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Mathematical and physical study of micro- and nano-scale gas flows on the basis of the Boltzmann equation

Research Project

Project/Area Number 20360046
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field Engineering fundamentals
Research InstitutionKyoto University

Principal Investigator

AOKI Kazuo  Kyoto University, 大学院・工学研究科, 教授 (10115777)

Co-Investigator(Kenkyū-buntansha) TAKATA Shigeru  京都大学, 大学院・工学研究科, 准教授 (60271011)
KOSUGE Shingo  京都大学, 大学院・工学研究科, 助教 (40335188)
NISHIBATA Shinya  東京工業大学, 大学院・情報理工学研究科, 教授 (80279299)
Research Collaborator CHARRIER Pierre  ボルドー第1大学, 教授(フランス)
DEGOND Pierre  トゥールーズ第3大学, 教授(フランス)
GOLSE Francois  エコール・ポリテクニク, 教授(フランス)
LIU Tai-ping  スタンフォード大学, 教授(アメリカ)
MARKOWICH Peter  ケンブリッジ大学, 教授(イギリス)
Project Period (FY) 2008 – 2010
Project Status Completed (Fiscal Year 2010)
Budget Amount *help
¥18,330,000 (Direct Cost: ¥14,100,000、Indirect Cost: ¥4,230,000)
Fiscal Year 2010: ¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000)
Fiscal Year 2009: ¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000)
Fiscal Year 2008: ¥8,710,000 (Direct Cost: ¥6,700,000、Indirect Cost: ¥2,010,000)
Keywordsボルツマン方程式 / 気体分子運動論 / マイクロ流体力学 / 移流拡散モデル / 応用数学
Research Abstract

Diffusion-type equations that describe gas flows through a micro-nano channel with a width much shorter than the length was derived on the basis of molecular gas dynamics by a systematic asymptotic analysis. With the help of the derived equations, the properties of gas flows (in particular, gas flows through a twisty channel) were clarified. In addition, a direct numerical method based on molecular gas dynamics was constructed for wider micro channels.

Report

(4 results)
  • 2010 Annual Research Report   Final Research Report ( PDF )
  • 2009 Annual Research Report
  • 2008 Annual Research Report
  • Research Products

    (74 results)

All 2011 2010 2009 2008 Other

All Journal Article (31 results) (of which Peer Reviewed: 31 results) Presentation (40 results) Remarks (3 results)

  • [Journal Article] Steady flows of a highly rarefied gas induced by non-uniform wall temperature2011

    • Author(s)
      S.Kosuge, K.Aoki, S.Takata, R.Hattori, D.Sakai
    • Journal Title

      Phys.Fluids 23

    • NAID

      120004754327

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Poiseuille flow and thermal transpiration of a rarefied polyatomic gas through a circular tube with applications to microflows2011

    • Author(s)
      H.Funagane, S.Takata, K.Aoki, K.Kugimoto
    • Journal Title

      Bollettino dell'Unione Matematica Italiana, Ser.9 4

      Pages: 19-46

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] On the speed of approach to equilibrium for a collisionless gas2011

    • Author(s)
      K.Aoki, F.Golse
    • Journal Title

      Kinetic and Related Models 4

      Pages: 87-107

    • NAID

      120003184078

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] A hierarchy of models related to nanoflows and surface diffusion2011

    • Author(s)
      K.Aoki, P.Charrier, P.Degond
    • Journal Title

      Kinetic and Related Models 4

      Pages: 53-85

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] A hierarchy of models related to nanoflows and surface diffusion2011

    • Author(s)
      K.Aoki, P.Charrier, P.Degond
    • Journal Title

      Kinetic and Related Models

      Volume: 4 Pages: 53-85

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On the speed of approach to equilibrium for a collisionless gas2011

    • Author(s)
      K.Aoki, F.Golse
    • Journal Title

      Kinetic and Related Models

      Volume: 4 Pages: 87-107

    • NAID

      120003184078

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Poiseuille flow and thermal transpiration of a rarefied polyatomic gas through a circular tube with applications to microflows2011

    • Author(s)
      H.Funagane, S.Takata, K.Aoki, K.Kugimoto
    • Journal Title

      Bollettino dell'Unione Matematica Italiana Ser.9

      Volume: 4 Pages: 19-46

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Steady flows of a highly rarefied gas induced by non-uniform wall temperature2011

    • Author(s)
      S.Kosuge, K.Aoki, S.Takata, R.Hattori, D.Sakai
    • Journal Title

      Phys.Fluids

      Volume: 23

    • NAID

      120004754327

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Decay of an oscillating plate in a free-molecular gas2011

    • Author(s)
      T.Tsuji, K.Aoki
    • Journal Title

      Rarefied Gas Dynamics

      Volume: (印刷中)

    • NAID

      120004920384

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Rarefied gas flows through a curved channel : Application of a diffusion-type equation2010

    • Author(s)
      K.Aoki, S.Takata, E.Tatsumi, H.Yoshida
    • Journal Title

      Phys.Fluids 22

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Relaxation of a free-molecular gas to equilibrium caused by interaction with vessel wall2010

    • Author(s)
      T.Tsuji, K.Aoki, F.Golse
    • Journal Title

      J.Stat.Phys. 140

      Pages: 518-543

    • NAID

      120002426865

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Slow evaporation and condensation on a spherical droplet in the presence of a noncondensable gas2010

    • Author(s)
      S.Kosuge, K.Aoki, M.Hatano
    • Journal Title

      Phys.Fluids 22

    • NAID

      120002462948

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Fluid modeling for the Knudsen compressor : Case of polyatomic gases2010

    • Author(s)
      S.Takata, H.Funagane, K.Aoki
    • Journal Title

      Kinetic and Related Models 3

      Pages: 353-372

    • NAID

      110008459341

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Small velocity and finite temperature variations in kinetic relaxation models2010

    • Author(s)
      K.Aoki, A.Jungel, P.A.Markowich
    • Journal Title

      Kinetic and Related Models 3

      Pages: 1-15

    • Related Report
      2010 Final Research Report 2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Relaxation of a free-molecular gas to equilibrium caused by interaction with vessel wall2010

    • Author(s)
      T.Tsuji, K.Aoki, F.Golse
    • Journal Title

      J.Stat.Phys.

      Volume: 140 Pages: 518-543

    • NAID

      120002426865

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Rarefied gas flows through a curved channel : Application of a diffusion-type equation2010

    • Author(s)
      K.Aoki, S.Takata, E.Tatsumi, H.Yoshida
    • Journal Title

      Phys.Fluids

      Volume: 22

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Asymptotic behaviors and classical limits of solutions to a quantum drift-diffusion model for semiconductors2010

    • Author(s)
      S.Nishibata, N.Shigeta, M.Suzuki
    • Journal Title

      Math.Models and Methods Appl.Sci.

      Volume: 20 Pages: 909-936

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Fluid modeling for the Knudsen compressor : Case of polyatomic gases2010

    • Author(s)
      S.Takata, H.Funagane, K.Aoki
    • Journal Title

      Kinetic and Related Models 3(印刷中)

    • NAID

      110008459341

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Slow evaporation and condensation on a spherical droplet in the presence of a noncondensable gas2010

    • Author(s)
      S.Kosuge, K.Aoki, M.Hatano
    • Journal Title

      Phys. Fluids 22(印刷中)

    • NAID

      120002462948

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Approach to steady motion of a plate moving in a free-molecular gas under a constant external force2009

    • Author(s)
      K.Aoki, T.Tsuji, G.Cavallaro
    • Journal Title

      Phys.Rev.E 80

    • Related Report
      2010 Final Research Report 2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Fluid models and simulations of internal rarefied gas flows2009

    • Author(s)
      K.Aoki, S.Takata
    • Journal Title

      Riv.Mat.Univ.Parma, Serie 8 1

      Pages: 1-69

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Kinetic theory analysis of a binary mixture reacting on a surface2009

    • Author(s)
      M.Groppi, L.Desvillettes, K.Aoki
    • Journal Title

      Eur.Phys.J.B 70

      Pages: 117-126

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Numerical simulations of rarefied gases in curved channels : Thermal creep, circulating flow, and pumping effect2009

    • Author(s)
      K.Aoki, P.Degond, L.Mieussens
    • Journal Title

      Commun.Comput.Phys. 6

      Pages: 919-954

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Diffusion approximation for the Knudsen compressor composed of circular tubes2009

    • Author(s)
      K.Aoki, S.Takata, K.Kugimoto
    • Journal Title

      in Rarefied Gas Dynamics, edited by T.Abe (AIP, Melville) 1084

      Pages: 953-958

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Asymptotic stability of a stationary solution to a heat-conductive hydrodynamic model for semiconductors2009

    • Author(s)
      S.Nishibata, M.Suzuki
    • Journal Title

      Arch.Rational Mech.Anal. 192

      Pages: 187-215

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Diffusion approximation for the Knudsen compressor composed of circular tubes2009

    • Author(s)
      K. Aoki, S. Takata, Ko Kugimoto
    • Journal Title

      Rarefied Gsa Dynamics 1084

      Pages: 953-958

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Fluid dynamics for gaseous mixtures derived from kinetic theory (Harold Grad Lecture)2009

    • Author(s)
      K. Aoki
    • Journal Title

      Rarefied Gsa Dynamics 1084

      Pages: 15-24

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Numerical simulations of rarefied gases in curved channels : Thermal creep, circulating flow, and pumping effect2009

    • Author(s)
      K. Aoki, P. Degond, L. Mieussens
    • Journal Title

      Communications in Computational Physics (印刷中)

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Kinetic theory analysis of a binary mixture reacting on a surface2009

    • Author(s)
      M. Groppi, L. Desvillettes, K. Aoki
    • Journal Title

      European Physical Journal B (印刷中)

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Fluid models and simulations of internal rarefied gas flows2009

    • Author(s)
      K. Aoki, S. Takata
    • Journal Title

      Rivista di Matematica dell' Universita degli Studi di Parma (印刷中)

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Shock structure analysis in chemically reacting gas mixtures by a relaxation-time kinetic model2008

    • Author(s)
      M. Groppi, K. Aoki, G. Spiga, V. Tritsch
    • Journal Title

      Physics of Fluids 20

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Presentation] Some remarks on collisionless gases (Invited Lecture)2011

    • Author(s)
      K.Aoki
    • Organizer
      Conference in Memory of Carlo Cercignani. Boltzmann equation : Mathematics, Modeling and Simulations, Institut Henri Poincar
    • Place of Presentation
      Paris, France
    • Related Report
      2010 Final Research Report
  • [Presentation] On the asymptotics of the Boltzmann equation and fluid-dynamic limits (Invited Lecture)2011

    • Author(s)
      K.Aoki
    • Organizer
      International Conference on Nonlinear Evolutionary Partial Differential Equations : Theories and Applications
    • Place of Presentation
      Shanghai Jiao Tong University, Shanghai, China
    • Related Report
      2010 Final Research Report
  • [Presentation] On the asymptotics of the Boltzmann equation and fluid-dynamic limits (40min)2011

    • Author(s)
      K.Aoki
    • Organizer
      International Conference on Nonlinear Evolutionary Partial Differential Equations
    • Place of Presentation
      Shanghai Jiao Tong Univ.(China)
    • Related Report
      2010 Annual Research Report
  • [Presentation] Some remarks on collisionless gases (45min)2011

    • Author(s)
      K.Aoki
    • Organizer
      Conference in Memory of Carlo Cercignani
    • Place of Presentation
      Institut Henri Poincare, Paris (France)
    • Related Report
      2010 Annual Research Report
  • [Presentation] On the speed of approach to equilibrium for a collisionless gas (Invited Lecture)2010

    • Author(s)
      K.Aoki
    • Organizer
      International Conference on Nonlinear Partial Differential Equations : Mathematical Theory, Computation, and Applications
    • Place of Presentation
      National University of Singapore, Singapore
    • Related Report
      2010 Final Research Report
  • [Presentation] Some basic problems of a collisionless gas : A numerical study (Invited Lecture)2010

    • Author(s)
      K.Aoki
    • Organizer
      NIMS Thematic Program Workshop on Conservation Laws, Plasma and Related Fields
    • Place of Presentation
      Seoul National University, Korea
    • Related Report
      2010 Final Research Report
  • [Presentation] Stokes fluid dynamics for a vapor-gas mixture derived from kinetic theory (Invited Lecture)2010

    • Author(s)
      K.Aoki
    • Organizer
      Workshop on Kinetic and Related Models
    • Place of Presentation
      Northwest University, Xi'an, China
    • Related Report
      2010 Final Research Report
  • [Presentation] Some decay problems of a collisionless gas : A numerical study (Invited Lecture)2010

    • Author(s)
      K.Aoki
    • Organizer
      Workshop : Fluid- Kinetic Modelling in Biology
    • Place of Presentation
      Physics & Engineering, Cambridge University, Cambridge, UK
    • Related Report
      2010 Final Research Report
  • [Presentation] Numerical study of some decay problems of a collisionless gas (Invited Lecture)2010

    • Author(s)
      K.Aoki
    • Organizer
      Workshop on Kinetic and Fluids
    • Place of Presentation
      Peking University, Beijing, China
    • Related Report
      2010 Final Research Report
  • [Presentation] Stokes fluid dynamics for a vapor-gas mixture derived from kinetic theory (Invited Lecture)2010

    • Author(s)
      K.Aoki
    • Organizer
      The 5th Pacific Rim Conference on Mathematics
    • Place of Presentation
      Stanford University, Stanford, USA
    • Related Report
      2010 Final Research Report
  • [Presentation] Relaxation of a Knudsen gas to equilibrium caused by interaction with vessel wall (35min)2010

    • Author(s)
      K.Aoki
    • Organizer
      Summer School : Methods and Models of Kinetic Theory
    • Place of Presentation
      Porto Ercole (Italy)
    • Related Report
      2010 Annual Research Report
  • [Presentation] Stokes fluid dynamics for a vapor-gas mixture derived from kinetic theory (45min)2010

    • Author(s)
      K.Aoki
    • Organizer
      The 5th Pacific Rim Conference on Mathematics
    • Place of Presentation
      Stanford Univ.(USA)
    • Related Report
      2010 Annual Research Report
  • [Presentation] Asymptotic behavior of solutions to the Euler-Poisson equation in plasma physics (45min)2010

    • Author(s)
      S.Nishibata
    • Organizer
      The 5th Pacific Rim Conference on Mathematics
    • Place of Presentation
      Stanford Univ.(USA)
    • Related Report
      2010 Annual Research Report
  • [Presentation] Numerical study of some decay problems of a collisionless gas (50min)2010

    • Author(s)
      K.Aoki
    • Organizer
      Workshop on Kinetic and Fluids
    • Place of Presentation
      Peking Univ.(China)
    • Related Report
      2010 Annual Research Report
  • [Presentation] Some decay problems of a collisionless gas : A numerical study (60min)2010

    • Author(s)
      K.Aoki
    • Organizer
      Workshop : Fluid-Kinetic Modelling in Biology, Physics & Engineering
    • Place of Presentation
      Cambridge Univ.(UK)
    • Related Report
      2010 Annual Research Report
  • [Presentation] Stokes fluid dynamics for a vapor-gas mixture derived from kinetic theory (45min)2010

    • Author(s)
      K.Aoki
    • Organizer
      Workshop on Kinetic and Related Models
    • Place of Presentation
      Northwest Univ., Xi'an (China)
    • Related Report
      2010 Annual Research Report
  • [Presentation] Some basic problems of a collisionless gas : A numerical study (40min)2010

    • Author(s)
      K.Aoki
    • Organizer
      NIMS Thematic Program Workshop on Conservation Laws, Plasma and Related Fields
    • Place of Presentation
      Seoul National Univ.(Korea)
    • Related Report
      2010 Annual Research Report
  • [Presentation] On the speed of approach to equilibrium for a collisionless gas (45min)2010

    • Author(s)
      K.Aoki
    • Organizer
      International Conference on Nonlinear Partial Differential Equations
    • Place of Presentation
      National Univ.of Singapore (Singapore)
    • Related Report
      2010 Annual Research Report
  • [Presentation] On a kinetic approach for nanoflows and surface diffusion (45min)2009

    • Author(s)
      K. Aoki
    • Organizer
      Conference on Kinetic Equations and Applications
    • Place of Presentation
      Marseille (France)
    • Year and Date
      2009-02-03
    • Related Report
      2008 Annual Research Report
  • [Presentation] Some remarks on collisionless gases (Invited Lecture)2009

    • Author(s)
      K.Aoki
    • Organizer
      The 7th East Asia Conference on PDEs
    • Place of Presentation
      The Chinese University of Hong Kong and City University of Hong Kong, Hong Kong
    • Related Report
      2010 Final Research Report
  • [Presentation] Some remarks on collisionless gases (Invited Lecture)2009

    • Author(s)
      K.Aoki
    • Organizer
      The 4th Workshop Theory and Numerics of Kinetic Equations
    • Place of Presentation
      University of Saarland, Saarbrucken, Germany
    • Related Report
      2010 Final Research Report
  • [Presentation] Kinetic theory of gases and its applications (Basic course)2009

    • Author(s)
      K.Aoki
    • Organizer
      The 34th Summer School of Mathematical Physics
    • Place of Presentation
      Ravello, Italy
    • Related Report
      2010 Final Research Report
  • [Presentation] Approach to steady motion of a plate moving in a collisionless gas under a constant external force (Invited Lecture)2009

    • Author(s)
      K.Aoki
    • Organizer
      Workshop and Summer School on Topics in Kinetic Theory
    • Place of Presentation
      University of Victoria, Victoria, Canada
    • Related Report
      2010 Final Research Report
  • [Presentation] Fluid dynamics for a vapor-gas mixture derived from kinetic theory (Invited Lecture)2009

    • Author(s)
      K.Aoki
    • Organizer
      Workshop on Theory and Applications of Classical and Quantum Kinetic Theory
    • Place of Presentation
      Banff International Research Station, Banff, Canada
    • Related Report
      2010 Final Research Report
  • [Presentation] Fluid dynamics for a vapor-gas mixture derived from kinetic theory (Invited Lecture)2009

    • Author(s)
      K.Aoki
    • Organizer
      IPAM Workshop II-The Boltzmann Equation : DiPerna-Lions Plus 20 Years
    • Place of Presentation
      University of California, Los Angeles, Los Angeles, USA
    • Related Report
      2010 Final Research Report
  • [Presentation] Some considerations on collisionless gases (Invited Lecture)2009

    • Author(s)
      K.Aoki
    • Organizer
      2009 Workshop on Kinetic Theory
    • Place of Presentation
      Institute of Mathematics, Academia Sinica, Taipei, Taiwan
    • Related Report
      2010 Final Research Report
  • [Presentation] Fluid dynamics for a vapor-gas mixture derived from kinetic theory (invited lecture, 30min)2009

    • Author(s)
      K.Aoki
    • Organizer
      Workshop on Theory and Applications of Classical and Quantum Kinetic Theory
    • Place of Presentation
      Banff (Canada)
    • Related Report
      2009 Annual Research Report
  • [Presentation] Approach to steady motion of a plate moving in a collision less gas (invited lecture, 50min)2009

    • Author(s)
      K.Aoki
    • Organizer
      Workshop and Summer School on Topics in Kinetic Theory
    • Place of Presentation
      Victoria (Canada)
    • Related Report
      2009 Annual Research Report
  • [Presentation] Kinetic theory of gases and its applications (basic course, 50min×12times)2009

    • Author(s)
      K.Aoki
    • Organizer
      The 34th Summer School of Mathematical Physics
    • Place of Presentation
      Ravello (Italy)
    • Related Report
      2009 Annual Research Report
  • [Presentation] Some remarks on collisionless gases (invited lecture, 45min)2009

    • Author(s)
      K.Aoki
    • Organizer
      The 4th Workshop Theory and Numerics of Kinetic Equations
    • Place of Presentation
      Saarbrucken (Germany)
    • Related Report
      2009 Annual Research Report
  • [Presentation] Some remarks on collisionless gases (invited lecture, 45min)2009

    • Author(s)
      K.Aoki
    • Organizer
      The 7th East Asia Conference on PDEs
    • Place of Presentation
      Hong Kong 中国
    • Related Report
      2009 Annual Research Report
  • [Presentation] Diffusion approximation for rarefied gas flows in a curved channel (invited lecture, 50min)2008

    • Author(s)
      K. Aoki
    • Organizer
      International Conference on Conservation Laws and Kinetic Equations 2008
    • Place of Presentation
      Shanghai (China)
    • Year and Date
      2008-12-14
    • Related Report
      2008 Annual Research Report
  • [Presentation] Slow flows of a vapor-gas mixture with large density and temperature variations in the near-continuum regime (invited lecture, 60min)2008

    • Author(s)
      K. Aoki
    • Organizer
      Mini-Workshop on Numerics for Kinetic Equations
    • Place of Presentation
      Oberwolfach-Walke(Germany)
    • Year and Date
      2008-11-16
    • Related Report
      2008 Annual Research Report
  • [Presentation] Diffusion approximation for the Knudsen compressor composed of circular tubes2008

    • Author(s)
      K. Kugimoto
    • Organizer
      26th International Symposium on Rarefied Gas Dynamics
    • Place of Presentation
      京都大学
    • Year and Date
      2008-07-24
    • Related Report
      2008 Annual Research Report
  • [Presentation] Fluid dynamics for gaseous mixtures derived from kinetic theory (Harold Grad Lecture, 60min)2008

    • Author(s)
      K. Aoki
    • Organizer
      26th International Symposium on Rarefied Gas Dynamics
    • Place of Presentation
      京都大学
    • Year and Date
      2008-07-23
    • Related Report
      2008 Annual Research Report
  • [Presentation] Diffusion approximation for rarefied gas flows in a curved channel (Invited Lecture)2008

    • Author(s)
      K.Aoki
    • Organizer
      International Conference on Conservation Laws and Kinetic Equations 2008
    • Place of Presentation
      Shanghai, China
    • Related Report
      2010 Final Research Report
  • [Presentation] Slow flows of a vapor-gas mixture with large density and temperature variations in the near-continuum regime (Invited Lecture)2008

    • Author(s)
      K.Aoki
    • Organizer
      Oberwolfach MiniWorkshop, Numerics for Kinetic Equations
    • Place of Presentation
      Mathematisches Forschungsinstitut Ober-wolfach, Oberwolfach-Walke, Germany
    • Related Report
      2010 Final Research Report
  • [Presentation] Molecular gas dynamics and the Boltzmann equation (Mini-Course)2008

    • Author(s)
      K.Aoki
    • Organizer
      The 3rd International Conference on the Boltzmann Equation and Related Topics
    • Place of Presentation
      Wuhan, China
    • Related Report
      2010 Final Research Report
  • [Presentation] Fluid models and simulations of internal rarefied gasflows (mini-course, 90min×5times)2008

    • Author(s)
      K. Aoki, S. Takata
    • Organizer
      Summer School : Methods and Models of Kinetic Theory
    • Place of Presentation
      Porto Ercole (Italy)
    • Related Report
      2008 Annual Research Report
  • [Presentation] Molecular gas dynamics and the Boltzmann equation, (Mini-Course, 90min×4times)2008

    • Author(s)
      K. Aoki
    • Organizer
      3rd International Conference on the Boltzmann Equation and Related
    • Place of Presentation
      Whuhan (China)
    • Related Report
      2008 Annual Research Report
  • [Remarks] ホームページ等

    • URL

      http://www.mfd.me.kyoto-u.ac.jp/member/aoki/aokij.htm

    • Related Report
      2010 Final Research Report
  • [Remarks]

    • URL

      http://www.mfd.me.kyoto-u.ac.jp/member/aoki/aokij.htm

    • Related Report
      2010 Annual Research Report
  • [Remarks]

    • URL

      http://www.mfd.me.kyoto-u.ac.jp/member/aoki/aokij.htm

    • Related Report
      2009 Annual Research Report

URL: 

Published: 2008-04-01   Modified: 2016-04-21  

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