Category Archives: Seminars

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.

分科会「運動論方程式,流体力学とその周辺」(第1回)

日時: 平成29年4月5日(水) 16:00-17:00
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: Swarming Models with Repulsive-Attractive Effects
Prof. Jose Antonio Carrillo (Department of Mathematics, Imperial College London, UK)
要旨: I will present a survey of the main results about first and second order models of swarming where repulsion and attraction are modeled through pairwise potentials.  We will mainly focus on the stability of the fascinating patterns that you get by random data particle simulations, flocks and mills, and their qualitative behavior. I will give an overview of the different levels of description of collective behavior models highlighting some of the interesting mathematical open problems in the subject. Calculus of variations, dynamical systems, mean-field limits for PDEs, control theory, kinetic and aggregation-diffusion equations together with their numerical simulations naturally show up as necessary tools to solve some of these questions.

分科会「非平衡現象の流体力学」(第25回)

日時: 平成28年12月26日(月) 16:00-17:00
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: Global well-posedness for Boltzmann equations with a class of large oscillating data
Prof. Renjun Duan (Department of Mathematics, The Chinise University of Hong Kong, China)
要旨: The global well-posedness of the Boltzmann equation with initial data of large
amplitude has remained a long-standing open problem. In this talk, we shall present a recent
result on the global existence and uniqueness of mild solutions to the Boltzmann equation in
the whole space or torus for a class of initial data whose amplitude can be arbitrarily large but
close to global Maxwellians in some integrable space. The large time behavior of solutions with
such large oscillating data is also obtained with the explicits rate of convergence to equilibrium
states.

分科会「非平衡現象の流体力学」(第24回)

日時: 平成28年11月8日(火) 16:00-17:00
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: Elastic mechanical response of amorphous solids
Prof. Hideyuki Mizuno (Department of Basic Science, 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 相関基礎科学系
要旨: While the classical theory of linear elasticity of solids is based on the concept of affineness, which is applicable to ordered crystalline materials whereby the constituent particles follow the imposed, homogeneous, affine deformation field. For amorphous materials, the particles also undergo inhomogeneous, non-affine displacements, which influence their mechanical response. To correctly understand the elastic modulus of amorphous materials, it is therefore necessary to take into account not only the affine component of the modulus, but also the non-affine component, that arises from energy relaxation during these non-affine deformations. In the present work, we execute a comprehensive analysis on the non-affine component, in static jammed amorphous packings of mono-disperse, deformable, frictionless spheres, which is directly related to the vibrational eigen modes of the system. We also elucidate the contribution of each vibrational mode to the non-affine modulus, which is achieved through an eigen-mode decomposition analysis.

Reference: H. Mizuno, K. Saitoh, and L. E. Silbert, Physical Review E 93, 062905 (2016).

分科会「非平衡現象の流体力学」(第23回)

日時: 平成28年9月13日(火) 14:45-16:45
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: PDE-based modelling of biological network formation
Dr. Jan Haskovec (Applied Mathematics and Computational Science, King Abdullah University of Science and Technology, Kingdom of Saudi Arabia)
要旨1: Motivated by recent papers describing rules for natural network formation in discrete settings, we propose  an elliptic-parabolic system of partial differential equations. The model describes the pressure field due to Darcy’s type equation and the dynamics of the conductance network under pressure force effects with a diffusion rate representing randomness in the material structure. We prove the existence of global weak solutions and of local mild solutions and study their long term behavior. Moreover, we study the structure and stability properties of steady states that play a central role to understand the pattern capacity of the system. We show that patterns (network structures) occur in the regime of small material randomness. Moreover, we present results of systematic numerical simulations of the system that provide further insights into the properties of the network-type solutions.
講演2: Transport phenomena in evolutionary domains
Prof. Francesco Salvarani
(CEREMADE – Université Paris-Dauphine, France & Dipartimento di Matematica, Università di Pavia, Italy)
要旨2:  We study the transport equation in a time-dependent vessel with absorbing boundary, in any space dimension. We first prove existence and uniqueness, and subsequently we consider the problem of the time-asymptotic convergence to equilibrium. We show that the convergence towards equilibrium heavily depends on the initial data and on the evolution law of the vessel.
Subsequently, we describe a numerical strategy to simulate the problem, based on a particle method implemented on general-purpose graphics processing units (GPGPU). We observe that the parallelization  procedure on GPGPU allows for a marked improvement of the performances when compared with the standard approach on CPU.

分科会「非平衡現象の流体力学」(第22回)

平成28年度第1回講演会(日本航空宇宙学会関西支部分科会)

日時: 平成28年4月7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: PDE modeling of Biological Transportation Networks
Prof. Peter Markowich
(DAMTP, Centre for Mathematical Sciences, University of Cambridge, UK)
要旨: We present a PDE model for the evolution and adaption of biological transportation networks. The model is based on the  Kirchhoff (conservation) law, Darcy’s law for porous media flows and local network energy minimization.  In particular we discuss qualitative (existence, uniqueness and regularity) and quantitative (this structures and steep local gradients) features  of the solutions.

分科会「非平衡現象の流体力学」(第21回)

平成27年度第8回講演会(日本航空宇宙学会関西支部分科会)
** ミニコースレクチャー **

日時: 平成28年2月4日(木)-5日(金)
PART1  2月4日(木) 16:30-17:30
PART2  2月5日(金) 14:45-15:45
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: Derivation of models for aerosol/spray flows
Prof. François Golse
(Centre de mathématiques Laurent Schwartz, Ecole Polytechnique, France)
要旨: This mini-course presents a strategy based on the kinetic theory of gases for deriving models for spray flows involving a fluid dynamical equation for the propellant and a kinetic model for the dispersed phase. The starting point is a coupled system of Boltzmann type equations for a binary gaseous mixture, where the dispersed phase and the propellant are described by the methods of kinetic theory. Asymptotic regimes leading to the Vlasov-Stokes and Vlasov-Navier-Stokes systems are identified.
The key idea is that dust particles or droplets in a spray are much heavier than gas molecules, so that the effect of a collision between any such particle and a gas molecule results in a small deflection angle in the trajectory of the particle. Therefore, we identify a grazing collision regime for the dispersed phase, which can be adequately described by a Vlasov type equation. Various models for the interaction between the gas molecules and the particles in the dispersed phase are discussed.

分科会「非平衡現象の流体力学」(第20回)

平成27年度第7回講演会(日本航空宇宙学会関西支部分科会)

日時: 平成27年11月13日(金) 13:30-14:30
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: Diffuse interface modeling of subcritical and supercritical flames
Prof. Vincent Giovangigli
(Centre de Mathematiques Appliquees, Ecole Polytechnique, France)
要旨: During the ignition of rocket engines, or in Diesel engines, a transition may occur from subcritical to supercritical pressure conditions and such dynamics cannot be described by current fluid models. There is thus a need for models that transition smoothly from subcritical to supercritical pressure conditions.
With this aim in mind we present a liquid/gas diffuse interface model of Van der Waals/Korteweg type valid at all pressures. In the subcritical regime, the model describes
the continuous interface between a liquid and a gas mixture whereas in the supercritical domain the model thickens high density gradient zones. The interface model is further
embedded into a nonideal multicomponent reactive fluid framework. The resulting equations are used to investigate the interface between cold dense and hot light oxygen as well as the structure of diffusion flames between cold dense oxygen and gaseous like hydrogen at all pressures, either subcritical or supercritical.