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Numerical and analytical studies on gas flows caused by the phase transition

Research Project

Project/Area Number 19560066
Research Category

Grant-in-Aid for Scientific Research (C)

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

Principal Investigator

TAKATA Shigeru  Kyoto University, 大学院・工学研究科, 准教授 (60271011)

Project Period (FY) 2007 – 2010
Project Status Completed (Fiscal Year 2010)
Budget Amount *help
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2010: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2009: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2008: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2007: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Keywordsボルツマン方程式 / 相変化 / 膨張波 / 対称性 / 相反性 / 気体分子運動論 / 分子気体力学 / 真空 / エントロピー生成
Research Abstract

We investigated the unsteady one-dimensional gas flows caused by a phase transition on the basis of the kinetic theory of gases. Main results are as follows. (1) Starting from the investigation of kinetic boundary-layer, we established a general theory of reciprocity for linearized problems. (2) We showed that from a certain class of initial states there occur two expansion waves traveling in the direction opposite to each other, which are separated by a highly rarefied region that evolves into a vacuum. This region is highly non-equilibrium and the temperature is strongly non-isotropic.

Report

(6 results)
  • 2010 Annual Research Report   Final Research Report ( PDF )
  • 2009 Annual Research Report   Self-evaluation Report ( PDF )
  • 2008 Annual Research Report
  • 2007 Annual Research Report
  • Research Products

    (39 results)

All 2011 2010 2009 2008 Other

All Journal Article (16 results) (of which Peer Reviewed: 16 results) Presentation (23 results)

  • [Journal Article] Symmetry of the linearized Boltzmann equation2011

    • Author(s)
      S.Takata
    • Journal Title

      Rarefied Gas Dynamics

      Volume: (In press 確定)

    • NAID

      120004920383

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Symmetry of the unsteady linearized Boltzmann equation in a fixed bounded domain2010

    • Author(s)
      S.Takata
    • Journal Title

      J.Stat.Phys. 140(5)

      Pages: 985-1005

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Symmetry of the unsteady linearized Boltzmann equation in a fixed bounded domain2010

    • Author(s)
      S.Takata
    • Journal Title

      Journal of Statistical Physics

      Volume: 140 Pages: 985-1005

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Note on the relation between thermophoresis and slow uniform flow problems for a rarefied gas2009

    • Author(s)
      S.Takata
    • Journal Title

      Phys.Fluids 21(11),112001

      Pages: 7-7

    • NAID

      120003386611

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Symmetry of the linearized Boltzmann equation II. Entropy production and Onsager-Casimir relation2009

    • Author(s)
      S.Takata
    • Journal Title

      J.Stat.Phys. 136(5)

      Pages: 945-983

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Symmetry of the linearized Boltzmann equation and its application2009

    • Author(s)
      S.Takata
    • Journal Title

      J.Stat.Phys. 136(4)

      Pages: 751-784

    • NAID

      120005848235

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Note on the relation between thermophoresis and slow uniform flow problems for a rarefied gas2009

    • Author(s)
      S. Takata
    • Journal Title

      Phys. Fluids 21(11)

      Pages: 112001-112001

    • NAID

      120003386611

    • Related Report
      2009 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] Symmetry of the linearized Boltzmann equation II. Entropy production and Onsager-Casimir relation2009

    • Author(s)
      S. Takata
    • Journal Title

      J. Stat. Phys. 136(5)

      Pages: 945-983

    • Related Report
      2009 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] Symmetry of the linearized Boltzmann equation and its application2009

    • Author(s)
      S. Takata
    • Journal Title

      J. Stat. Phys. 136(4)

      Pages: 751-784

    • NAID

      120005848235

    • Related Report
      2009 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] Note on the relation between thermophoresis and slow uniform flow…2009

    • Author(s)
      S.Takata
    • Journal Title

      Phys. Fluids 21

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Symmetry of the linearized Boltzmann equation II. Entropy…2009

    • Author(s)
      S.Takata
    • Journal Title

      J. Stat. Phys. 136

      Pages: 945-983

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Symmetry of the linearized Boltzmann equation and its application2009

    • Author(s)
      S.Takata
    • Journal Title

      J. Stat. Phys. 2009

      Pages: 751-784

    • NAID

      120005848235

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On the long time behavior of gas flows by evaporation from a plane condensed phase2008

    • Author(s)
      S.Takata
    • Journal Title

      Bulletin of the Institute of Mathematics, Academia Sinica (New Series) 3(1)

      Pages: 115-147

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] On the long time behavior of gas flows by evaporation from a plane condensed phase2008

    • Author(s)
      S. Takata
    • Journal Title

      Bulletin of the Institute of Mathematics, Academia Sinica (New Series) 3(1)

      Pages: 115-147

    • Related Report
      2009 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] On the long time behavior of gas flows by evaporation from a plane condensed phase2008

    • Author(s)
      Shigeru TAKATA
    • Journal Title

      Bulletin of the Institute of Mathematics, Academia Sinica (New Series) 3

      Pages: 115-147

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Symmetry of the linearized Boltzmann equation

    • Author(s)
      S.Takata
    • Journal Title

      Proceedings of the 27th International Symposium on Rarefied Gas Dynamics 印刷中

    • NAID

      120004920383

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Presentation] Symmetry of the linearized Boltzmann equation : A theory from steady to unsteady problem2010

    • Author(s)
      S.Takata
    • Organizer
      International Conference on Nonlinear Partial Differential Equations : Mathematical Theory, Computation, and Applications
    • Place of Presentation
      シンガポール(招待講演)
    • Year and Date
      2010-12-03
    • Related Report
      2010 Annual Research Report
  • [Presentation] On the symmetry of the linearized Boltzmann equation2010

    • Author(s)
      S.Takata
    • Organizer
      The 27^<th> International Symposium on Rarefied Gas Dynamics
    • Place of Presentation
      カリフォルニア(米国)(招待講演)
    • Year and Date
      2010-07-10
    • Related Report
      2010 Annual Research Report
  • [Presentation] 定常系における線形化ボルツマン方程式の対称性について2010

    • Author(s)
      高田滋
    • Organizer
      日本航空宇宙学会関西支部第425回航空懇談会
    • Place of Presentation
      大阪大学工学研究科,吹田市
    • Year and Date
      2010-02-12
    • Related Report
      2010 Final Research Report
  • [Presentation] 定常系における線形化ボルツマン方程式の対称性について2010

    • Author(s)
      高田滋
    • Organizer
      日本航空宇宙学会関西支部第425回航空懇談会
    • Place of Presentation
      大阪大学
    • Year and Date
      2010-02-12
    • Related Report
      2009 Annual Research Report
  • [Presentation] Symmetry of the linearized Boltzmann equation : A theory from steady to unsteady problem2010

    • Author(s)
      高田滋
    • Organizer
      International Conference on Nonlinear Partial Differential Equations : Mathematical Theory, Computation, and Applications
    • Place of Presentation
      Singapore (Singapore)
    • Related Report
      2010 Final Research Report
  • [Presentation] On the symmetry of the linearized Boltzmann equation2010

    • Author(s)
      高田滋
    • Organizer
      The 27th International Symposium on Rarefied Gas Dynamics, Invited lecture of the session "Boltzmann and Related Equations," Pacific Grove
    • Place of Presentation
      California (USA)
    • Related Report
      2010 Final Research Report
  • [Presentation] 分子気体力学における解析と数値計算2009

    • Author(s)
      高田滋
    • Organizer
      CompView GCOE Symposium 「Workshop1 :偏微分方程式の理論と実践-流体解析を中心として
    • Place of Presentation
      東京工業大学,目黒区
    • Year and Date
      2009-12-03
    • Related Report
      2010 Final Research Report
  • [Presentation] 分子気体力学における解析と数値計算, CompView GCOE Symposium「Workshopl : 偏微分方程式の理論と実践-流体解析を中心として」2009

    • Author(s)
      高田滋
    • Organizer
      東京工業大学
    • Place of Presentation
      目黒区
    • Year and Date
      2009-12-03
    • Related Report
      2009 Self-evaluation Report
  • [Presentation] 分子気体力学における解析と数値計算2009

    • Author(s)
      高田滋
    • Organizer
      CompView GCOE Symposium Workshop 1:偏微分方程式の理論と実践-流体解析を中心として
    • Place of Presentation
      東京工業大学
    • Year and Date
      2009-12-03
    • Related Report
      2009 Annual Research Report
  • [Presentation] 分子気体力学における漸近解析-流体力学極限の理論とその周辺-2009

    • Author(s)
      高田滋
    • Organizer
      未来研究ラボ「非線形ダイナミクス」研究会「流体力学における漸近解析」
    • Place of Presentation
      大阪大学基礎工学研究科,吹田市
    • Related Report
      2010 Final Research Report
  • [Presentation] Symmetry of the linearized Boltzmann equation and the Onsager-Casimir relation2009

    • Author(s)
      高田滋
    • Organizer
      2009 NIMS Hot Topics Workshop on Kinetic Theory and Fluid Dynamics
    • Place of Presentation
      Seoul National University, Seoul (Korea)
    • Related Report
      2010 Final Research Report
  • [Presentation] Symmetry of the linearized Boltzmann equation, Modern Topics in Nonlinear Kinetic Equations2009

    • Author(s)
      高田滋
    • Organizer
      Department of Applied Mathematics and Theoretical Physics
    • Place of Presentation
      University of Cambridge, Cambridge (UK)
    • Related Report
      2010 Final Research Report
  • [Presentation] Symmetry of the linearized Boltzmann equation2009

    • Author(s)
      高田滋
    • Organizer
      2009 Workshop on Kinetic Theory, Institute of Mathematics
    • Place of Presentation
      Academia Sinica, Taipei (Taiwan)
    • Related Report
      2010 Final Research Report
  • [Presentation] Symmetry of the linearized Boltzmann equation and the Onsager-Casimir relation2009

    • Author(s)
      S. Takata
    • Organizer
      2009 NIMS Hot Topics Workshop on Kinetic Theory and Fluid Dynamics, Seoul National University
    • Place of Presentation
      Seoul (Korea)
    • Related Report
      2009 Self-evaluation Report
  • [Presentation] Symmetry of the linearized Boltzmann equation, Modern Topics in Nonlinear Kinetic Equations, Department of Applied Mathematics and Theoretical Physics2009

    • Author(s)
      S. Takata
    • Organizer
      University of Cambridge
    • Place of Presentation
      Cambridge (UK)
    • Related Report
      2009 Self-evaluation Report
  • [Presentation] Symmetry of the linearized Boltzmann equation, 2009 Workshop on Kinetic Theory, Institute of Mathematics2009

    • Author(s)
      S. Takata
    • Organizer
      Academia Sinica
    • Place of Presentation
      Taipei (Taiwan)
    • Related Report
      2009 Self-evaluation Report
  • [Presentation] Symmetry of the linearized Boltzmann equation and its applications2009

    • Author(s)
      S.Takata
    • Organizer
      2009 NIMS Hot Topics Workshop on Kinetic Theory and Fluid Dynamics (2hour short courses)
    • Place of Presentation
      Seoul National University (Korea)
    • Related Report
      2009 Annual Research Report
  • [Presentation] 分子気体力学における漸近解析-流体力学極限の理論とその周辺2009

    • Author(s)
      高田滋
    • Organizer
      未来研究ラボ「非線形ダイナミクス」研究会「流体力学における漸近解析」
    • Place of Presentation
      大阪大学
    • Related Report
      2009 Annual Research Report
  • [Presentation] Symmetry of the linearized Boltzmann equation and the Onsager-Casimir relation2009

    • Author(s)
      S.Takata
    • Organizer
      2009 NIMS Hot Topics Workshop on Kinetic Theory and Fluid Dynamics
    • Place of Presentation
      Seoul National University (Korea)
    • Related Report
      2009 Annual Research Report
  • [Presentation] Symmetry of the linearized Boltzmann equation2009

    • Author(s)
      S.Takata
    • Organizer
      Modern Topics in Nonlinear Kinetic Equations
    • Place of Presentation
      University of Cambridge (UK)
    • Related Report
      2009 Annual Research Report
  • [Presentation] Symmetry of the linearized Boltzmann equation2008

    • Author(s)
      Shigeru TAKATA
    • Organizer
      Kinetic Theory Day, Institute of Mathematics, Academia Scinica
    • Place of Presentation
      台北市(台湾)
    • Year and Date
      2008-12-23
    • Related Report
      2008 Annual Research Report
  • [Presentation] 分子気体力学による流体力学極限の研究とその応用2008

    • Author(s)
      高田滋
    • Organizer
      2008年春季 第55回応用物理学関係連合講演会 日本真空協会企画シンポジウム「真空中の気体の流れ」
    • Place of Presentation
      日本大学理工学部 船橋キャンパス,船橋市
    • Year and Date
      2008-03-27
    • Related Report
      2010 Final Research Report
  • [Presentation] 分子気体力学による流体力学極限の研究とその応用, 2008年春季第55回応用物理学関係連合講演会 日本真空協会企画シンポジウム「真空中の気体の流れ」2008

    • Author(s)
      高田滋
    • Organizer
      日本大学理工学部
    • Place of Presentation
      船橋キャンパス, 船橋市
    • Year and Date
      2008-03-27
    • Related Report
      2009 Self-evaluation Report

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Published: 2007-04-01   Modified: 2016-04-21  

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