慶應義塾大学 理工学部 数理科学科
平成30年度

セミナー案内

セミナー案内

タイトル | Kinetic theory for a simple modeling of phase transition |
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開催日時 |
2018年10月24日 16:45 ～ |

主催者 | |

講演者 | 高田 滋 氏（京大・工） |

場所 | 慶應義塾大学理工学部 14棟 734 (創想館 7階 ミーティング4) |

内容 | A simple kinetic model, which is presumably minimum, for the phase transition of the van der Waals fluid is presented. In the model, intermolecular collisions for a dense gas has not been treated faithfully. Instead, the expected interactions as the non-ideal gas effect are confined in a self-consistent force term. Collision term plays just a role of thermal bath. Accordingly, it conserves neither momentum nor energy, even globally. It is demonstrated that (i) by a natural separation of the mean-field self-consistent potential, the potential for the non-ideal gas effect is determined from the equation of state for the van der Waals fluid, with the aid of the balance equation of momentum, (ii) a functional which monotonically decreases in time is identified by the H theorem and is found to have a close relation to the Helmholtz free energy in thermodynamics, and (iii) the Cahn--Hilliard-type equation is obtained in the continuum limit of the present kinetic model. Numerical simulations have also been carried out for both the Cahn--Hilliard-type equation and the kinetic equation to demonstrate the occurrence of phase transition from unstable uniform equilibrium states. The present talk is based on the references below. [1] S. Takata and T. Noguchi, J. Stat. Phys., Vol. 172, 880 (2018) [2] S. Takata, T. Matsumoto, A. Hirahara, and M. Hattori, arxiv:1807.04630 |

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