諸分野のための数学研究会

過去の記録 ~03/27次回の予定今後の予定 03/28~

開催情報 火曜日 10:30~11:30 数理科学研究科棟(駒場) 056号室
担当者 儀我美一、石村直之(中央大学)、齊藤宣一、山本昌宏
セミナーURL http://coe.math.sci.hokudai.ac.jp/sympo/various/
目的 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。

過去の記録

2010年04月21日(水)

10:30-11:30   数理科学研究科棟(駒場) 056号室
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)までの情報が掲載されております。
佐崎元 氏 (北海道大学低温科学研究所)
高分解光学顕微法による結晶成長素過程の直接観察 (JAPANESE)
[ 講演概要 ]
近年の光学顕微法の様々な発展により,結晶表面上での分子ス ケール高さ(Å - nm)の単位ステップや個々の分子の動的な振る舞いを,直接観 察することが可能になって来た.講演では,様々な結晶表面上でのステップの協 同的な運動を多数のムービーでご覧いただくことで,数学的な問題と繋げていた だければ幸いである.

2010年04月14日(水)

10:30-11:30   数理科学研究科棟(駒場) 056号室
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)までの情報が掲載されております。
横山悦郎 氏 (学習院大学計算機センター)
国際宇宙ステーション「きぼう」における「氷の結晶成長における形態不安定化」実験解析ー氷の底面及び樹枝先端の成長速度解析とその理論的考察 (JAPANESE)
[ 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
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)までの情報が掲載されております。
須藤孝一 氏 (大阪大学)
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
横山悦郎 氏 (学習院大学)
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
野原勉 氏 (武蔵工業大学)
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.

2009年01月08日(木)

16:30-17:30   数理科学研究科棟(駒場) 056号室
※今回は開催日、開催時間共に通常と異なりますことをご了承下さい。
伊東一文 氏 (North Carolina State University)
Calibration problems for Black-Scholes American Options under the GMMY process
[ 講演概要 ]
The calibration problem is formulated as a control problem for the parabolic variational inequality. The well-posedness of the formulation is discussed and the necessary optimality is derived. A numerical approximation method is also presented.

2008年10月29日(水)

10:30-11:30   数理科学研究科棟(駒場) 056号室
木村芳文 氏 (名古屋大学(多元数理科学研究科))
Stratified turbulence as an element of geophysical fluid dynamics
[ 講演概要 ]
Density stratification and rotation are the two major mechanisms that characterize the whole geophysical flows. In this talk, focusing on stable stratification, I will introduce some statistical, mechanical and geometrical aspects of stratified turbulence by showing the recent results of large scale computer simulations.

2008年08月06日(水)

10:30-14:00   数理科学研究科棟(駒場) 056号室
伊東一文氏(10:30-11:30)
Yimin Wei氏(13:00-14:00)

Kazufumi Ito 氏 (North Carolina State University) 10:30-11:30
Adaptive Tikhonov Regularization for Inverse Problems
[ 講演概要 ]
Tikhonov regularization method plays a critical role in ill-posed inverse problems, arising in applications including computerized tomography, inverse scattering and image processing. The goodness of the inverse solution heavily depends on selection of the regularization parameter. Commonly used methods rely on a priori knowledge of the noise level. A method that automatically estimates the noise level and selects the regularization parameter automatically is presented.
Yimin Wei 氏 (Fudan University) 13:00-14:00
On mixed and componentwise condition numbers for Moore-Penrose inverse and linear least squares problems
[ 講演概要 ]
Classical condition numbers are normwise: they measure the size of both input perturbations and output errors using some norms. To take into account the relative of each data component, and a possible data sparseness, componentwise condition numbers have been increasingly considered. These are mostly of two kinds: mixed and componentwise. In this talk, we give explicit expressions, computable from the data, for the mixed and componentwise condition numbers for the computation of the Moore-Penrose inverse as well as for the computation of solutions and residues of linear least squares problems. In both cases the data matrices have full column (row) rank.

2008年07月23日(水)

10:30-11:30   数理科学研究科棟(駒場) 056号室
7月23日(水)は午前中の講演のみです。午後の討論会はありません。
ご注意下さい。

Andrei Constantinescu 氏 (Ecole Polytechnique)
Identification of residual stresses: problem settings and results.
[ 講演概要 ]
Identification of residual stresses is an important task in many engineering fields such as fatigue or fracture mechanics, where their presence can significantly increase or decrease the apparent strength of mechanical components.

The present talk will try to make a review of existing problem settings identification results.
More precisely we shall:

1. discuss the linearization procedure strain and materials behaviour in finite elasticity around a stressed state in order to define in a mathematical precise way the problem settings for the identification of residual stresses.

2. present a series of measurement techniques currently used in industry and research for the measurement of residual stresses like the X-ray technique and strain measurements.

3. present existing results in the identification of residual stresses for the different

2008年07月23日(水)

10:30-14:00   数理科学研究科棟(駒場) 056号室
伊東一文氏(10:30-11:30)
Yimin Wei氏(13:00-14:00)

伊東一文 氏 (North Carolina State University) 10:30-11:30
Adaptive Tikhonov Regularization for Inverse Problems
[ 講演概要 ]
Tikhonov regularization method plays a critical role in ill-posed inverse problems, arising in applications including computerized tomography, inverse scattering and image processing. The goodness of the inverse solution heavily depends on selection of the regularization parameter. Commonly used methods rely on a priori knowledge of the noise level. A method that automatically estimates the noise level and selects the regularization parameter automatically is presented.
Yimin Wei 氏 (Fudan University) 13:00-14:00
On mixed and componentwise condition numbers for Moore-Penrose inverse and linear least squares problems
[ 講演概要 ]
Classical condition numbers are normwise: they measure the size of both input perturbations and output errors using some norms. To take into account the relative of each data component, and a possible data sparseness, componentwise condition numbers have been increasingly considered. These are mostly of two kinds: mixed and componentwise. In this talk, we give explicit expressions, computable from the data, for the mixed and componentwise condition numbers for the computation of the Moore-Penrose inverse as well as for the computation of solutions and residues of linear least squares problems. In both cases the data matrices have full column (row) rank.

2008年01月07日(月)

13:30-14:30   数理科学研究科棟(駒場) 056号室
伊藤一文 氏 (North Carolina State University)
An Optimal Feedback Solution to Quantum Control Problems.
[ 講演概要 ]
Control of quantum systems described by Schrodinger equation is considered. Feedback control laws are developed for the orbit tracking via a controled Hamiltonian. Asymptotic tracking properties of the feedback laws are analyzed. Numerical integrations via time-splitting are also analyzed and used to demonstrate the feasibility of the proposed feedback laws.
[ 参考URL ]
http://coe.math.sci.hokudai.ac.jp/sympo/various/index.html

2007年12月04日(火)

15:00-17:15   数理科学研究科棟(駒場) 122号室
Pavel Krejci 氏 (Weierstrass Institute for Applied Analysis and Stochastics) 15:00-16:00
Quasilinear hyperbolic equations with hysteresis
[ 講演概要 ]
We consider a wave propagation problem in a rate independent elastoplastic material described by a counterclockwise convex hysteresis operator. Unlike in viscoelasticity, the speed of propagation is bounded above by the speed of the corresponding elastic waves. The smoothening dissipative effect is due to the convexity of the hysteresis branches. We present some recent results on the long time behavior of solutions under various boundary conditions, including the stability of time periodic solutions under periodic forcing.
[ 参考URL ]
http://coe.math.sci.hokudai.ac.jp/sympo/various/index.html
Victor Isakov 氏 (Wichita State University) 16:15-17:15
Carleman estimates for second order operators with two large parameters
[ 講演概要 ]
We obtain new Carleman type estimates for general second order linear partial differential operators. These estimates hold for the weight functions under pseudoconvexity conditions relating the operator and weight function. We discuss these conditions. We give applications to uniqueness and stability of the continuation and inverse problems for elasticity system with residual stress without smallness assumptions on residual stress. This is a joint work with Nanhee Kim.
[ 参考URL ]
http://coe.math.sci.hokudai.ac.jp/sympo/various/index.html

2007年04月12日(木)

16:30-17:30   数理科学研究科棟(駒場) 056号室
Boris Khesin 氏 (University of Toronto)
Dynamics on diffeomorphism groups: shocks of the Burgers equation and hydrodynamical instability
[ 講演概要 ]
We describe a simple relation between curvatures of the group of volume-preserving diffeomorphisms (responsible for Lagrangian instability of ideal fluids via Arnold's approach) and the generation of shocks for potential solutions of the inviscid
Burgers equation (important in mass transport). For this we characterize focal points of the group of volume-preserving diffeomorphism, regarded as a submanifold in all diffeomorphisms and the corresponding conjugate points along geodesics in the Wasserstein space of densities.

Further, we consider the non-holonomic optimal transport problem,
related to the following non-holonomic version of the classical Moser theorem: given a bracket-generating distribution on a manifold two volume forms of equal total volume can be isotoped by the flow of a vector field tangent to this distribution.
[ 参考URL ]
http://coe.math.sci.hokudai.ac.jp/

2007年04月11日(水)

10:30-11:30   数理科学研究科棟(駒場) 056号室
C. W. Oosterlee 氏 (Delft University of Technology)
The numerical treatment of pricing early exercise options under L'evy processes
[ 講演概要 ]
In this presentation we will discuss the pricing of American and Bermudan options under L'evy process dynamics.

Two different approaches will be discussed: First of all, modelling with differential operators gives rise to the numerical solution of a partial-integro differential equation for obtaining European option prices. For American prices a linear complementarity problem with the partial integro-differential operator needs to be solved. We outline the difficulties and possible solutions in this context.

At the same time we would also like to present a different pricing approach based on numerical integration and the fast Fourier Transform. Both approaches are compared in terms of accuracy and efficiency.
[ 参考URL ]
http://coe.math.sci.hokudai.ac.jp/

2007年03月07日(水)

14:00-15:00   数理科学研究科棟(駒場) 056号室
Seung Yeal Ha 氏 (Seoul National University)
Stability theory in L^p for the space-inhomogeneous Boltzmann equation
[ 講演概要 ]
In this talk, I will present kinetic nonlinear funtionals which are similar in sprit to Glimm type functionals in one-dimensional hyperbolic conservation laws. These functionals measures the dispersive mechanism of the Boltzmann equation near vacuum and can be used to the study of the large-time behavior and L^p-stability of the Boltzmann equation near vacuum. This is a joint work with M. Yamazaki (Univ. of Tsukuba) and Seok-Bae Yun (Seoul National Univ.)
[ 参考URL ]
http://coe.math.sci.hokudai.ac.jp/index.html.en

2007年01月31日(水)

10:30-11:30   数理科学研究科棟(駒場) 123号室
小谷正博 氏 (学習院大学)
ガラスに吸着した色素分子の一分子観察――ランダムウォークと拡散――
[ 講演概要 ]
夜空の星を望遠鏡で観察できる。星の望遠鏡観察から星の一生、ひいては宇宙の成因まで議論できる。同様に蛍光を使えば色素分子一匹を顕微鏡で見ることができる。一分子観察は個々の分子の挙動が見えるので、分子レベルでの確率的な過程を調べる手段、分子のおかれた環境の不均一を研究する手段になることが認識されてきた。

ガラスの上に希薄に吸着した蛍光性の色素を使って分子の表面拡散をしらべた。平均自乗偏位は時間に比例して増大するようにみえ、これから拡散係数を見積もることができる。

このようにして求めた拡散係数は測定環境の湿度に大きく依存することがわかった。こうして、問題はガラス表面にある数ナノメートルの吸着水のなかでの色素分子の運動の議論になってきた。拡散係数に場所ムラはあるのか、時間依存性はあるのか、実験は進行中である。
[ 参考URL ]
http://coe.math.sci.hokudai.ac.jp/sympo/various/index.html

2006年12月13日(水)

10:30-11:30   数理科学研究科棟(駒場) 056号室
C. M. Elliott 氏 (University of Sussex)
Computational Methods for Geometric PDEs
[ 講演概要 ]
Computational approaches to evolutionary geometric partial differential equations such as anisotropic motion by mean curvature and surface diffusion are reviewed. We consider methods based on graph, parametric , level set and phase field descriptions of the surface. We also discuss the approximation of partial differential equations which hold on the evolving surfaces. Numerical results will be presented along with some approximation results.
[ 参考URL ]
http://coe.math.sci.hokudai.ac.jp/sympo/various/index.html

2006年12月06日(水)

10:30-11:30   数理科学研究科棟(駒場) 056号室
横山悦郎 氏 (学習院大学)
Formation of rims surrounding a chondrule during solidification in 3- dimensions using the phase field model
[ 講演概要 ]
Chondrules are small particles of silicate material of the order of a few millimeters in radius, and are the main component of chondritic meteorite.

In this paper, we present a model of the growth starting from a seed crystal at the location of an outer part of pure melt droplet into spherical single crystal corresponding to a chondrule. The formation of rims surrounding a chondrule during solidification is simulated by using the phase field model in three dimensions. Our results display a well developed rim structure when we choose the initial temperature of a melt droplet more than the melting point under the condition of larger supercooling. Furthermore, we show that the size of a droplet plays an important role in the formation of rims during solidification.
[ 参考URL ]
http://coe.math.sci.hokudai.ac.jp/sympo/various/index.html

2006年11月29日(水)

10:30-11:30   数理科学研究科棟(駒場) 056号室
塚本 史郎 氏 (東京大学生産技術研究所)
Atomistic view of InAs quantum dot self-assembly from inside the growth chamber
[ 講演概要 ]
A 'quantum dot' is a tiny region of a solid, typically just nanometres in each direction, in which electrons can be confined. Semiconductor quantum dots are the focus of intense research geared towards exploiting this property for electronic devices. The most economical method of producing quantum dots is by self-assembly, where billions of dots can be grown simultaneously. The precise mechanism of self-assembly is not understood and is hampering efforts to control the characteristics of the dots. We have used a unique microscope to directly image semiconductor quantum dots as they are growing, which is a unique scanning tunnelling microscope placed within the molecular beam epitaxy growth chamber. The images elucidate the mechanism of InAs quantum dot nucleation on GaAs(001) substrate, demonstrating directly that not all deposited In is initially incorporated into the lattice, hence providing a large supply of material to rapidly form quantum dots via islands containing tens of atoms. kinetic Monte Carlo simulations based on first-principles calculations show that alloy fluctuations in the InGaAs wetting layer prior to are crucial in determining nucleation sites.
[ 参考URL ]
http://coe.math.sci.hokudai.ac.jp/sympo/various/index.html

2006年11月08日(水)

10:30-11:30   数理科学研究科棟(駒場) 056号室
Fredric Flin 氏 (Hokkaido University)
Crystal growth in dry deposited snow: experiment, theoretical modeling and simulation
[ 講演概要 ]
Snow, from its fall until its full melting, undergoes transformations of its microstructure with time. This process, named “metamorphism”, drastically influences its physical, thermal and mechanical properties and is of great interest in snow and ice sciences.
The recent possibility of acquiring 3D images of small snow samples opens new opportunities for investigating snow in details. For this purpose, we developed specific algorithms in order to extract the relevant geometrical and physical parameters from the imaged samples (e.g. normal and curvature fields, specific surface area). We then used these estimators to develop 3D models that simulate the time-lapse transformations of snow directly from an experimentally observed microstructure. These models, which can be checked with experiments in cold room, offer new outlooks for the study of snow metamorphism.
[ 参考URL ]
http://coe.math.sci.hokudai.ac.jp/sympo/various/index.html

2006年10月05日(木)

16:30-17:30   数理科学研究科棟(駒場) 123号室
成田誠 氏 (Department of Mathematics, National Taiwan University)
Global existence and asymptotic behavior of Gowdy symmetric spacetimes with nonlinear scalar field
[ 講演概要 ]
We study global properties of Gowdy symmetric (the existence of a symmetry group with two-dimensional spacelike orbits) spacetimes with nonlinear scalar field, which naturally arises in modern cosmology based on superstring theory.
The system of the Einstein and scalar field equations becomes a system consisting of wave map and nonlinear wave equations in one space dimension. We prove a global existence theorem for this system. Also, asymptotic energy decay will be discussed.
[ 参考URL ]
http://coe.math.sci.hokudai.ac.jp/sympo/various/index.html

2006年07月05日(水)

10:30-11:30   数理科学研究科棟(駒場) 056号室
Y. H. Richard Tsai 氏 (University of Texas)
Level Set Methods and Multi-valued solutions
[ 講演概要 ]
We review the level set methods for computing multi-valued
solutions to a class of nonlinear first order partial differential
equations, including Hamilton-Jacobi equations, quasi-linear
hyperbolic equations, and conservative transport equations with
multi-valued transport speeds.
The multivalued solutions are embedded as the zeros of a set of scalar functions that solve the initial value problems of a time dependent partial differential equation in an augmented space.
We discuss the essential ideas behind the techniques, the coupling of these techniques to the projection of the interaction of zero level sets and a collection of applications including the omputation of the semiclassical limit for Schr\\"{o}dinger quations and the high frequency geometrical optics limits of linear wave equations.
[ 参考URL ]
http://coe.math.sci.hokudai.ac.jp/sympo/various/index.html

2006年04月19日(水)

10:30-11:30   数理科学研究科棟(駒場) 056号室
横山 悦郎 氏 (学習院大学)
Oscillatory growth of a crystal controlled by interface kinetics and transport process
[ 講演概要 ]
Periodic texture in a crystal -such as growth banding and growth striations- are believed to be caused by oscillatory growth. The origin of oscillatory growth falls into two categories, i.e., external and internal. Since the growth rate of a crystal depends strongly on the growth conditions, periodic changes of external conditions, such as temperature, concentration, convection etc., are common reasons for explaining oscillatory growth. On the other hand, it is thought that oscillatory growth can also have an internal cause, but there is no clear understanding. In this talk we propose the hypothesis of a hysteresis behaviour of growth rate to explain the formation of periodic structures of a growing crystal without a change of external conditions. Recently, evidence for our hypothesis is observed not only in the growth of a crystal but also in the motion of steps on the surface of crystals. Possibly such self-oscillatory growth can be controlled in experiments in near future.
[ 参考URL ]
http://coe.math.sci.hokudai.ac.jp/sympo/various/005.html

2006年04月04日(火)

16:30-17:30   数理科学研究科棟(駒場) 128号室
Maria Reznikoff 氏 (Department of Mathematics, Princeton University)
Thermally-Driven Rare Events and Action Minimization
[ 参考URL ]
http://coe.math.sci.hokudai.ac.jp/sympo/various/004.html

2005年11月22日(火)

16:30-17:30   数理科学研究科棟(駒場) 128号室
Hans Heesterbeek 氏 (University of Utrecht)
Mathematics in the epidemiology and control of infectious diseases
[ 講演概要 ]
In this lecture I will give examples of the way in which mathematics helps in getting insight into the spread and control of infectious diseases. I will do this by discussing the population phenomena that are observed after an infectious agent enters a population (invasion, epidemic, recurrent epidemic, endemic, regulation, control). Along the way I will also give insight into the historical development of mathematical modelling in infectious disease epidemiology. Examples will be taken from human and animal infections. Special topics treated in some detail are threshold quantities such as the basic reproduction number R_0, the importance of understanding the structure of contacts in a population, the use of R_0 to estimate control effort with vaccines. In the last part of the lecture a number of important epidemiological problems will be discussed where input of new mathematical theory is needed.
[ 参考URL ]
http://coe.math.sci.hokudai.ac.jp/sympo/various/index.html

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