慶應義塾大学 理工学部 数理科学科

非線形解析セミナー

タイトル Kinetic theory for a simple modeling of phase transition
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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