2020 Fiscal Year Final Research Report
Study on feasibility of the kinetic equation with thermal bath
| Project/Area Number |
17K18840
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| Research Category |
Grant-in-Aid for Challenging Research (Exploratory)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Fluid engineering, Thermal engineering, and related fields
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| Research Institution | Kyoto University |
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Principal Investigator |
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| Project Period (FY) |
2017-06-30 – 2021-03-31
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| 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 |
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| 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.
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| Free Research Field |
分子気体力学
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| 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．
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