|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 ～|
|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.
 S. Takata and T. Noguchi, J. Stat. Phys., Vol. 172, 880 (2018)
 S. Takata, T. Matsumoto, A. Hirahara, and M. Hattori, arxiv:1807.04630