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Study on the discontinuity and singularity in the kinetic theory of gases

Research Project

Project/Area Number 23656068
Research Category

Grant-in-Aid for Challenging Exploratory Research

Allocation TypeMulti-year Fund
Research Field Engineering fundamentals
Research InstitutionKyoto University

Principal Investigator

TAKATA Shigeru  京都大学, 大学院・工学研究科, 教授 (60271011)

Research Collaborator FUNAGANE Hitoshi  新日鐵住金(株), 技術開発本部
LIU Tai-ping  Stanford University (USA), Department of Mathematics, Professor Emeritus (Institute of Mathematics, Academia Sinica (Taiwan), Professor)
CHEN I-kun  Department of Applied Mathematics, ational Chiao Tung University (Taiwan), Assistant Professor
Project Period (FY) 2011 – 2012
Project Status Completed (Fiscal Year 2012)
Budget Amount *help
¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2011: ¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000)
Keywordsボルツマン方程式 / 対数特異性 / 速度分布関数 / 気体分子運動論 / 希薄気体 / 国際研究者交流
Research Abstract

In the kinetic theory, the gas behavior is investigated through the velocity distribution of innumerable gas molecules. In the present study, we have clarified that the macroscopic quantities, such as density, temperature, flow velocity, varies indefinitely steeply near the surface of planar body in its normal direction; to be more precisely, the variation rate is logarithmic. We have also identified that the source of this divergence is the discontinuous jump of velocity distribution of gas molecules on the surface of planar body.

Report

(3 results)
  • 2012 Annual Research Report   Final Research Report ( PDF )
  • 2011 Research-status Report
  • Research Products

    (8 results)

All 2013 2012

All Journal Article (2 results) (of which Peer Reviewed: 2 results) Presentation (6 results) (of which Invited: 2 results)

  • [Journal Article] Singular behaviour of a rareed gas on a planar boundary2013

    • Author(s)
      Shigeru Takata and Hitoshi Funagane
    • Journal Title

      J. Fluid Mech.

      Volume: 717 Pages: 30-47

    • DOI

      10.1017/jfm.2012.559

    • Related Report
      2012 Annual Research Report 2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Hagen-Poiseuille and thermal transpiration flows of a highly rarefied gas through a circular pipe2012

    • Author(s)
      H. Funagane and S. Takata
    • Journal Title

      Fluid Dyn. Res

      Volume: 44 Issue: 5 Pages: 55506-55506

    • DOI

      10.1088/0169-5983/44/5/055506

    • Related Report
      2012 Annual Research Report 2012 Final Research Report
    • Peer Reviewed
  • [Presentation] On a gradient singularity of flow of a rarefied gas over a planar boundary2013

    • Author(s)
      Shigeru Takata
    • Organizer
      Workshop on Boundary Phenomena for Evolutionary Partial Differential Equations
    • Place of Presentation
      Taipei (Taiwan)
    • Related Report
      2012 Final Research Report
  • [Presentation] On a gradient singularity of flow velocity of a rarefied gas over a planar boundary2013

    • Author(s)
      Shigeru Takata
    • Organizer
      Workshop on Boundary Phenomena for Evolutionary Partial Differential Equations
    • Place of Presentation
      Taipei (Taiwan)
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Singular behavior of a rarefied gas on a planar boundary2012

    • Author(s)
      Shigeru Takata
    • Organizer
      Workshop on Kinetic Theory and Gas Dynamics
    • Place of Presentation
      Stanford (USA)
    • Year and Date
      2012-07-17
    • Related Report
      2012 Annual Research Report 2012 Final Research Report
  • [Presentation] Singular behavior of a rarefied gas on a planar boundary2012

    • Author(s)
      Shigeru Takata
    • Organizer
      RIMS研究集会「流体と気体の数学解析」
    • Place of Presentation
      京都
    • Related Report
      2012 Final Research Report
  • [Presentation] Singular behavior of a rarefied gas on a planar boundary2012

    • Author(s)
      Shigeru Takata
    • Organizer
      14th International Conference on Hyperbolic Problems: Theory, Numerics, and Applications
    • Place of Presentation
      Padova (Italy)
    • Related Report
      2012 Annual Research Report 2012 Final Research Report
  • [Presentation] Singular behavior of a rarefied gas on a planar boundary2012

    • Author(s)
      Shigeru Takata
    • Organizer
      RIMS研究集会「流体と気体の数学解析」
    • Place of Presentation
      京都大学数理科学研究所(京都)
    • Related Report
      2012 Annual Research Report
    • Invited

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Published: 2011-08-05   Modified: 2019-07-29  

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