Modeling and experiments on thermophoresis in microfluidic systems
Prof. Tetsuro Tsuji (Department of Advanced Mathematical Sciences, Kyoto University, Japan) 辻徹郎 准教授（京都大学大学院 情報学研究科 先端数理科学専攻）
Thermophoresis is the motion of tiny particles induced by the temperature gradient of surrounding fluids. Recent advances in experimental techniques to produce a steep temperature gradient in fluids have developed novel manipulation methods of nano- and microscale materials using thermophoresis. In the present talk, some trials to understand thermophoresis and its applications to microfluidics will be presented. More specifically, in the first part of the talk, a kinetic model on thermophoresis of Brownian particles is introduced to elucidate the mass effect on thermophoretic mobility. Furthermore, a molecular dynamics simulation is carried out to investigate the effect of interaction potential on the direction of thermophoretic motion. The second part of the talk will include the results of some microfluidic experiments. The aims of the experiments are two-fold: one is to obtain fundamental characteristics of thermophoresis and the other is to apply thermophoresis in microfluidic devices for concentration and separation. Some ongoing trials to investigate the origin of thermophoresis will be also presented.
Kinetic description of polyatomic gases undergoing resonant collisions
Prof. Francesco Salvarani (Pôle Universitaire Léonard de Vinci, France & Dipartimento di Matematica, Università di Pavia, Italy)
This talk is devoted to the study of a kinetic model describing a polyatomic gas in which the microscopic internal and kinetic energies are separately conserved during a collision process (resonant collisions). This behaviour has been observed in some physical phenomena, for example in the collisions between selectively excited CO2 molecules. After describing the model itself, we prove the related H-theorem and show that, at the equilibrium, two temperatures are expected. We moreover prove a compactness property of the corresponding linearized Boltzmann operator. The peculiar structure of resonant collision rules allows to tensorize the problem and separately treat the internal energy contributions. We also propose a geometric variant of Grad’s proof of the compactness property in the monatomic case.
Spectroscopy of the asteroid Ryugu: Access to the records of our ancient Solar System
Dr. Eri Tatsumi (Instituto de Astrofísica de Canarias, Spain) 巽 瑛理 氏 （カナリア天体物理学研究所）
Asteroids are building blocks of planets and keep the compositional information of the early Solar System. Especially the primitive asteroids, which are characterized by dark surfaces, are the key for water and organics on the Earth. My approach to constrain the composition and its evolusion on asteroids is the telescopic and remote-sensing observations. Recently the Hayabusa2 spacecraft by JAXA brought the sample materials from the primitive asteroid (162173) Ryugu. The sample return mission can connect the spectroscopic information to the compositional information directly, which gives strong constrains to our knowledge of the ancient Solar System. In this talk, the spectroscopic results of Ryugu from the Hayabusa2 remote-sensing observations and ground-based observations will be discussed. The Hayabusa2 spacecraft equipped the multi-band Optical Navigation Camera (ONC) which mapped the whole surface of Ryugu up to 5 cm/pix in visible wavelengths. Using the images obtained by ONC, we could extract the evolutional history of Ryugu such as the parent body history, the impact history, and the recent trajectry changes. Besides, it is important to put the asteroid in the context of the Solar System. To do this, we investigated the distribution of the asteroids which have the similar spectral feature to Ryugu. Especially the UV region is useful to characterize hydrated minerals on asteroids. We found the very peculiar distribution of the asteroid with the spectral feature similar to Ryugu. Connecting the spectra to the material information which will be brought from the Ryugu sample analyses will make a new compositional map of the Solar System.
New lattice Boltzmann model for simulating compressible flows
Prof. Takeshi Kataoka (Department of Mechanical Engineering, Kobe University, Japan) 片岡 武 准教授 （神戸大学大学院 工学研究科 機械工学専攻）
We have developed a new type of simple lattice Boltzmann (LB) model for the compressible Euler and NS equations based on the kinetic-equation approach proposed by Sone in 2002. The model uses the kinetic equation of the free-molecular type in the streaming process, and modifies the distribution function to its Chapman-Enskog type in the collision process. Compared with the conventional LB models which solve the kinetic equation of the BGK type, the proposed model is superior in the following two points: (i) any flow parameters, including the specific-heat ratio and three transport coefficients, can be chosen freely according to our convenience; (ii) there are no inherent errors associated with the Knudsen number. Numerical tests and error estimates confirm these merits.
Mathematical analysis of Chorin’s projection method
Prof. Kohei Soga (Department of Mathematics, Faculty of Science and Technology, Keio University, Japan) 曽我 幸平 准教授 （慶應義塾大学 理工学研究科 基礎理工学専攻）
Chorin’s projection method, originally introduced by Alexandre Joel Chorin in 1969, is a numerical technique of computational fluid dynamics. The method can be seen as the most elementary and direct approach to solve the incompressible Navier-Stokes equations in a general setting. Nowadays, many versions of the original method are known. In this talk, we revisit Chorin’s original projection method and discuss its potential to be a mathematical tool beyond a computational technique for smooth solutions. We first observe that the method yields a Leray-Hopf weak solution. Then, we apply the method to investigate time-periodic solutions, which is an attempt to capture qualitative features of flows through discrete approximation. Finally, we investigate the accuracy of the method.
Recent Developments of Nonequilibrium Thermodynamic Theories of Gases
Prof. Takashi Arima (Department of Engineering for Innovation, National Institute of Technology, Tomakomai College, Japan) 有馬 隆司 准教授 （苫小牧工業高等専門学校 創造工学科 総合自然科学系）
Nonequilibrium thermodynamic theories of continuous media of which applicable range goes beyond the local thermodynamic equilibrium have been developed. Starting from the pioneering works of Grad in the context of kinetic theory, of Cattaneo for a rigid heat conductor, and of Müller for the first phenomenological version of extended thermodynamics, several attempts have been made, for example, Rational Extended Thermodynamics, Extended Irreversible Thermodynamics, General Equation for the Nonequilibrium Reversible–Irreversible Coupling, the regularized moment approach, and others.
In this talk, we present the state of the art on these modern nonequilibrium theories focusing on Rational Extended Thermodynamics. In particular, we consider rarefied gases and discuss the linkage with the kinetic theory. Conceptual discussions of the differences among these nonequilibrium theories are also summarized.
Some formulations of the volume force in the immersed boundary method and a new approach in combination with the lattice Boltzmann method
Prof. Kosuke Suzuki (Institute of Engineering, Academic Assembly, Shinshu University, Japan) 鈴木 康祐 准教授 （信州大学 学術研究院 (工学系) ）
One of the important issues in computational fluid dynamics is to simulate moving-boundary flows efficiently. The immersed boundary method (IBM), which was proposed by Peskin in 1970s in order to simulate blood flows in the heart, has been reconsidered as an efficient method for simulating moving-boundary flows on a fixed Cartesian grid. In the IBM, it is assumed that the boundary is regarded as an infinitely thin shell, an incompressible viscous fluid fills in both inside and outside of the boundary, and the no-slip condition on the boundary is satisfied by volume force applied only near the boundary. The way to determine the volume force is the key concept of the IBM. In this talk, I introduce some formulations of the volume force in the IBM. Then, I present a new approach in combination with the lattice Boltzmann method (LBM). In this approach, the volume force of the IBM is regarded as the discontinuity of the stress tensor, and the stress tensor is calculated from the desired particle distribution functions of the LBM. This approach enables us to calculate the stress tensor on the boundary which is blurred by the volume force.
Mathematical Analysis of Moving Boundary Problems in the Kinetic Theory of Gases
Dr. Kai Koike (Department of Aeronautics and Astronautics, Graduate School of Engineering, Kyoto University, Japan) 小池 開 氏 （日本学術振興会 特別研究員(PD)）
Moving boundary problems for kinetic equations have become an active area of research mainly due to its importance in MEMS applications. It has also proved to be a source of interesting mathematical problems. Despite this, it’s mathematical theory has not developed to a satisfactory level although there are some recent progresses. In this talk, I would like to review these results hoping to stir interaction between the engeneering and the mathematical community further, which has always been an important element in this field.