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Study on feasibility of the kinetic equation with thermal bath

Research Project

Project/Area Number 17K18840
Research Category

Grant-in-Aid for Challenging Research (Exploratory)

Allocation TypeMulti-year Fund
Research Field Fluid engineering, Thermal engineering, and related fields
Research InstitutionKyoto University

Principal Investigator

Takata Shigeru  京都大学, 工学研究科, 教授 (60271011)

Project Period (FY) 2017-06-30 – 2021-03-31
Project Status Completed (Fiscal Year 2020)
Budget Amount *help
¥6,240,000 (Direct Cost: ¥4,800,000、Indirect Cost: ¥1,440,000)
Fiscal Year 2019: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2018: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2017: ¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000)
Keywords相転移 / cahn-Hilliard方程式 / ボルツマン方程式 / 運動論方程式 / 多孔質 / パーコレーション / 気体分子運討論 / 実在気体効果 / Cercignani-Lampis条件 / スピノーダル分解 / バイノーダル分解 / 多孔質気体輸送 / Knudsen気体 / 気体分子運動論 / 熱浴近似 / 流体 / 統計力学 / 流体力学 / カーン・ヒリアード
Outline of Final Research Achievements

The main findings in the project are classified into three categories: (1) A simple kinetic model that reproduces a Cahn-Hilliard type equation in the fluid-dynamic limit has been found. For this model, a monotonic functional in time is found as well. Thus, the minimization problem can be formulated. The modeling in this direction is being developed to a new simple modeling of the dense gas dynamics. (2) A stochastic numerical code that simulates the gas transport in the porous media has been developed. It is used to accumulate the big data, which are used in the combination with the percolation theory to develop a new simple kinetic model that give a good prediction for the mass flow conductance against a give pressure difference. (3) From the viewpoint of thermal bath concept, the conventional boundary condition for kinetic equation is revisited, which leads to finding a Langevin picture (a stochastic dynamical picture) of the Cercignani-Lampis model.

Academic Significance and Societal Importance of the Research Achievements

本研究では,「熱浴」という概念を介在させることで,種々の現象をなるべく単純かつ効率よく,統一的に扱う考え方を提案し,一定の成果を収めた.例えば,合金の相分離の模擬に典型的に用いられるカーン・ヒリアード型の方程式を,気体を対象としてきた運動論方程式から導いた報告例はこれまでなかった.このことは,細胞のコロニー形成の運動論モデルを模索する研究者たちにも注目された.また,多孔質内気体輸送では,従前の運動論コミュニティでとられるものとは全く異なるアプローチをとり,別途発展してきたパーコレーション理論との融合により,簡便な運動論モデルを提案することができ,大幅な解析の簡易化に道筋をつけた.

Report

(5 results)
  • 2020 Annual Research Report   Final Research Report ( PDF )
  • 2019 Research-status Report
  • 2018 Research-status Report
  • 2017 Research-status Report
  • Research Products

    (22 results)

All 2021 2020 2019 2018 2017

All Journal Article (5 results) (of which Peer Reviewed: 5 results) Presentation (17 results) (of which Int'l Joint Research: 7 results,  Invited: 8 results)

  • [Journal Article] A revisit to the Cercignani--Lampis model: Langevin picture and its numerical simulation2021

    • Author(s)
      S. Takata, S. Akasobe, and M. Hattori
    • Journal Title

      Recent advances in kinetic equations and applications, Springer INdAM Series

      Volume: -

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Modeling of gas transport in porous medium: Stochastic simulation of the Knudsen gas and a kinetic model with homogeneous scatterer2020

    • Author(s)
      Takata Shigeru、Hatakenaka Kisho、Hattori Masanari、Kasahara Fumiyoshi
    • Journal Title

      Physics of Fluids

      Volume: 32 Issue: 10 Pages: 102004-102004

    • DOI

      10.1063/5.0024636

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On the entropic property of the Ellipsoidal Statistical model with the prandtl number below 2/32020

    • Author(s)
      Takata Shigeru、Hattori Masanari、Miyauchi Takumu
    • Journal Title

      Kinetic & Related Models

      Volume: 13 Issue: 6 Pages: 1163-1174

    • DOI

      10.3934/krm.2020041

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A Simple Kinetic Model for the Phase Transition of the van der Waals Fluid2018

    • Author(s)
      Takata Shigeru、Noguchi Takashi
    • Journal Title

      Journal of Statistical Physics

      Volume: 172 Issue: 3 Pages: 880-903

    • DOI

      10.1007/s10955-018-2068-z

    • Related Report
      2018 Research-status Report
    • Peer Reviewed
  • [Journal Article] Kinetic theory for a simple modeling of a phase transition: Dynamics out of local equilibrium2018

    • Author(s)
      Takata Shigeru、Matsumoto Takuya、Hirahara Anna、Hattori Masanari
    • Journal Title

      Physical Review E

      Volume: 98 Issue: 5 Pages: 052123-052123

    • DOI

      10.1103/physreve.98.052123

    • Related Report
      2018 Research-status Report
    • Peer Reviewed
  • [Presentation] Some attempts on the simple kinetic modeling of dense gases with phase changes2021

    • Author(s)
      Shigeru Takata
    • Organizer
      JSPS/SAC Seminar on Gas Kinetic/Dynamics ans Life Science
    • Related Report
      2020 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Prandtl数が2/3を下回るEllipsoidal Statisticalモデルのエントロピー特性2020

    • Author(s)
      宮内 拓夢
    • Organizer
      日本流体力学会 年会2020
    • Related Report
      2020 Annual Research Report
  • [Presentation] Van der Waals流体の相分離に関する分子運動論的解析:局所場近似を外力に用いないモデル2020

    • Author(s)
      川村健人,髙田滋
    • Organizer
      第2回先端流体理工学研究部門公開セミナー
    • Related Report
      2019 Research-status Report
  • [Presentation] A revisit to the Cercignani-Lampis model: Langevin picture and its numerical simulation2019

    • Author(s)
      Shigeru Takata
    • Organizer
      INdAM workshop on "Recent advances in kinetic equations and applications"
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] 多孔質内気体のKnudsen 拡散: 粒子シミュレーションと均質化モデルの換算Knudsen 数2019

    • Author(s)
      畠中貴翔
    • Organizer
      第1回先端流体理工学研究部門公開セミナー
    • Related Report
      2018 Research-status Report
  • [Presentation] A construction of kinetic model for nonideal gases2018

    • Author(s)
      Shigeru Takata
    • Organizer
      31st International Symposium on Rarefied Gas Dynamics
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Kinetic model for the phase transition of the van derWaals fluid2018

    • Author(s)
      Shigeru Takata
    • Organizer
      12th AIMS Conference on Dynamical Systems, Differential Equations and Applications
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] A simple kinetic model for phase transition2018

    • Author(s)
      Shigeru Takata
    • Organizer
      International Workshop on kinetic theory and related topics
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Kinetic theory for a simple modeling of phase transition2018

    • Author(s)
      Shigeru Takata
    • Organizer
      慶應大学「非線形解析セミナー」
    • Related Report
      2018 Research-status Report
    • Invited
  • [Presentation] Cercignani--Lampis モデルのLangevin 系:力学的描像と数値シミュレーション2018

    • Author(s)
      赤曽部成寛
    • Organizer
      日本流体力学会年会2018
    • Related Report
      2018 Research-status Report
  • [Presentation] 相変化記述のための簡単な運動論モデル2018

    • Author(s)
      平原杏奈
    • Organizer
      日本流体力学会年会2018
    • Related Report
      2018 Research-status Report
  • [Presentation] Cercignani--Lampis モデルのLangevin 系: 力学的描像と数値シミュレーション2018

    • Author(s)
      高田滋
    • Organizer
      第55回中部・関西支部合同秋期大会
    • Related Report
      2018 Research-status Report
  • [Presentation] A kinetic model for the phase transition of the van der Waals fluid2017

    • Author(s)
      S. Takata
    • Organizer
      Workshop ``Recent advances in kinetic equations and applications''
    • Related Report
      2017 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Kinetic model for the phase transition of the van der Waals fluid2017

    • Author(s)
      S. Takata
    • Organizer
      International Confer- ence on Nonlinear Analysis: Kinetic Theory, Gas Dynamics, and Related Fields
    • Related Report
      2017 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] ファンデルワールス流体に対する相変化の運動論モデル2017

    • Author(s)
      高田滋,野口尚史
    • Organizer
      第54回日本航空宇宙学会関西・中部支部合同秋期大会
    • Related Report
      2017 Research-status Report
  • [Presentation] 気流により二次元的に流動化された粒子群の運 動の統計解析2017

    • Author(s)
      小山志穂里,松野友樹,野口 尚史
    • Organizer
      第54回日本航空宇宙学会関西・中部支部合同秋期大会
    • Related Report
      2017 Research-status Report
  • [Presentation] 気流により流動化した単粒子層の運動の 統計解析2017

    • Author(s)
      小山志穂里,松野友樹,野口 尚史
    • Organizer
      日本流体力学会 年会 2017
    • Related Report
      2017 Research-status Report

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Published: 2017-07-21   Modified: 2022-12-28  

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