平成26年度講演者リスト

番号 開催日時 講演者 (所属)
2014年4月15日(火) 16:30〜18:00 藤原宏志 助教(京都大学)
タイトル: Fast and Reliable Numerical Methods for Near-infrared Light Propagation in Human Bodies
(生体内の近赤外光伝播の高速・高信頼シミュレーションのための数値的手法)
アブストラクト: We will present a fast and reliable numerical approach for near-infrared light (NIR) propagation in human bodies. In particular, an accurate numerical quadrature rule on the unit sphere and degenerate kernel approximations are shown to realize numerical computations in the three dimensions.

The use of NIR light is considered as a safe and simple technology for monitoring our bodies, in particular, brain activities. The radiative transport equation (RTE) is widely accepted as a mathematical model of NIR light propagation in our bodies. It is an integro-differential equations and the boundary value problem in the three dimensions is essentially a five dimensional large-scale problem. An accurate numerical quadrature rule and degenerate kernel approximations have been developed to reduce the size of discretization problems and computational times. Error analysis and numerical experiments with biomedical data of a human head are also shown.

This talk is based on a joint work with Prof. Iso (Kyoto Univ.), Prof. Higashimori (Hitotsubashi Univ.), and Human Brain Research Center in Kyoto University.

備考: 
10 2014年5月13日(火) 16:30〜18:00 Bartosz Protas 准教授 (McMaster Univ.)
タイトル: Extreme vortex states and the hydrodynamic blow-up problem
アブストラクト: In the presentation we will discuss our research program concerning the study of extreme vortex events in viscous incompressible flows. These vortex states arise as the flows saturating certain fundamental mathematical estimates, such as the bounds on the maximum enstrophy growth in 3D. They are therefore intimately related to the question of spontaneous singularity formation in the 3D Navier-Stokes system, known as the hydrodynamic “blow-up” problem. We demonstrate how new insights concerning such problems can be obtained by formulating them as variational PDE optimization problems which can be solved computationally using suitable discrete gradient flows. In offering a systematic approach to finding flow solutions which may saturate known estimates, the proposed paradigm provides a bridge between mathematical analysis and scientific computation. In particular, it allows one to determine whether or not certain mathematical estimates are “sharp”, or if they may still be improved. In the presentation we will review a number of new results concerning 2D and 3D vortex flows characterized by the maximum possible growth of, respectively, palinstrophy and enstrophy. We will also discuss their relation to the available theoretical bounds obtained with rigorous methods of mathematical analysis. [Joint work with Diego Ayala]
備考:本セミナーは坂上クレスト連携セミナーとしても開催されます. 
11 2014年6月3日(火) 16:30〜18:00 石本健太 (京都大学数理解析研究所,D3)
タイトル:Hydrodynamics of cell swimming near boundaries(境界近傍における細胞遊泳の流体力学)
アブストラクト: It is known that some microorganisms such as bacteria and spermatozoa accumulate near a boundary, which has been recently considered to be a phenomenon driven by non-linear hydrodynamic interaction between the cel and the boundary, whereby the time-reversal symmetry highlighted by the scallop theorem of the low Reynolds number flow still holds even in presence of boundaries. In this talk, swimming stability of (i) a squirmer and (ii) a model spermatozoon near a boundary will be discussed after a brief review of the hydrodynamics of swimming microorganism. The squirmer is a simple mathematical model of a swimming microorganism that propel with surface deformation. The stability behaviour can be characterised by boundary conditions at the surface as well as cell geometry and swimming morphology. The swimming dynamics of the model spermatozoon illustrates the stable planar beat near a no-slip boundary, though the dynamics can be unstable for abnormal cell morphology, implying biological significance of the swimming stability for mammalian spermatozoa in female reproductive tract. (Joint work with Dr. E. A. Gaffeny at University of Oxford)
備考:本セミナーは坂上クレスト連携セミナーとしても開催されます. 
12 2014年10月14日(火) 16:30〜18:00 小野寺有紹 助教 (九州大学)
タイトル: A flow approach to an inverse problem in potential theory
アブストラクト: A new geometric flow describing the motion of quadrature surfaces is introduced, where a quadrature surface is a closed hypersurface inducing the same electrostatic potential as a given electric charge density. This characterization enables us to study quadrature surfaces through the investigation of the flow. It is proved that the flow is uniquely solvable under the geometric condition that the initial surface has positive mean curvature. As a consequence, a bifurcation criterion for quadrature surfaces is obtained.
備考:本セミナーは坂上クレスト連携セミナーおよびApplied and Computational Complex Analysis (ACCA-JP)のセミナーとしても開催されます. 
13 2014年11月18日(火) 16:30〜18:00 伊藤 昇 助教 (早稲田大学)
タイトル: Strong and weak (1, 3) homotopy equivalence classes of spherical curves
(球面曲線のstrong、あるいはweak (1, 3) ホモトピー同値類について)
アブストラクト: 自己交差が横断的な2重点しかない球面曲線は球面イソトピーを除けば、3種類のReidemeister movesの局所変形列で単純閉曲線に移される。瀧村祐介氏(学習院中等科)、谷山公規氏(早稲田大学教育学部)との共同研究[1]においては、third Reidemeister moveを2種類(strong 3, weak 3)に分け、それぞれfirst Reidemeister moveと組ませた2種類の同値関係 strong (1, 3) homotopyとweak (1, 3) homotopyによる球面曲線の同値類について論じている。モチベーションのベースとして、Reidemeister movesの第1と第3のみからなる球面曲線の同値類がほとんど何もわかっていない、ということがある。[1]では例えば「球面曲線 Pがstrong (1, 3) homotopyで単純閉曲線になることの必要十分条件が、P が有限個のsimple closed curve、∞、三葉結び目の射影図の連結和となることである」ことを証明している。また[2]では「球面曲線Pがweak (1, 3) homotopyで単純閉曲線になることの必要十分条件が、Pが有限個のsimple closed curve、∞の連結和である」ことを証明している。本講演では、詳細のテクニックよりも「どういう問題意識でどのような問題をどのように考えたか」に重きを置き、その経緯を詳しく述べたい。

参考文献:
[1] N. Ito, Y. Takimura, and K. Taniyama, Strong and weak (1, 3) homotopies on knot projections, to appear in Osaka J. Math. [2] N. Ito and Y. Takimura, (1, 2) and weak (1, 3) homotopies on knot projections. J. Knot Theory Ramifications 22 (2013), 1350085 (14 pages).

備考:本講演は日本語で行われますが,資料は英語で作成していただきます.また,本セミナーは坂上クレスト連携セミナーとしても開催されます. 
14 2015年1月6日(火)16:30〜18:00 カレル シュワドレンカ 准教授(京都大学)
タイトル: Evolutionary free boundary problems: their analysis and numerical solution
アブストラクト: A simple model for motion of bubbles on obstacles is given by a free boundary problem of parabolic or hyperbolic type. In this talk, a method of analysis of such equations based on time semi-discretization will be presented, which allows direct application to numerical approximation. Moreover, this method seems promising in studying hyperbolic free boundary problems, a field with almost no established theory. An example of such an application will be explained. Extension to the more general vector-valued case will also be mentioned.
備考:本セミナーは坂上クレスト連携セミナーとしても開催されます. 
15 2015年2月17日(火)11:00〜12:00 Kim, Sun-Chul 教授(Chung-Ang Univ., Korea)
タイトル:Vortex sheet evolution on the spheroid
アブストラクト: Vortex sheet is an interface of discontinuity between two different velocity fluid flow. The dynamics of vortex sheet has been studied a lot for the plane and also for the sphere. In this talk, we study the motion of vortex sheet on the speroid numerically. More precisely, we asymptotically calculate the linear stability and compute the time evolution of roll ups.The effect of eccentricity is also considered.
16 2015年2月17日(火)13:30〜14:30 竹広 真一 准教授(京都大学数理解析研究所)
タイトル:On axial 2-dimensional vortices exited by thermal convection in a rapidly rotating thin spherical shell
アブストラクト: Dynamics of axial 2-dimensional vortices in a rapidly rotating thin spherical shell is discussed. It is presented that the vortices excieted by thermal convection in a rotating spherical shell are affected by the inner and outer spherical boundaries and propagte as topographic Rossby waves, which transport momentum and induce a longitudinally banded strcture of mean zonal flows.
17 2015年2月17日(火)14:30〜15:30 Sohn, Sung-Ik 教授(Gangneung-Wonju National Univ., Korea)
タイトル:Singularity and Nonuniqueness of Hydrodynamic Instabilities
アブストラクト: In this talk, the singularity and nonuniqueness of the solutions of hydrodynamic instabilities are presented. We discuss the nonuniqueness of the steady-state solution of the bubble evolution in the Rayleigh-Taylor and Saffman-Taylor instabilities, and the selection of the physically significant solution. The Kelvin-Helmholtz instability is known to evolve a finite-time singularity, and the nonuniqueness of weak solutions has been recently established. We study whether the solutions of different regularization models converge to distinct or the same weak solution, and what the weak solutions are.
備考:いつもの開催時刻と異なりますのでご注意下さい.また,15回〜17回のセミナーはA3 Workshop on Vortex Dynamics(日中韓A3フォーサイトプログラム;代表 西浦廉政教授)の一部として主催されます.

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