日時：  平成29年4月5日（水） 16:0017:00 
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 RepulsiveAttractive 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, meanfield limits for PDEs, control theory, kinetic and aggregationdiffusion equations together with their numerical simulations naturally show up as necessary tools to solve some of these questions. 
Author Archives: Shigeru Takata
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） 16:0017:00 
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 wellposedness 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 wellposedness of the Boltzmann equation with initial data of large amplitude has remained a longstanding 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） 16:0017:00 
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, nonaffine 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 nonaffine component, that arises from energy relaxation during these nonaffine deformations. In the present work, we execute a comprehensive analysis on the nonaffine component, in static jammed amorphous packings of monodisperse, 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 nonaffine modulus, which is achieved through an eigenmode 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） 14:4516:45 
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：  PDEbased 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 ellipticparabolic 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 networktype solutions. 
講演2：  Transport phenomena in evolutionary domains 
Prof. Francesco Salvarani (CEREMADE – Université ParisDauphine, France & Dipartimento di Matematica, Università di Pavia, Italy) 

要旨2：  We study the transport equation in a timedependent vessel with absorbing boundary, in any space dimension. We first prove existence and uniqueness, and subsequently we consider the problem of the timeasymptotic 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 generalpurpose 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） 16:3017:30 
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） 16:3017:30 PART2 2月5日（金） 14:4515:45 
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 minicourse 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 VlasovStokes and VlasovNavierStokes 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） 13:3014:30 
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. 
分科会「非平衡現象の流体力学」（第19回）
平成27年度第6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9日（月） 13:3014:30 
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：  Boundary layers for the discrete Boltzmann equation: mixtures, polyatomic molecules, chemical reactions and quantum extensions 
Prof. Niclas Bernhoff (Dept. of Mathematics, Karlstad University, Karlstad, Sweden) 

要旨：  In the talk we will address two different questions. 1) An important aspect of constructing discrete velocity models (DVMs) for the Boltzmann equation is to obtain the right number of collision invariants. It is a wellknown fact that DVMs can also have extra collision invariants, so called spurious collision invariants, in plus to the physical ones. A DVM with only physical collision invariants, and so without spurious ones, is called normal. The construction of such normal DVMs has been studied a lot in the literature for single species, but there are also several works where normal DVMs for binary mixtures are constructed. In this talk we will address ways of constructing DVMs for multicomponent mixtures and for polyatomic molecules (here in the meaning that the molecules have one of a finite number of different internal energies, which can be changed, or not, during a collision). We present some general algorithms for constructing such models, but we also give some concrete examples of such constructions. The two different approaches above can be combined to obtain multicomponent mixtures with a finite number of different internal energies, and then they can be applied for DVMs for chemical reactions. 2) We also consider some problems related to the nonlinear halfspace problem of condensation and evaporation for the discrete Boltzmann equation (DBE; the general discrete velocity model) for mixtures, polyatomic molecules, and chemical reactions, and for the discrete quantum Boltzmann equation. We assume that the flow tends to a stationary point (Maxwellian for the DBE) at infinity and that the outgoing flow is known at the wall (complete absorption at the wall). The number of conditions on the assigned data at the wall needed for existence of a unique solution is found. The number of parameters to be specified in the boundary conditions depends on if we have subsonic or supersonic condensation or evaporation. We obtain similar results for more general boundary conditions at the wall.All our results are valid for any finite number of velocities. 
分科会「非平衡現象の流体力学」（第18回）
平成27年度第5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7月29日（水） 16:3017:30 
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：  Nonlinear stability of the Boltzmann Equation in a periodic box 
Dr. KungChien Wu (Department of Mathematics, National Kaohsiung Normal University, Taiwan) 

要旨：  We study the nonlinear stability of the Boltzmann equation in the 3dimensional periodic box. The initial perturbation is not necessary smooth. The convergence rate is algebraic for small time region and exponential for large time region. Moreover, the exponential decay rate depends on the size of the domain. 
分科会「非平衡現象の流体力学」（第17回）
平成27年度第4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7月1日（水） 13:3014:30 
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：  Hydrodynamics models derived from kinetic theory for weakly ionized plasma flow out of thermal and chemical equilibrium with consistent thermodynamics (joint work with B. Graille and T. Magin) 
Prof. Marc Massot (Laboratoire EM2C, Ecole Centrale Paris, France) 

要旨：  Based on kinetic theory, we give a complete description of the Kolesnikov effect in multicomponent partially ionized plasmas, or crossed contributions to the mass and energy transport fluxes coupling the electrons and heavy particles. The electromagnetic field influence, an ionization mechanism, and a possible thermal nonequilibrium of the translational energy of the electrons and heavy particles, given their strong disparity of mass, are accounted for. We conduct a dimensional analysis of the Boltzmann equation and use a multiscale ChapmanEnskog method with a mixed hyperbolic/parabolic scaling to derive, for the continuum regime, macroscopic conservation equations and expressions for the transport coefficients and chemical production rates. The model satisfies the law of mass action and the first and second laws of thermodynamics and has a well defined mathematical structure. 