduction equation for description of a temperature field of a stationary gas in the continuum limit: Examination by asymptotic analysis and numerical computation of the Boltzmann equation. Zbl 1027.76649
Sone, Yoshio; Aoki, Kazuo; Takata, Shigeru; Sugimoto, Hiroshi; Bobylev, A. V.
1996
Steady gas flows past bodies at small Knudsen numbers. Boltzmann and hydrodynamic systems. Zbl 0622.76082
Sone, Yoshio; Aoki, Kazuo
1987
Knudsen layer for gas mixtures. Zbl 1124.82314
Aoki, Kazuo; Bardos, Claude; Takata, Shigeru
2003
Evaporation and condensation on a plane condensed phase: Numerical analysis of the linearized Boltzmann equation for hard-sphere molecules. Zbl 0681.76077
Sone, Yoshio; Ohwada, Taku; Aoki, Kazuo
1989
Shock-wave structure for a binary gas mixture: Finite difference analysis of the Boltzmann equation for hard-sphere molecules. Zbl 0980.76078
Kosuge, Shingo; Aoki, Kazuo; Takata, Shigeru
2001
The ghost effect in the continuum limit for a vapor-gas mixture around condensed phases: asymptotic analysis of the Boltzmann equation. Zbl 1106.82359
Takata, Shigeru; Aoki, Kazuo
2001
Numerical analysis of thermal-slip and diffusion-slip flows of a binary mixture of hard-sphere molecular gases. Zbl 1186.76516
Takata, Shigeru; Yasuda, Shugo; Kosuge, Shingo; Aoki, Kazuo
2003
Kinetic theory analysis of gas flows condensing on a plane condensed phase: Case of a mixture of a vapor and a noncondensable gas. Zbl 0818.76087
Sone, Yoshio; Aoki, Kazuo; Doi, Toshiyuki
1992
On the motion of a body in thermal equilibrium immersed in a perfect gas. Zbl 1133.76046
Aoki, Kazuo; Cavallaro, Guido; Marchioro, Carlo; Pulvirenti, Mario
2008
On the speed of approach to equilibrium for a collisionless gas. Zbl 1218.82019
Aoki, Kazuo; Golse, François
2011
Two-surface problems of a multicomponent mixture of vapors and noncondensable gases in the continuum limit in the light of kinetic theory. Zbl 1149.76559
Takata, Shigeru; Aoki, Kazuo
1999
Vapor flows with evaporation and condensation in the continuum limit: Effect of a trace of noncondensable gas. Zbl 1175.76142
Aoki, Kazuo; Takata, Shigeru; Taguchi, Satoshi
2003
A rarefied gas flow caused by a discontinuous wall temperature. Zbl 1184.76033
Aoki, Kazuo; Takata, Shigeru; Aikawa, Hidefumi; Golse, François
2001
The Bénard problem for a rarefied gas: formation of steady flow patterns and stability of array of rolls. Zbl 1185.76871
Sone, Yoshio; Aoki, Kazuo; Sugimoto, Hiroshi
1997
Gas flows caused by evaporation and condensation on two parallel condensed phases and the negative temperature gradient: Numerical analysis by using a nonlinear kinetic equation. Zbl 0826.76081
Aoki, Kazuo; Masukawa, Noboru
1994
A study of unsteady strong condensation on a plane condensed phase with special interest in formation of steady profile. Zbl 0607.76100
Sone, Yoshio; Aoki, Kazuo; Yamashita, Ichiro
1986
One-way flow of a rarefied gas induced in a channel with a periodic temperature distribution. Zbl 1027.76650
Sone, Yoshio; Waniguchi, Yorifumi; Aoki, Kazuo
1996
The Bénard problem of rarefied gas dynamics. Zbl 0939.76579
Sone, Yoshio; Aoki, Kazuo; Sugimoto, Hiroshi; Motohashi, Hideto
1994
Diffusion models for Knudsen compressors. Zbl 1182.76027
Aoki, Kazuo; Degond, Pierre; Takata, Shigeru; Yoshida, Hiroaki
2007
A note on the propagation of boundary induced discontinuities in kinetic theory. Zbl 1012.82014
Aoki, Kazuo; Bardos, Claude; Dogbe, Christian; Golse, François
2001
Numerical simulations of rarefied gases in curved channels: thermal creep, circulating flow, and pumping effect. Zbl 1364.76168
Aoki, Kazuo; Degond, Pierre; Mieussens, Luc
2009
Numerical analysis of the shear flow of a binary mixture of hard-sphere gases over a plane wall. Zbl 1186.76586
Yasuda, Shugo; Takata, Shigeru; Aoki, Kazuo
2004
Vapor flows condensing at incidence onto a plane condensed phase in the presence of a noncondensable gas. I: Subsonic condensation. Zbl 1185.76362
Taguchi, Satoshi; Aoki, Kazuo; Takata, Shigeru
2003
Moving boundary problems for a rarefied gas: spatially one-dimensional case. Zbl 1349.82059
Tsuji, Tetsuro; Aoki, Kazuo
2013
Evaporation and condensation of a binary mixture of vapors on a plane condensed phase: numerical analysis of the linearized Boltzmann equation. Zbl 1187.76580
Yasuda, Shugo; Takata, Shigeru; Aoki, Kazuo
2005
Vapor flows condensing at incidence onto a plane condensed phase in the presence of a noncondensable gas. II: Supersonic condensation. Zbl 1186.76514
Taguchi, Satoshi; Aoki, Kazuo; Takata, Shigeru
2003
Homogenization of a flow in a periodic channel of small section. Zbl 1107.76060
Aoki, K.; Degond, P.
2003
Cylindrical couette flows of a rarefied gas with evaporation and condensation: Reversal and bifurcation of flows. Zbl 1147.76503
Sone, Yoshio; Sugimoto, Hiroshi; Aoki, Kazuo
1999
Numerical analysis of a flow induced in a rarefied gas between noncoaxial circular cylinders with different temperatures for the entire range of the Knudsen number. Zbl 0661.76079
Aoki, Kazuo; Sone, Yoshio; Yano, Takeru
1989
Slightly rarefied gas flow over a specularly reflecting body. Zbl 0356.76056
Sone, Yoshio; Aoki, Kazuo
1977
Relaxation of a free-molecular gas to equilibrium caused by interaction with Vessel wall. Zbl 1203.76134
Tsuji, Tetsuro; Aoki, Kazuo; Golse, François
2010
Various transport coefficients occurring in binary gas mixtures and their database. Zbl 1062.76591
Takata, Shigeru; Yasuda, Shugo; Aoki, Kazuo; Shibata, Takumi
2003
Decay of a linear pendulum in a free-molecular gas and in a special Lorentz gas. Zbl 1245.82066
Tsuji, Tetsuro; Aoki, Kazuo
2012
A numerical and experimental investigation of the modeling of microwave heating for liquid layers using a rectangular wave guide (effects of natural convection and dielectric properties). Zbl 1012.80004
Ratanadecho, P.; Aoki, K.; Akahori, M.
2002
Shock structure analysis in chemically reacting gas mixtures by a relaxation-time kinetic model. Zbl 1182.76290
Groppi, M.; Aoki, K.; Spiga, G.; Tritsch, V.
2008
Cylindrical Couette flow of a vapor-gas mixture: Ghost effect and bifurcation in the continuum limit. Zbl 1262.76041
Yoshida, Hiroaki; Aoki, Kazuo
2006
A technique for time-dependent boundary value problems in the kinetic theory of gases. I. Basic analysis. Zbl 0545.76078
Aoki, K.; Cercignani, C.
1984
Backward clusters, hierarchy and wild sums for a hard sphere system in a low-density regime. Zbl 1314.35077
Aoki, Kazuo; Pulvirenti, Mario; Simonella, Sergio; Tsuji, Tetsuro
2015
Fluid modeling for the Knudsen compressor: case of polyatomic gases. Zbl 1203.82074
Takata, Shigeru; Funagane, Hitoshi; Aoki, Kazuo
2010
Vapor flows along a plane condensed phase with weak condensation in the presence of a noncondensable gas. Zbl 1134.82039
Taguchi, Satoshi; Aoki, Kazuo; Latocha, Vladimir
2006
A rarefied gas flow induced by a temperature field: Numerical analysis of the flow between two coaxial elliptic cylinders with different uniform temperatures. Zbl 0910.76072
Aoki, K.; Sone, Y.; Waniguchi, Y.
1998
Evaporation and condensation of a rarefied gas between its two parallel plane condensed phases with different temperatures and negative temperature-gradient phenomenon. Numerical analysis of the Boltzmann equation for hard-sphere molecules. Zbl 0725.76079
Sone, Yoshio; Ohwada, Taku; Aoki, Kazuo
1991
Vapor flows in the continuum limit in the presence of a small amount of noncondensable gas. Zbl 1187.76511
Taguchi, Satoshi; Aoki, Kazuo; Takata, Shigeru
2004
A similarity solution of the linearized Boltzmann equation with application to thermophoresis of a spherical particle. Zbl 0549.76055
Sone, Yoshio; Aoki, Kazuo
1983
Slightly rarefied gas flow over a body with small accommodation coefficient. Zbl 1334.76129
Aoki, Kazuo; Inamuro, Takaji; Onishi, Yoshimoto
1979
A kinetic model for a polyatomic gas with temperature-dependent specific heats and its application to Shock-wave structure. Zbl 1448.76136
Kosuge, Shingo; Kuo, Hung-Wen; Aoki, Kazuo
2019
Numerical analysis of the Taylor-vortex flow of a slightly rarefied gas. Zbl 1360.35136
Aoki, Kazuo; Kagaya, Ryo; Kosuge, Shingo; Yoshida, Hiroaki
2016
The steady Boltzmann and Navier-Stokes equations. Zbl 1321.35129
Aoki, Kazuo; Golse, François; Kosuge, Shingo
2015
Rarefied gas flow around a sharp edge induced by a temperature field. Zbl 1250.76147
Taguchi, Satoshi; Aoki, Kazuo
2012
A diffusion model for rarefied flows in curved channels. Zbl 1149.76045
Aoki, K.; Degond, P.; Mieussens, L.; Takata, S.; Yoshida, H.
2008
The velocity distribution function in an infinitely strong shock wave. Zbl 1184.76541
Takata, Shigeru; Aoki, Kazuo; Cercignani, Carlo
2000
Derivation of hydrodynamic limits from either the Liouville equation or kinetic models: Study of an example. Zbl 0968.82523
Aoki, Kazuo; Bardos, Claude; Golse, François; Sone, Yoshio
2000
A technique for time-dependent boundary value problems in the kinetic theory of gases. II. Application to sound propagation. Zbl 0565.76077
Aoki, K.; Cercignani, C.
1984
A force acting on an oblate spheroid with discontinuous surface temperature in a slightly rarefied gas. Zbl 1416.76260
Aoki, Kazuo; Takata, Shigeru; Tomota, Tatsunori
2014
On the second-order temperature jump coefficient of a dilute gas. Zbl 1275.76180
2012
Poiseuille flow and thermal transpiration of a rarefied polyatomic gas through a circular tube with applications to microflows. Zbl 1431.76110
Funagane, Hitoshi; Takata, Shigeru; Aoki, Kazuo; Kugimoto, Ko
2011
A hierarchy of models related to nanoflows and surface diffusion. Zbl 1218.82029
Aoki, Kazuo; Charrier, Pierre; Degond, Pierre
2011
Rarefied gas flows through a curved channel: application of a diffusion-type equation. Zbl 1308.76239
Aoki, Kazuo; Takata, Shigeru; Tatsumi, Eri; Yoshida, Hiroaki
2010
Slow flows of a vapor-gas mixture with large density and temperature variations in the near-continuum regime. Zbl 1182.76426
Laneryd, Carl-Johan Tor; Aoki, Kazuo; Takata, Shigeru
2007
Introduction: Special issue dedicated to Prof. Yoshio Sone. Zbl 1131.01305
Aoki, Kazuo
2007
Finite-difference methods for the Boltzmann equation for binary gas mixtures. Zbl 1106.76047
Aoki, Kazuo; Kosuge, Shingo
2004
Numerical analysis of steady flows of a gas condensing on or evaporating from its plane condensed phase on the basis of kinetic theory: Effect of gas motion along the condensed phase. Zbl 0787.76089
Aoki, Kazuo; Nishino, Kenji; Sone, Yoshio; Sugimoto, Hiroshi
1993
A kinetic model for a polyatomic gas with temperature-dependent specific heats and its application to Shock-wave structure. Zbl 1448.76136
Kosuge, Shingo; Kuo, Hung-Wen; Aoki, Kazuo
2019
Numerical analysis of the Taylor-vortex flow of a slightly rarefied gas. Zbl 1360.35136
Aoki, Kazuo; Kagaya, Ryo; Kosuge, Shingo; Yoshida, Hiroaki
2016
Backward clusters, hierarchy and wild sums for a hard sphere system in a low-density regime. Zbl 1314.35077
Aoki, Kazuo; Pulvirenti, Mario; Simonella, Sergio; Tsuji, Tetsuro
2015
The steady Boltzmann and Navier-Stokes equations. Zbl 1321.35129
Aoki, Kazuo; Golse, François; Kosuge, Shingo
2015
A force acting on an oblate spheroid with discontinuous surface temperature in a slightly rarefied gas. Zbl 1416.76260
Aoki, Kazuo; Takata, Shigeru; Tomota, Tatsunori
2014
Moving boundary problems for a rarefied gas: spatially one-dimensional case. Zbl 1349.82059
Tsuji, Tetsuro; Aoki, Kazuo
2013
Decay of a linear pendulum in a free-molecular gas and in a special Lorentz gas. Zbl 1245.82066
Tsuji, Tetsuro; Aoki, Kazuo
2012
Rarefied gas flow around a sharp edge induced by a temperature field. Zbl 1250.76147
Taguchi, Satoshi; Aoki, Kazuo
2012
On the second-order temperature jump coefficient of a dilute gas. Zbl 1275.76180
2012
On the speed of approach to equilibrium for a collisionless gas. Zbl 1218.82019
Aoki, Kazuo; Golse, François
2011
Poiseuille flow and thermal transpiration of a rarefied polyatomic gas through a circular tube with applications to microflows. Zbl 1431.76110
Funagane, Hitoshi; Takata, Shigeru; Aoki, Kazuo; Kugimoto, Ko
2011
A hierarchy of models related to nanoflows and surface diffusion. Zbl 1218.82029
Aoki, Kazuo; Charrier, Pierre; Degond, Pierre
2011
Relaxation of a free-molecular gas to equilibrium caused by interaction with Vessel wall. Zbl 1203.76134
Tsuji, Tetsuro; Aoki, Kazuo; Golse, François
2010
Fluid modeling for the Knudsen compressor: case of polyatomic gases. Zbl 1203.82074
Takata, Shigeru; Funagane, Hitoshi; Aoki, Kazuo
2010
Rarefied gas flows through a curved channel: application of a diffusion-type equation. Zbl 1308.76239
Aoki, Kazuo; Takata, Shigeru; Tatsumi, Eri; Yoshida, Hiroaki
2010
Numerical simulations of rarefied gases in curved channels: thermal creep, circulating flow, and pumping effect. Zbl 1364.76168
Aoki, Kazuo; Degond, Pierre; Mieussens, Luc
2009
On the motion of a body in thermal equilibrium immersed in a perfect gas. Zbl 1133.76046
Aoki, Kazuo; Cavallaro, Guido; Marchioro, Carlo; Pulvirenti, Mario
2008
Shock structure analysis in chemically reacting gas mixtures by a relaxation-time kinetic model. Zbl 1182.76290
Groppi, M.; Aoki, K.; Spiga, G.; Tritsch, V.
2008
A diffusion model for rarefied flows in curved channels. Zbl 1149.76045
Aoki, K.; Degond, P.; Mieussens, L.; Takata, S.; Yoshida, H.
2008
Diffusion models for Knudsen compressors. Zbl 1182.76027
Aoki, Kazuo; Degond, Pierre; Takata, Shigeru; Yoshida, Hiroaki
2007
Slow flows of a vapor-gas mixture with large density and temperature variations in the near-continuum regime. Zbl 1182.76426
Laneryd, Carl-Johan Tor; Aoki, Kazuo; Takata, Shigeru
2007
Introduction: Special issue dedicated to Prof. Yoshio Sone. Zbl 1131.01305
Aoki, Kazuo
2007
Cylindrical Couette flow of a vapor-gas mixture: Ghost effect and bifurcation in the continuum limit. Zbl 1262.76041
Yoshida, Hiroaki; Aoki, Kazuo
2006
Vapor flows along a plane condensed phase with weak condensation in the presence of a noncondensable gas. Zbl 1134.82039
Taguchi, Satoshi; Aoki, Kazuo; Latocha, Vladimir
2006
Evaporation and condensation of a binary mixture of vapors on a plane condensed phase: numerical analysis of the linearized Boltzmann equation. Zbl 1187.76580
Yasuda, Shugo; Takata, Shigeru; Aoki, Kazuo
2005
Numerical analysis of the shear flow of a binary mixture of hard-sphere gases over a plane wall. Zbl 1186.76586
Yasuda, Shugo; Takata, Shigeru; Aoki, Kazuo
2004
Vapor flows in the continuum limit in the presence of a small amount of noncondensable gas. Zbl 1187.76511
Taguchi, Satoshi; Aoki, Kazuo; Takata, Shigeru
2004
Finite-difference methods for the Boltzmann equation for binary gas mixtures. Zbl 1106.76047
Aoki, Kazuo; Kosuge, Shingo
2004
Knudsen layer for gas mixtures. Zbl 1124.82314
Aoki, Kazuo; Bardos, Claude; Takata, Shigeru
2003
Numerical analysis of thermal-slip and diffusion-slip flows of a binary mixture of hard-sphere molecular gases. Zbl 1186.76516
Takata, Shigeru; Yasuda, Shugo; Kosuge, Shingo; Aoki, Kazuo
2003
Vapor flows with evaporation and condensation in the continuum limit: Effect of a trace of noncondensable gas. Zbl 1175.76142
Aoki, Kazuo; Takata, Shigeru; Taguchi, Satoshi
2003
Vapor flows condensing at incidence onto a plane condensed phase in the presence of a noncondensable gas. I: Subsonic condensation. Zbl 1185.76362
Taguchi, Satoshi; Aoki, Kazuo; Takata, Shigeru
2003
Vapor flows condensing at incidence onto a plane condensed phase in the presence of a noncondensable gas. II: Supersonic condensation. Zbl 1186.76514
Taguchi, Satoshi; Aoki, Kazuo; Takata, Shigeru
2003
Homogenization of a flow in a periodic channel of small section. Zbl 1107.76060
Aoki, K.; Degond, P.
2003
Various transport coefficients occurring in binary gas mixtures and their database. Zbl 1062.76591
Takata, Shigeru; Yasuda, Shugo; Aoki, Kazuo; Shibata, Takumi
2003
A consistent BGK-type model for gas mixtures. Zbl 1001.82093
Andries, Pierre; Aoki, Kazuo; Perthame, Benoit
2002
A numerical and experimental investigation of the modeling of microwave heating for liquid layers using a rectangular wave guide (effects of natural convection and dielectric properties). Zbl 1012.80004
Ratanadecho, P.; Aoki, K.; Akahori, M.
2002
Shock-wave structure for a binary gas mixture: Finite difference analysis of the Boltzmann equation for hard-sphere molecules. Zbl 0980.76078
Kosuge, Shingo; Aoki, Kazuo; Takata, Shigeru
2001
The ghost effect in the continuum limit for a vapor-gas mixture around condensed phases: asymptotic analysis of the Boltzmann equation. Zbl 1106.82359
Takata, Shigeru; Aoki, Kazuo
2001
A rarefied gas flow caused by a discontinuous wall temperature. Zbl 1184.76033
Aoki, Kazuo; Takata, Shigeru; Aikawa, Hidefumi; Golse, François
2001
A note on the propagation of boundary induced discontinuities in kinetic theory. Zbl 1012.82014
Aoki, Kazuo; Bardos, Claude; Dogbe, Christian; Golse, François
2001
The velocity distribution function in an infinitely strong shock wave. Zbl 1184.76541
Takata, Shigeru; Aoki, Kazuo; Cercignani, Carlo
2000
Derivation of hydrodynamic limits from either the Liouville equation or kinetic models: Study of an example. Zbl 0968.82523
Aoki, Kazuo; Bardos, Claude; Golse, François; Sone, Yoshio
2000
Two-surface problems of a multicomponent mixture of vapors and noncondensable gases in the continuum limit in the light of kinetic theory. Zbl 1149.76559
Takata, Shigeru; Aoki, Kazuo
1999
Cylindrical couette flows of a rarefied gas with evaporation and condensation: Reversal and bifurcation of flows. Zbl 1147.76503
Sone, Yoshio; Sugimoto, Hiroshi; Aoki, Kazuo
1999
A rarefied gas flow induced by a temperature field: Numerical analysis of the flow between two coaxial elliptic cylinders with different uniform temperatures. Zbl 0910.76072
Aoki, K.; Sone, Y.; Waniguchi, Y.
1998
The Bénard problem for a rarefied gas: formation of steady flow patterns and stability of array of rolls. Zbl 1185.76871
Sone, Yoshio; Aoki, Kazuo; Sugimoto, Hiroshi
1997
Inappropriateness of the heat-conduction equation for description of a temperature field of a stationary gas in the continuum limit: Examination by asymptotic analysis and numerical computation of the Boltzmann equation. Zbl 1027.76649
Sone, Yoshio; Aoki, Kazuo; Takata, Shigeru; Sugimoto, Hiroshi; Bobylev, A. V.
1996
One-way flow of a rarefied gas induced in a channel with a periodic temperature distribution. Zbl 1027.76650
Sone, Yoshio; Waniguchi, Yorifumi; Aoki, Kazuo
1996
Gas flows caused by evaporation and condensation on two parallel condensed phases and the negative temperature gradient: Numerical analysis by using a nonlinear kinetic equation. Zbl 0826.76081
Aoki, Kazuo; Masukawa, Noboru
1994
The Bénard problem of rarefied gas dynamics. Zbl 0939.76579
Sone, Yoshio; Aoki, Kazuo; Sugimoto, Hiroshi; Motohashi, Hideto
1994
Numerical analysis of a uniform flow of a rarefied gas past a sphere on the basis of the Boltzmann equation for hard-sphere molecules. Zbl 0806.76081
Takata, Shigeru; Sone, Yoshio; Aoki, Kazuo
1993
Numerical analysis of steady flows of a gas condensing on or evaporating from its plane condensed phase on the basis of kinetic theory: Effect of gas motion along the condensed phase. Zbl 0787.76089
Aoki, Kazuo; Nishino, Kenji; Sone, Yoshio; Sugimoto, Hiroshi
1993
Kinetic theory analysis of gas flows condensing on a plane condensed phase: Case of a mixture of a vapor and a noncondensable gas. Zbl 0818.76087
Sone, Yoshio; Aoki, Kazuo; Doi, Toshiyuki
1992
Numerical analysis of steady flows of a gas condensing on or evaporating from its plane condensed phase on the basis of kinetic theory: Effect of gas motion along the condensed phase. Zbl 0825.76718
Aoki, Kazuo; Nishino, Kenji; Sone, Yoshio; Sugimoto, Hiroshi
1991
Evaporation and condensation of a rarefied gas between its two parallel plane condensed phases with different temperatures and negative temperature-gradient phenomenon. Numerical analysis of the Boltzmann equation for hard-sphere molecules. Zbl 0725.76079
Sone, Yoshio; Ohwada, Taku; Aoki, Kazuo
1991
Numerical analysis of gas flows condensing on its plane condensed phase on the basis of kinetic theory. Zbl 0721.76085
Aoki, Kazuo; Sone, Yoshio; Yamada, Tatsuo
1990
Numerical analysis of the Poiseuille and thermal transpiration flows between two parallel plates on the basis of the Boltzmann equation for hard-sphere molecules. Zbl 0696.76092
Ohwada, Taku; Sone, Yoshio; Aoki, Kazuo
1989
Numerical analysis of the shear and thermal creep flows of a rarefied gas over a plane wall on the basis of the linearized Boltzmann equation for hard-sphere molecules. Zbl 0695.76032
Ohwada, Taku; Sone, Yoshio; Aoki, Kazuo
1989
Temperature jump and Knudsen layer in a rarefied gas over a plane wall: Numerical analysis of the linearized Boltzmann equation for hard-sphere molecules. Zbl 0661.76082
Sone, Yoshio; Ohwada, Taku; Aoki, Kazuo
1989
Evaporation and condensation on a plane condensed phase: Numerical analysis of the linearized Boltzmann equation for hard-sphere molecules. Zbl 0681.76077
Sone, Yoshio; Ohwada, Taku; Aoki, Kazuo
1989
Numerical analysis of a flow induced in a rarefied gas between noncoaxial circular cylinders with different temperatures for the entire range of the Knudsen number. Zbl 0661.76079
Aoki, Kazuo; Sone, Yoshio; Yano, Takeru
1989
Steady gas flows past bodies at small Knudsen numbers. Boltzmann and hydrodynamic systems. Zbl 0622.76082
Sone, Yoshio; Aoki, Kazuo
1987
A study of unsteady strong condensation on a plane condensed phase with special interest in formation of steady profile. Zbl 0607.76100
Sone, Yoshio; Aoki, Kazuo; Yamashita, Ichiro
1986
A technique for time-dependent boundary value problems in the kinetic theory of gases. I. Basic analysis. Zbl 0545.76078
Aoki, K.; Cercignani, C.
1984
A technique for time-dependent boundary value problems in the kinetic theory of gases. II. Application to sound propagation. Zbl 0565.76077
Aoki, K.; Cercignani, C.
1984
A similarity solution of the linearized Boltzmann equation with application to thermophoresis of a spherical particle. Zbl 0549.76055
Sone, Yoshio; Aoki, Kazuo
1983
Slightly rarefied gas flow over a body with small accommodation coefficient. Zbl 1334.76129
Aoki, Kazuo; Inamuro, Takaji; Onishi, Yoshimoto
1979
Slightly rarefied gas flow over a specularly reflecting body. Zbl 0356.76056
Sone, Yoshio; Aoki, Kazuo
1977
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#### Cited by 531 Authors

 43 Aoki, Kazuo 36 Takata, Shigeru 27 Sone, Yoshio 16 Sharipov, Felix M. 14 Spiga, Giampiero 12 Bisi, Marzia 12 Taguchi, Satoshi 11 Groppi, Maria 9 Golse, François 9 Ohwada, Taku 9 Sugimoto, Hiroshi 9 Torrilhon, Manuel 9 Zhang, Yonghao 8 Brull, Stephane 8 Kalempa, Denize 8 Kosuge, Shingo 8 Siewert, C. E. 8 Valougeorgis, Dimitris 8 Wu, Lei 8 Yoshida, Hiroaki 7 Cercignani, Carlo 7 Doi, Toshiyuki 7 Hadjiconstantinou, Nicolas G. 7 Liu, Tai-Ping 7 Mieussens, Luc 6 Chen, I-Kun 6 Shu, Chang 6 Struchtrup, Henning 6 Tsuji, Tetsuro 6 Yang, Xiongfeng 5 Bobylev, Alexandre Vasiljévitch 5 Emerson, David R. 5 Garcia, Roberto D. M. 5 Gu, Xiaojun 5 Loyalka, S. K. 5 Martalò, Giorgio 5 Szalmás, Lajos 5 Xu, Kun 5 Ytrehus, Tor 5 Yu, Shih-Hsien 4 Asinari, Pietro 4 Baranger, Céline 4 Conforto, Fiammetta 4 Frezzotti, Aldo 4 Graur, Irina A. 4 Klar, Axel 4 Kuo, Hung-Wen 4 Lockerby, Duncan A. 4 Marchioro, Carlo 4 Meland, Roar 4 Méolans, J. Gilbert 4 Mokhtar-Kharroubi, Mustapha 4 Pirner, Marlies 4 Rana, Anirudh Singh 4 Reese, Jason M. 4 Sader, John E. 4 Titarev, Vladimir A. 4 Yun, Seok-Bae 3 Bardos, Claude Williams 3 Barichello, Liliane Basso 3 Cavallaro, Guido 3 Chen, Xuwen 3 Chew, Yong-Tian 3 Duan, Renjun 3 Fan, Jing 3 Funagane, Hitoshi 3 Galkin, V. S. 3 Gibelli, Livio 3 Guo, Zhaoli 3 Gupta, Vinay Kumar 3 Hattori, Masanari 3 Ho, Minh Tuan 3 Illner, Reinhard 3 Kim, Chanwoo 3 Mathiaud, Julien 3 Monaco, Roberto 3 Niu, Xiaodong 3 Pavan, Vincent 3 Perrier, Pierre C. 3 Puppo, Gabriella 3 Rattanadecho, Phadungsak 3 Roohi, Ehsan 3 Russo, Giovanni 3 Salvarani, Francesco 3 Shakhov, E. M. 3 Simonella, Sergio 3 Slemrod, Marshall 3 Soares, Ana Jacinta 3 Strauss, Walter Alexander 3 Tompson, R. V. jun. 3 Wang, Weike 3 Wang, Yong 3 Yang, Tong 3 Yasuda, Shugo 3 Yushkanov, Aleksandr Alekseevich 2 Alaoui, Mohammed 2 Babovsky, Hans 2 Baker, Lowell L. 2 Baliti, Jamal 2 Barber, Robert W. ...and 431 more Authors
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#### Cited in 87 Serials

 80 Physics of Fluids 48 Journal of Computational Physics 37 European Journal of Mechanics. B. Fluids 36 Journal of Statistical Physics 30 Journal of Fluid Mechanics 15 Transport Theory and Statistical Physics 14 Physics of Fluids, A 11 Archive for Rational Mechanics and Analysis 10 Computers and Fluids 10 Continuum Mechanics and Thermodynamics 9 Communications in Mathematical Physics 9 Kinetic and Related Models 8 Computers & Mathematics with Applications 8 ZAMP. Zeitschrift für angewandte Mathematik und Physik 7 Journal of Differential Equations 6 Fluid Dynamics 6 International Journal of Heat and Mass Transfer 6 Journal of Mathematical Physics 5 Acta Applicandae Mathematicae 5 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 4 Applied Mathematical Modelling 4 International Journal of Modern Physics C 3 International Journal for Numerical Methods in Fluids 3 Quarterly of Applied Mathematics 3 Journal of Scientific Computing 2 Computer Methods in Applied Mechanics and Engineering 2 Journal of Mathematical Analysis and Applications 2 Mathematical Methods in the Applied Sciences 2 Physica A 2 Theoretical and Mathematical Physics 2 Zhurnal Vychislitel’noĭ Matematiki i Matematicheskoĭ Fiziki 2 Journal of Functional Analysis 2 Ricerche di Matematica 2 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 2 Physica D 2 Computational Mathematics and Mathematical Physics 2 Journal of Non-Equilibrium Thermodynamics 2 SIAM Journal on Mathematical Analysis 2 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 2 Comptes Rendus. Mathématique. Académie des Sciences, Paris 2 Multiscale Modeling & Simulation 2 Communications in Applied and Industrial Mathematics 1 Acta Mechanica 1 Computer Physics Communications 1 International Journal of Engineering Science 1 Journal of Applied Mathematics and Mechanics 1 Physics of Fluids 1 Reports on Mathematical Physics 1 Wave Motion 1 Applied Mathematics and Computation 1 International Journal of Mathematics and Mathematical Sciences 1 Inventiones Mathematicae 1 Journal of Computational and Applied Mathematics 1 Meccanica 1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 1 Applied Numerical Mathematics 1 Acta Mathematicae Applicatae Sinica. English Series 1 Numerical Methods for Partial Differential Equations 1 Applied Mathematics Letters 1 Journal of the American Mathematical Society 1 Mathematical and Computer Modelling 1 Japan Journal of Industrial and Applied Mathematics 1 Applications of Mathematics 1 Communications in Partial Differential Equations 1 International Journal of Computer Mathematics 1 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 1 Journal of Mathematical Sciences (New York) 1 Monte Carlo Methods and Applications 1 Mathematical Problems in Engineering 1 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 Nonlinear Analysis. Real World Applications 1 Acta Mathematica Scientia. Series B. (English Edition) 1 Communications on Pure and Applied Analysis 1 Analysis and Applications (Singapore) 1 Acta Numerica 1 Journal of Statistical Mechanics: Theory and Experiment 1 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 1 Annali dell’Università di Ferrara. Sezione VII. Scienze Matematiche 1 Journal of Physics A: Mathematical and Theoretical 1 Inverse Problems and Imaging 1 Mathematical Modelling of Natural Phenomena 1 Advances in Mathematical Physics 1 International Journal of Advances in Engineering Sciences and Applied Mathematics 1 Séminaire Laurent Schwartz. EDP et Applications 1 AMM. Applied Mathematics and Mechanics. (English Edition) 1 Proceedings of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 1 Mathematics in Engineering
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#### Cited in 22 Fields

 403 Fluid mechanics (76-XX) 194 Statistical mechanics, structure of matter (82-XX) 101 Partial differential equations (35-XX) 51 Numerical analysis (65-XX) 38 Classical thermodynamics, heat transfer (80-XX) 7 Integral equations (45-XX) 6 Mechanics of deformable solids (74-XX) 5 Operator theory (47-XX) 5 Mechanics of particles and systems (70-XX) 5 Optics, electromagnetic theory (78-XX) 4 Dynamical systems and ergodic theory (37-XX) 3 Ordinary differential equations (34-XX) 3 Probability theory and stochastic processes (60-XX) 2 Quantum theory (81-XX) 2 Biology and other natural sciences (92-XX) 1 General and overarching topics; collections (00-XX) 1 History and biography (01-XX) 1 Measure and integration (28-XX) 1 Sequences, series, summability (40-XX) 1 Approximations and expansions (41-XX) 1 Integral transforms, operational calculus (44-XX) 1 Computer science (68-XX)