Category Archives: Kinetic theory, fluid dynamics, and related topics

分科会「運動論方程式,流体力学とその周辺」(第11回)

日時: 2019年12月19日(木)16:15-17:15
場所: 京都大学 桂キャンパスCクラスタ総合研究棟III(C3棟)3階 b3n03室(航空宇宙工学専攻会議室)
講演: Solid-state physics of glasses
Hideyuki Mizuno, PhD (Graduate School of Arts and Sciences, The University of Tokyo, Japan)
水野 英如 助教 (東京大学 大学院総合文化研究科 広域科学専攻)
要旨: In our lives, there are two types of solid-states materials. One is crystals, and the other is noncrystalline, glasses. We already have a good level of understanding of crystals. Their thermal and transport properties can be described in terms of phonons; their heat capacity and thermal conductivity are well described by the Debye theory and the phonon-gas theory, respectively. By contrast, we have only a limited understanding of glasses that exhibit fundamentally different properties from those of crystals. Because glasses are materials commonly encountered in our daily lives and are widely employed in modern technologies (examples include silicate glasses, metallic glasses, plastic materials, ceramics, and many other rigid, disordered materials), their understanding is crucial not only in physics and materials science but also in engineering. In this seminar, I would introduce the latest progress in understanding of glasses.

分科会「運動論方程式,流体力学とその周辺」(第10回)

普段とは違い,場所は吉田キャンパスです.ご注意ください.

日時: 2019年11月1日(金)16:30-17:30
場所: 京都大学 吉田キャンパス 工学部総合校舎 111講義室
講演: On the homogenization problem for the linear Boltzmann equation
Prof. Francesco Salvarani (CEREMADE – Université Paris-Dauphine, France & Dipartimento di Matematica, Università di Pavia, Italy)
要旨: In this talk, we study the homogenization problem for the linear Boltzmann equation when the optical parameters are highly heterogeneous in the energy variable. We employ the method of two-scale convergence to arrive at the homogenization result. In doing so, we show the induction of a memory effect in the homogenization limit and we discuss its link with the self-shielding effect in nuclear reactor physics. The results presented here have been obtained in collaboration with Harsha Hutridurga and Olga Mula.

分科会「運動論方程式,流体力学とその周辺」(第9回)

日時: 2019年7月23日(火)16:15-17:15
場所: 京都大学 桂キャンパスCクラスタ総合研究棟III(C3棟)3階 b3n03室(航空宇宙工学専攻会議室)
講演: Compressible fluid approximation for rarefied gases in bounded domains
Prof. Renjun Duan (Department of Mathematics, The Chinese University of Hong Kong, Hong Kong)
要旨: In this talk I will talk about two recent results on the mathematical justification of the compressible viscous fluid approximation of solutions to the Boltzmann equation in bounded domains when the Knudsen number is small. The first result is concerned with the situation where the diffusive reflection boundary condition is considered and the fluid equations are solved under the non-slip boundary conditions. The second result is focused on a specific case of the one-dimensional heat transfer for a steady rarefied gas flow between two parallel plates with diffusive reflection boundaries of different temperatures where the temperature difference is small but does not depend on the Knudsen number, and we show the existence of steady solutions by taking the approximation of fluid equations with slip boundaries together with the Knudsen layer equations.

分科会「運動論方程式,流体力学とその周辺」(第8回)

日時: 2019年5月14日(火)16:15-17:15
場所: 京都大学 桂キャンパスCクラスタ総合研究棟III(C3棟)3階 b3n03室(航空宇宙工学専攻会議室)
講演: The Mpemba and Kovacs effects in granular gases
Prof. Andrés Santos (Department of Physics, Universidad de Extremadura, Spain)
要旨: Experimental observations reveal that the response to an excitation in a complex condensed matter system may depend on the entire system’s history, and not just on the instantaneous value of the macroscopic state variables. These memory effects signal the breakdown of the macroscopic description. Some typical memory effects include shape memory in polymers, aging and rejuvenation in spin glasses, active matter, and granular gases. In this talk I will focus on the last class of systems and consider two prototypical memory phenomena: the Mpemba and Kovacs effects. The Mpemba effect is a counterintuitive phenomenon according to which, given two samples of fluid, the initially hotter one may cool more rapidly than the initially cooler one. In the Kovacs effect, a system relaxing to a low temperature is suddenly put in contact with a reservoir at the same temperature as the instantaneous value the system has after a given waiting time; however, the system’s temperature does not remain constant but exhibits a nonmonotonic evolution before reaching its asymptotic steady value. Both the Mpemba and Kovacs effects in granular gases will be addressed by minimal descriptions based on kinetic theory, the theoretical predictions being numerically confirmed by the direct simulation Monte Carlo method and by event-driven molecular dynamics.

分科会「運動論方程式,流体力学とその周辺」(第7回)

日時: 2019年1月18日(金) 16:30-17:30
場所: 京都大学 桂キャンパスCクラスタ総合研究棟III(C3棟) 3階 b3n03室(航空宇宙工学専攻会議室)
講演: Data-driven modelling of dynamical system based on delay-embedding
Prof. Naoto Nakano (Center for Innovative Research and Education in Data Science, Institute for Liberal Arts and Sciences & Graduate School of Science, Kyoto University, Japan)
中野 直人 講師 (京都大学 国際高等教育院附属データ科学イノベーション教育研究センターおよび理学研究科)
要旨: Delay embedding is well-known for non-linear time-series analysis, and it is used in several research fields such as physics, informatics, neuroscience and so forth. The celebrated theorem of Takens (1981) ensures validity of the delay embedding analysis: embedded data preserves topological properties which the original dynamics possesses. This method is easy to implement for time-series analysis, however, resultant embedded dataset may easily vary with the delay width and the delay dimension, namely, “the way of embedding”. In a practical sense, this sensitivity may sometimes interfere with users’interpretation of embedded objects. In this study, to derive an appropriate embedding Ansatz, we investigate the mathematical structure of delay-embedding from a view point of linear operator theory. In this talk, we will briefly overview its framework, and we will show some numerical results of time-series analysis by the present method. For example, prediction, attractor reconstruction, causality detection and control problems.

分科会「運動論方程式,流体力学とその周辺」(第6回)

日時: 平成30年8月24日(金) 15:00-17:00
場所: 京都大学 桂キャンパスCクラスタ総合研究棟III(C3棟) 3階 b3n03室(航空宇宙工学専攻会議室)
講演1: Entropy methods and cross-diffusion systems: derivation and entropy structure
Prof. Ansgar Jüngel
(Institute for Analysis and Scientific Computing, Vienna University of Technology, Austria)
要旨1: Nature is dominated by systems composed of many individuals, belonging to various species, with a collective behavior. Instead of calculating the trajectories of all individuals, it is computationally much simpler to describe the dynamics of the individuals on a macroscopic level by averaged quantities such as population densities. This leads to systems of highly nonlinear partial differential equations with cross diffusion, which may reveal surprising effects such as uphill diffusion and diffusion-induced instabilities. In this talk, we detail some approaches on the derivation of cross-diffusion equations from kinetic, fluiddynamical, and stochastic models. Relations to thermodynamic principles and the results of Kawashima and Shizuta are detailed. The entropy structure can also be found in nonstandard applications like van-der-Waals fluids, population dynamics, and exotic financial derivatives. It allows for a mathematical existence theory and stable numerical approximations with guaranteed lower and upper bounds.
講演2: Linear Boltzmann equation and fractional diffusion
Prof. François Golse
(Centre de mathématiques Laurent Schwartz, Ecole Polytechnique, France)
要旨2: Consider the linear Boltzmann equation of radiative transfer in a half-space, with constant scattering coefficient σ. Assume that, on the boundary of the half-space, the radiation intensity satisfies the Lambert (i.e. diffuse) reflection law with albedo coefficient α. Moreover, assume that there is a tem- perature gradient on the boundary of the half-space, which radiates energy in the half-space according to the Stefan-Boltzmann law. In the asymptotic regime where σ → +∞ and 1 – α ~ C/σ, we prove that the radiation pressure exerted on the boundary of the half-space is governed by a fractional diffusion equation. This result provides an example of fractional diffusion asymptotic limit of a kinetic model which is based on the harmonic extension definition of √-Δ. This fractional diffusion limit therefore differs from most of other such limits for kinetic models reported in the literature, which are based on specific properties of the equilibrium distributions (“heavy tails”) or of the scattering coefficient as in [U. Frisch-H. Frisch: Mon. Not. R. Astr. Not. 181 (1977), 273-280].

分科会「運動論方程式,流体力学とその周辺」(第5回)

日時: 平成30年7月17日(火) 16:30-17:30
場所: 京都大学 桂キャンパスCクラスタ総合研究棟III(C3棟) 3階 b3n03室(航空宇宙工学専攻会議室) 1階 b1S01室(講義室2)
講演: A new approach for Burger’s equation without Hopf-Cole transform
Prof. Shih-Hsien Yu (Department of Mathematics, National University of Singapore, Singapore)
要旨: In this talk, we will give a different approach to study the Burger’s equation. It will reveal the role “nonlinearity” when to become significant in terms of analysis.

分科会「運動論方程式,流体力学とその周辺」(第4回)

日時: 平成30年4月24日(火) 16:30-17:30
場所: 京都大学 桂キャンパスCクラスタ総合研究棟III(C3棟) 3階 b3n03室(航空宇宙工学専攻会議室)
講演: Shock Wave Theory and Boltzmann Equation
Prof. Tai-Ping Liu (Institute of Mathematics, Academia Sinica, Taiwan & Professor Emeritus, Department of Mathematics, Stanford University, USA)
要旨: Over the years, the speaker and Shih-Hsien Yu have tried to generalized the techniques in the shock wave theory for the study of the Boltzmann equation. We soon found out that there are similarities and also essential differences between the two fields. Specific examples will be given to illustrate this. We will start with the construction of the Green’s function for viscous conservation laws and for the Boltzmann equation. We then proceed with examples on nonlinear waves and boundary phenomena.

分科会「運動論方程式,流体力学とその周辺」(第3回)

日時: 平成29年12月14日(木) 16:30-17:30
場所: 京都大学 桂キャンパスCクラスタ総合研究棟III(C3棟) 3階 b3n03室(航空宇宙工学専攻会議室)
講演: Self-organized pattern formation of run-and-tumble chemotactic bacteria
Prof. Shugo Yasuda (Graduate School of Simulation Studies, University of Hyogo, Japan)
安田 修悟 准教授 (兵庫県立大学 大学院シミュレーション学研究科 シミュレーション学専攻)
要旨: Self-organized pattern formation of run-and-tumble chemotactic bacteria is investigated based on a mesoscopic kinetic chemotaxis model, in which a kinetic transport equation for chemotactic bacteria is coupled with a reaction-diffusion equation for chemical cues. The instability analysis of the kinetic chemotaxis model [1] and the traveling wave analysis of the related flux-limited Keller-Segel system [2] are introduced in this talk. The special focus is put on the multiscale mechanism between the macroscopic pattern formation and individual motions of chemotactic bacteria with stiff response.

References:
[1] B. Perthame, S. Yasuda, “Self-organized pattern formation of run-and-tumble chemotactic bacteria: Instability analysis of a kinetic chemotaxis model”, arXiv: 1703.08386.
[2] V. Calvez, B. Perthame, S. Yasuda, “Traveling wave and aggregation in a flux-limited Keller-Segel model”, arXiv: 1709.07296.

分科会「運動論方程式,流体力学とその周辺」(第2回)

日時: 平成29年10月25日(水) 16:00-18:00
場所: 京都大学 桂キャンパスCクラスタ総合研究棟III(C3棟) 3階 b3n03室(航空宇宙工学専攻会議室)
講演1: Behaviors of Navier-Stokes(Euler)-Fokker-Planck equations
Prof. Hailiang Li
(Department of Mathematics, Capital Normal University, China)
要旨1: We consider the behaviors of global solutions to the initial value problems for the multi-dimensional compressible Navier-Stokes(Euler)-Fokker-Planck equations. It is shown that due the micro-macro coupling effects, the sound wave type propagation of this NSFP or EFP system for two-phase fluids is observed with the wave speed determined by the two-phase fluids. This phenomena can not be observed for the pure Fokker-Planck equation.
講演2: Cross diffusion equations for non-isothermal gaseous mixtures
Prof. Francesco Salvarani
(CEREMADE – Université Paris-Dauphine, France & Dipartimento di Matematica, Università di Pavia, Italy)
要旨2: The diffusive behavior of multicomponent gaseous mixtures has recently gained interest in the mathematical community. In this talk, I will study a system describing diffusive phenomena for a mixture in a non-isothermal setting. I will prove local existence and uniqueness of the solution and discuss some effects of the temperature
on the mixture’s behavior.