Shigeru Takata
Shigeru
Takata (Kyoto University, Japan)
Shigeru Takata is a fluid-dynamics and kinetic theory researcher who graduated from Kyoto University with a B.S. in 1989, a M.Eng. in 1991, and a D.Eng. in 1994. His main research interest is gas flows in low pressure circumstances, fluid flows with phase change, and related non-equilibrium phenomena. He is currently a full professor at the Department of Aeronautics and Astronautics, Kyoto University. He is also a member of the Advisory Committee of the International Symposium on Rarefied Gas Dynamics, a fellow member of the Japan Society of Fluid Mechanics, and a member of editorial board of Networks and Heterogeneous Media.
Title: Single droplet/bubble and its stability: Kinetic theory and dynamical system approaches
Abstract: Steady solutions of a single droplet/bubble in the van der Waals fluid are investigated on the basis of the kinetic model equation that has been recently proposed by Miyauchi et al. [Gas Dynamics with Applications in Industry and Life Sciences (Springer, Cham, 2023), Vol. 429, pp. 19-39]. Under the thermal equilibrium condition and isotropic assumption with respect to the origin of the coordinates, the kinetic equation is reduced to an ordinary differential equation for the density, which can be regarded as a low-dimensional dynamical system. The possible density distribution is studied as a "flow" in the low-dimensional phase space. It is clarified that a single droplet or bubble can be understood as a "flow" that goes into a fixed point and that the "flow" is qualitatively different in the unstable and metastable parameter regions. The features of the obtained density distributions in individual regions are also clarified. Finally, the stability of those solutions is studied by direct numerical experiments of the kinetic equation. The present talk is based on a joint work with Takumu Miyauchi.
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