カレル シュワドレンカ 准教授(京都大学)
「Evolutionary free boundary problems: their analysis and numerical solution」

概要: 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.



Kim, Sun-Chul 教授(Chung-Ang Univ., Korea)
「Vortex sheet evolution on the spheroid」

概要: 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.




竹広 真一 准教授(京都大学数理解析研究所)
「On axial 2-dimensional vortices exited by thermal convection in a rapidly rotating thin spherical shell」

概要: 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.




Sohn, Sung-Ik 教授(Gangneung-Wonju National Univ., Korea)
「Singularity and Nonuniqueness of Hydrodynamic Instabilities」

概要: 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.



牧野和久 准教授(京都大学)
「The complexity issues on stochastic games」

概要: Stochastic games were introduced in 1953 by Shapley for the discounted case, and extended to the undiscounted case in 1957 by Gillette. Each such game is a dynamic game with probabilistic transitions played by two players on a finite set of states. The game is played in the infinite sequence of rounds. In the round, the game is in some state. The players choose actions. Then they receive payoffs and the game moves to a new random state, where the payoffs and the transition probability depend on the previous state and the actions chosen by the players. The procedure is repeated at the new state. Stochastic games generalize parity games, cyclic games, simple stochastic games, and BWR games, which all belong to NP and coNP, but are not known to be solved in polynomial time. In this talk, I briefly survey the algorithmic issues on these games, as well as the properties on the optimal strategies for them. I also discuss recent works obtained with Endre Boros, Khaled Elbassioni, and Vladimir Gurvich.

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.また,本セミナーは東大数理052室で中継されます.詳細は,齊藤宣一noriazu@ms.u- tokyo.ac.jpにお問い合わせ下さい.



松本正和 准教授(岡山大学)
「Water as a network」

概要: Water is one of the simplest molecule, but its physical properties in the condensed phases are quite complex. For example, there are more than 16 ice polymorphs and hypothetically two liquid phases. Water is the only liquid that expands when cooled. These complexities originate in hydrogen bond network structures. We regard these phases as graphs and investigate the relationship between topology and properties.

備考: 本セミナーは東大数理052室で中継されます.詳細は,齊藤宣一noriazu@ms.u- tokyo.ac.jpにお問い合わせ下さい.



大林一平 助教(東北大学)
「Inverse problem on persistence diagrams」

概要: 本講演ではパーシステントホモロジーの可視化手法の一つであるパーシステンス図の逆問題について考える.

備考: 本セミナーは東大数理052室で中継されます.詳細は,齊藤宣一noriazu@ms.u- tokyo.ac.jpにお問い合わせ下さい.



小布施祈織 助教(岡山大学)
「Behaviour of a low-Reynolds-number treadmilling microswimmer near a semi-infinite wall」

概要: We investigate the behavior of a treadmilling microswimmer in a two-dimensional unbounded domain with a semi-infinite no-slip wall. The wall can also be regarded as a probe or pipette inserted into the flow. We solve the governing evolution equations in an analytical form by utilizing complex analysis, and numerically calculate trajectories of the swimmer for several different initial positions and orientations. We then compute the probability that the treadmilling swimmers can escape the vicinity of the wall. We find that many trajectories in a ‘wedge’ around the wall are likely to escape. This suggests that inserting a probe or pipette in a suspension of organism may push away treadmilling swimmers.

備考: 本セミナーは坂上クレスト連携セミナーおよびACCA-JPのセミナーとしても開催されます.また,東大数理052室へ中継されます.詳細は ,齊藤宣一 norikazu@ms.u- tokyo.ac.jpにお問い合わせ下さい.



Dr. Christopher Green (Queensland Univ. of Technology)
「Using the Schottky-Klein prime function to solve free boundary problems in multiply connected domains」

概要: The Schottky-Klein prime function is a special transcendental function which plays a central role in problems involving multiply connected domains. This function can be used to great advantage in many varied applications. In this talk, we will explore two different free boundary problems (arising in fluid mechanics) defined over two distinct multiply connected geometries. For both problems, we will show that it has been expedient to employ the Schottky-Klein prime function and its associated function theory in order to construct analytical solutions.

備考: 本セミナーは坂上クレスト連携セミナーおよびACCA-JPのセミナーとしても開催されます.また,東大数理052室へ中継されます.詳細は ,齊藤宣一 norikazu@ms.u- tokyo.ac.jpにお問い合わせ下さい.



土屋卓也 教授 (愛媛大学)

概要: Lagrange補間の誤差評価については、古くより研究が積み重ねられてきた。区間上の誤差解析は、すでに19世紀に完成しているが、有限要素法の数学的理論において重要な、三角形および四面体上の誤差解析については、21世紀の現在でも、完全に理解されているとは言えない状況である。この講演では、三角形・四面体上のLagrange補間の誤差評価の歴史について概観し、さらに最近得られた結果を紹介したい。

備考: 本セミナーは東大数理052室へ中継されます.詳細は ,齊藤宣一 norikazu@ms.u- tokyo.ac.jpにお問い合わせ下さい.



石岡圭一 准教授 (京都大学)

概要: 回転球面上における2次元非圧縮流体において, 平行流(帯状流)がシア不安定(順圧不安定)である場合, 微小擾乱が指数関数的に発達していくが, その発達はいずれ頭打ちになる. この擾乱発達の上限を弱非線形等の近似を用いずに,系の保存量を組み合わせることによって見積る試みは Shepherd(1988)によって最初に行なわれた. Ishioka and Yoden(1996)では, より tight な上限値を求めるための異なる 2つの手法を提案した. その際の数値計算において, その2つの手法から得られる上限値が等しくなるのではないかという予想が立てられたが, 数学的な証明は与えられていなかった. Ishioka(2013)において, この 2つの手法から得られる上限値が等しいものになることについての証明を与えることに成功し, その証明の過程で使われる手順が上限値の効率的な計算法を与えることも示した. 本講演では, 以上の研究の流れの概観と, 気象学者が何故このような上限値問題に興味を持ったのかについての背景等についても簡単に紹介したい.

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.また,東大数理052室へ中継されます.詳細は,齊藤宣一 norikazu@ms.u- tokyo.ac.jpにお問い合わせ下さい.



木村正人 教授 (金沢大学)

概要: We consider a nonlinear diffusion equation with irreversible property and construct a unique strong solution by using implicit time discretization. A new regularity estimate for the classical obstacle problem is established and is used in the construction of the strong solution.
As an application, we consider a quasi-static fracture model of brittle material using the idea of the phase field model. The Francfort-Marigo energy which is based on the classical Griffith theory is introduced, where the sharp crack profile is approximated by a smooth damage function using the idea of the Ambrosio-Tortorelli regularization. The crack propagation model is derived as a gradient flow of the energy of the damage variable with an irreversible constraint. Some numerical examples in various settings computed by finite element method are also presented in the talk.
The contents is based on the joint works with Goro Akagi (Kobe Univ.) and with Takeshi Takaishi (Hiroshima Kokusai Gakuin Univ.).

備考: 本セミナーは東大数理052室へ中継されます.詳細は ,齊藤宣一 norikazu@ms.u- tokyo.ac.jpにお問い合わせ下さい.



河村洋史 研究員(海洋研究開発機構)

概要: 水平方向に周期的なシリンダー形状のHele-Shaw セルにおける振動対流の位相 記述法を定式化する.この手法は無限次元力学系(振動対流を記述する偏微分 方程式系)におけるリミット・トーラス解(「時間の位相」と「空間の位相」 という2つの位相を持つ解)の位相縮約法である。各点各時刻に加えられた弱 い摂動に対する振動対流の時間的・空間的な位相応答を定量化する2つの位相 感受関数を導出し,弱く結合した2つの振動対流の間の時間的・空間的な位相 同期現象を解析する.

備考: 本セミナーは坂上クレスト連携セミナーおよびACCA-JPのセミナーとしても開催されます.また,東大数理052室へ中継されます.詳細は,齊藤宣一 norikazu@ms.u- tokyo.ac.jpにお問い合わせ下さい.
[Y. Kawamura and H. Nakao, Physica D 295-296, 11-29 (2015).]