諸分野のための数学研究会

開催情報 火曜日　10:30～11:30　数理科学研究科棟(駒場) 056号室 儀我美一、石村直之(一橋大学)、齊藤宣一、山本昌宏 http://coe.math.sci.hokudai.ac.jp/sympo/various/ 北海道大学のHPには、第1回(2005年6月22日)～第22回(2009年2月18日)の情報が掲載されております。

2017年10月24日(火)

10:30-11:30   数理科学研究科棟(駒場) 056号室
Christian Klingenberg 氏 (Würzburg University)
The initial value problem for the multidimensional system of gas dynamics may have infinitely many weak solutions (English)
[ 講演概要 ]
We consider the isentropic compressible Euler equations in two space dimensions together with particular initial data. This data consists of two constant states only, where one state lies on the lower and the other state on the upper half plane. The aim is to investigate if there exists a unique entropy solution or if the convex integration method produces infinitely many entropy solutions. In this lecture we will show that the solution of this Riemann problem for the 2-d isentropic Euler equations is non-unique (except if the solution is smooth). Next we are able to show that there exist Lipschitz data that may lead to infinitely many solutions even for the full system of Euler equations. This is joint work with Simon Markfelder.

2016年11月17日(木)

10:30-11:30   数理科学研究科棟(駒場) 056号室
※ 通常の曜日と異なります。

Convexity preserving properties for nonlinear evolution equations (English)
[ 講演概要 ]
It is well known that convexity of solutions to a general class of nonlinear parabolic equations in the Euclidean space is preserved as time develops. In this talk, we first revisit this property for the normalized infinity Laplace equation and the curvature flow equation by introducing an alternative approach based on discrete game theory. We then extend our discussion to Hamilton-Jacobi equations in the Heisenberg group and in more general geodesic metric spaces.

2015年10月06日(火)

13:30-14:30   数理科学研究科棟(駒場) 056号室
※ 通常と時間が異なります。
Mohammad Hassan Farshbaf Shaker 氏 (Weierstrass Institute, Berlin)
Multi-material phase field approach to structural topology optimization and its relation to sharp interface approach (English)
[ 講演概要 ]
A phase field approach for structural topology optimization which allows for topology changes and multiple materials is analyzed. First order optimality conditions are rigorously derived and it is shown via formally matched asymptotic expansions that these conditions converge to classical first order conditions obtained in the context of shape calculus. Finally, we present several numerical results for mean compliance problems and a cost involving the least square error to a target displacement. This is joint work with Luise Blank, Harald Garcke and Vanessa Styles.

2015年09月08日(火)

10:30-11:30   数理科学研究科棟(駒場) 056号室
Monika Muszkieta 氏 (Wroclaw University of Technology)
Duality based approaches to total variation-like flows with applications to image processing (English)
[ 講演概要 ]
During the last years, total variation models have became very popular in image processing and analysis. They have been used to solve such problems as image restoration, image deblurring or image inpainting. Their interesting and successful applications became the motivation for many authors to rigorous analysis of properties of solutions to the corresponding total variation flows. The main difficulty in numerical approximation of solutions to these flows is caused by the lack of di fferentiability of the total variation term, and the commonly used approach to overcome this difficulty consists in considering of the dual formulation. In the talk, we consider two total variation flow models. The first one is the anisotropic total variation flow on $L^2$ with additional regularization, and the second one, is the total variation flow on $H^{-s}$. We introduce duality based numerical schemes for approximate solutions to corresponding equations and present some applications to image processing.
This talk is based on joint work with Y. Giga, P. Mucha and P. Rybka.

2015年04月14日(火)

13:30-14:30   数理科学研究科棟(駒場) 056号室
※ 通常の時間と異なります。

[ 講演概要 ]

また、ミクロな気液二相流や微粒子が分散した懸濁液の蒸発プロセス等、工学的に重要であり、また現象としても興味深い事例を時間の許す限り紹介する。

2015年01月27日(火)

10:30-11:30   数理科学研究科棟(駒場) 056号室

[ 講演概要 ]

2014年10月14日(火)

10:30-11:30   数理科学研究科棟(駒場) 056号室

Fluid flow and electromagnetic fields, from viewpoint of theoretical physics -- Is the Navier-Stokes Equation sufficient to describe turbulence at very high Reynolds numbers? -- (JAPANESE)
[ 講演概要 ]
There exists analogy between the fluid flow and electromagnetic fields with respect to their mathematical representations. This is reasonable because both are continuous physical fields having energy and momentum in space-time. In particular, fluid’s vorticity is analogous to magnetic field.

On the other hand, for simulation of atmospheric global motion on the giant computer Earth Simulator, many empirical physical parameters must be introduced in order to obtain realistic results for weather prediction, etc. This implies that the present system of equations of fluid flows may not be sufficient to describe fluid motions of large scales at very high Reynolds numbers. We consider whether the above-mentioned analogy is useful for improvement of the theory of turbulence at very high Reynolds numbers.

2014年06月10日(火)

10:30-11:30   数理科学研究科棟(駒場) 056号室

The self-similar collapse solution of a point vortex system and complex time singularities (JAPANESE)
[ 講演概要 ]
A system of N point vortices is a Hamiltonian dynamical system with N degrees of freedom,and it is known that under certain parameter and initial conditions, there are self-similar collapse solutions for which N vortices collide at a point while rotating without changing the initial shape of configuration. In this talk, I will introduce such collision solutions and discuss some properties of complex time singularities in relation with those solutions.

2013年11月26日(火)

10:30-11:30   数理科学研究科棟(駒場) 056号室

Huaxiong Huang 氏 (York University)
An immersed boundary method for mass transfer across permeable moving interfaces (ENGLISH)
[ 講演概要 ]
In this talk, we present an immersed boundary method for mass transfer across permeable deformable moving interfaces interacting with the surrounding fluids. One of the key features of our method is the introduction of the mass flux as an independent variable, governed by a non-standard vector transport equation. The flux equation, coupled with the mass transport and the fluid flow equations, allows for a natural implementation of an immersed boundary algorithm when the flux across the interfaces is proportional to the jump in concentration. As an example, the oxygen transfer from red blood cells in a capillary to its wall is used to illustrate the applicability of the proposed method. We show that our method is capable of handling multi-physics problems involving fluid- structure interaction with multiple deformable moving interfaces and (interfacial) mass transfer simultaneously.
This is joint work with X. Gong and Z. Gong.

2013年06月11日(火)

10:30-11:30   数理科学研究科棟(駒場) 056号室

[ 講演概要 ]

2013年01月23日(水)

10:30-11:30   数理科学研究科棟(駒場) 056号室

Chun Liu 氏 (Pennsylvania State University)
Ionic Fluids and Their Transport: From Kinetic Descriptions to Continuum Models (ENGLISH)
[ 講演概要 ]
The problems of distribution and transport of charged particles and ionic fluids are ubiquitous in our daily life and crucial in physical and biological applications. The multiscale and multiphysics nature of these problems provides major challenges and motivations.
In this talk, I will present the derivation of the continuum models such as Poisson-Nerest-Planck (PNP) system from the kinetic formulations.
Our focus is on the multiple species solutions and the corresponding boundary conditions for bounded containers.

2011年11月21日(月)

13:30-14:30   数理科学研究科棟(駒場) 056号室

Ernie Esser 氏 (University of California, Irvine)
A convex model for non-negative matrix factorization and dimensionality reduction on physical space (ENGLISH)
[ 講演概要 ]
A collaborative convex framework for factoring a data matrix X into a non-negative product AS, with a sparse coefficient matrix S, is proposed. We restrict the columns of the dictionary matrix A to coincide with certain columns of the data matrix X, thereby guaranteeing a physically meaningful dictionary and dimensionality reduction. We focus on applications of the proposed framework to hyperspectral endmember and abundances identification and also show an application to blind source separation of NMR data.
This talk is based on joint work with Michael Moeller, Stanley Osher, Guillermo Sapiro and Jack Xin.

2011年11月08日(火)

16:30-17:30   数理科学研究科棟(駒場) 052号室

Ralph Bruckschen 氏 (ベルリン工科大学、MATHEON)
Interactive Data Visualization challenges, approaches and examples (ENGLISH)
[ 講演概要 ]
Data visualization is probably the most important method to analyze scientific datasets. In the time of petaflop supercomputers and high resolution sensors, the visualization of such datasets became a challenge because of the sheer magnitude. Using the latest technology I will describe some of the challenges and approaches to visualize large and massive datasets. The main bottle necks will be explained, as some algorithms and data structures to widen them. Finally I will show some examples of data visualization using a CAVE environment and virtual prototyping from the 3D Labor at the Technical University of Berlin.

2011年10月05日(水)

10:00-11:00   数理科学研究科棟(駒場) 056号室

Chun Liu 氏 (University of Tokyo / Pennsylvania State University)
Energetic Variational Approaches for Ionic Fluids (ENGLISH)
[ 講演概要 ]
In this talk, I will present our recent study on the ionic transport through ion channels in cell membranes. Motivated by our earlier work on energetic variational approaches, developed for various complex fluids, especially electrorheological (ER) fluids (Phys. Rev. Lett. 101, 194503 (2008)), we derived/proposed a coupled system for ionic solutions, which takes into account of the solvent water, the diffusion and electro-static interaction of different ions. In particular, I will emphasize on the selectivity effects of the ion channels, under the simplest geometric and molecular structures.

2011年06月29日(水)

10:30-11:30   数理科学研究科棟(駒場) 056号室

[ 講演概要 ]

また、具体例として、局所的な画像信号パターンのアピアランスモデル、およびランドマーク候補間の距離に基づいた解剖学的構造物の認識手法についても紹介する。
[ 講演参考URL ]
http://info.ms.u-tokyo.ac.jp/seminar/mathvar/future.html

2011年05月18日(水)

10:30-11:30   数理科学研究科棟(駒場) 056号室

[ 講演概要 ]

[ 講演参考URL ]
http://info.ms.u-tokyo.ac.jp/seminar/mathvar/future.html

2011年01月19日(水)

10:30-11:30   数理科学研究科棟(駒場) 056号室

Mullins方程式の本質への探求 (JAPANESE)
[ 講演概要 ]
1957年にMullinsは、蒸発-凝縮機構による固体表面の発展方程式を提案した。その方程式の定性的本質を探る事によって、どのような知見が得られるかについて議論する。具体的には、曲率と駆動力との間の関係が形態に与える影響について明らかにする。

2010年10月20日(水)

10:30-11:30   数理科学研究科棟(駒場) 056号室

[ 講演概要 ]
3次元空間に埋め込まれた、厚みのある2次元曲面での粒子の拡散を考察する。

このとき通常の拡散流に加えて、面の厚さ:ε展開において、

さらに、3次元に埋め込まれた1次元の場合(チューブ)を考察し、

2010年07月07日(水)

10:30-11:30   数理科学研究科棟(駒場) 056号室

[ 講演概要 ]

また,ステップが一方向を向いて階段状になっている微斜面と呼ばれる結晶表面が現れる場合がしばしばある。

2010年05月19日(水)

10:30-11:30   数理科学研究科棟(駒場) 056号室

[ 講演概要 ]

れている現象が数多く存在する。その例として、(1)造影剤の濃度カーブを用い
た腎臓癌の転移危険性及び肝臓における血液灌流の評価、(2)大動脈瘤に対する
ステント治療の予後予測、について紹介する。前者は、血管からの造影剤の浸出

のである。後者は、個人差の大きい大動脈形状による血流の違いを数値シミュ
レーションによって求め、統計学的なクラスタリングと併せて予後を予測するも
のである。どちらも、モデリングにあたっては臨床医療の現場との緊密な連携が

の手順や困難な点、今後の展望などについて報告したい。

2010年04月21日(水)

10:30-11:30   数理科学研究科棟(駒場) 056号室

[ 講演概要 ]

2010年04月14日(水)

10:30-11:30   数理科学研究科棟(駒場) 056号室

[ 講演概要 ]
2008年12月から2009年2月にかけて国際宇宙ステーション「きぼう」において「氷の結晶成長における形態不安定化」という実験が実施された(研究代表者・北大研・古川義純)。そこでは、微小重力下において重水から成長する氷単結晶のその場観察が130回以上行うことができた。得られた明視野及び干渉縞の動画像の記録を解析し、次の2つの結果を得た。1)氷の底面の成長速度(c軸方向の速度)は、成長が測定できる臨界過冷却度(約0.1K)が存在し、臨界過冷却度以上では成長速度は過冷却度の2乗に比例する。2)樹枝先端の成長速度(a軸方向の速度)は、0.2K以上で過冷却度の2.5乗に比例する。このセミナーでは、得られた結果が理論モデルと一致することについて解説する。

2009年06月03日(水)

10:30-11:30   数理科学研究科棟(駒場) 056号室

Evolution of microstructures on crystal surfaces by surface diffusion
[ 講演概要 ]
We have studied the shape evolution of microstructures fabricated on silicon surfaces by surface diffusion during annealing. Various interesting phenomena, such as corner rounding, facet growth, and void formation, have been experimentally observed. We discuss these observations both from macroscopic and mesoscopic viewpoints. The evolution of macroscopic surface profiles is discussed using evolution equations based on the continuum surface picture. We analyze the mesoscopic scale aspects of the shape evolution using a step-flow model.

2009年04月08日(水)

10:30-11:30   数理科学研究科棟(駒場) 056号室

Growth of an Ice Disk from Supercooled Water: Theory and Space Experiment in Kibo of International Space Station
[ 講演概要 ]
We present a model of the time evolution of a disk crystal of ice with radius $R$ and thickness $h$ growing from supercooled water and discuss its morphological stability. Disk thickening, {\\it i.e.}, growth along the $c$ axis of ice, is governed by slow molecular rearrangements on the basal faces. Growth of the radius, {\\it i.e.}, growth parallel to the basal plane, is controlled by transport of latent heat. Our analysis is used to understand the symmetry breaking obtained experimentally by Shimada and Furukawa under the one-G condition. We also introduce that the space experiment of the morphological instability on the ice growing in supercooled water, which was carried out on the Japanese Experiment Module "Kibo" of International Space Station from December 2008 and February 2009.

http://kibo.jaxa.jp/experiment/theme/first/ice_crystal_end.html

We show the experimental results under the micro-G condition and discuss the feature on the "Kibo" experoments.

2009年02月18日(水)

10:30-11:30   数理科学研究科棟(駒場) 056号室

Non-existence theorem of periodic solutions except out-of-phase
and in-phase solutions in the coupled van der Pol equation system
[ 講演概要 ]
We consider the periodic solutions of the coupled van der Pol equation system $\\Sigma$, which is quite different from the ordinary van der Pol equation. We show the necessary and sufficient condition for the periodic solutions of $\\Sigma$. Non-existence theorem of periodic solutions except out-of-phase and in-phase solutions in $\\Sigma$ is presented.