| 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. |
Category Archives: Seminars
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） |
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| 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) |
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| 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) |
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| 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） |
| 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） |
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| 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: |
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) |
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| 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) |
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| 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） |
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| 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). |