## Seminar on Mathematics for various disciplines

Seminar information archive ～10/02｜Next seminar｜Future seminars 10/03～

Date, time & place | Tuesday 10:30 - 11:30 056Room #056 (Graduate School of Math. Sci. Bldg.) |
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**Seminar information archive**

### 2010/04/21

10:30-11:30 Room #056 (Graduate School of Math. Sci. Bldg.)

Direct observation of elementary processes of crystal growth by advanced optical microscopy (JAPANESE)

**Gen Sazaki**(Hokkaido University)Direct observation of elementary processes of crystal growth by advanced optical microscopy (JAPANESE)

[ Abstract ]

### 2010/04/14

10:30-11:30 Room #056 (Graduate School of Math. Sci. Bldg.)

Analysis of growth rates of an ice crystal from supercooled heavy water under microgravity condition in KIBO of International Space Station

--basal plane growth rate and dendritic growth velocity

(JAPANESE)

**Etsuro Yokoyama**(Gakushuin University)Analysis of growth rates of an ice crystal from supercooled heavy water under microgravity condition in KIBO of International Space Station

--basal plane growth rate and dendritic growth velocity

(JAPANESE)

### 2009/06/03

10:30-11:30 Room #056 (Graduate School of Math. Sci. Bldg.)

Evolution of microstructures on crystal surfaces by surface diffusion

**須藤孝一**(大阪大学)Evolution of microstructures on crystal surfaces by surface diffusion

[ Abstract ]

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.

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.

### 2009/04/08

10:30-11:30 Room #056 (Graduate School of Math. Sci. Bldg.)

Growth of an Ice Disk from Supercooled Water: Theory and Space Experiment in Kibo of International Space Station

**横山悦郎**(学習院大学)Growth of an Ice Disk from Supercooled Water: Theory and Space Experiment in Kibo of International Space Station

[ Abstract ]

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.

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.

### 2009/02/18

10:30-11:30 Room #056 (Graduate School of Math. Sci. Bldg.)

Non-existence theorem of periodic solutions except out-of-phase

and in-phase solutions in the coupled van der Pol equation system

**野原勉**(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

[ Abstract ]

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.

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.

### 2009/01/08

16:30-17:30 Room #056 (Graduate School of Math. Sci. Bldg.)

Calibration problems for Black-Scholes American Options under the GMMY process

**伊東一文**(North Carolina State University)Calibration problems for Black-Scholes American Options under the GMMY process

[ Abstract ]

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.

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.

### 2008/10/29

10:30-11:30 Room #056 (Graduate School of Math. Sci. Bldg.)

Stratified turbulence as an element of geophysical fluid dynamics

**木村芳文**(名古屋大学(多元数理科学研究科))Stratified turbulence as an element of geophysical fluid dynamics

[ Abstract ]

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.

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.

### 2008/08/06

10:30-14:00 Room #056 (Graduate School of Math. Sci. Bldg.)

Adaptive Tikhonov Regularization for Inverse Problems

On mixed and componentwise condition numbers for Moore-Penrose inverse and linear least squares problems

**Kazufumi Ito**(North Carolina State University) 10:30-11:30Adaptive Tikhonov Regularization for Inverse Problems

[ Abstract ]

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.

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**(Fudan University) 13:00-14:00On mixed and componentwise condition numbers for Moore-Penrose inverse and linear least squares problems

[ Abstract ]

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.

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.

### 2008/07/23

10:30-11:30 Room #056 (Graduate School of Math. Sci. Bldg.)

Identification of residual stresses: problem settings and results.

**Andrei Constantinescu**(Ecole Polytechnique)Identification of residual stresses: problem settings and results.

[ Abstract ]

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

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

### 2008/07/23

10:30-14:00 Room #056 (Graduate School of Math. Sci. Bldg.)

Adaptive Tikhonov Regularization for Inverse Problems

On mixed and componentwise condition numbers for Moore-Penrose inverse and linear least squares problems

**伊東一文**(North Carolina State University) 10:30-11:30Adaptive Tikhonov Regularization for Inverse Problems

[ Abstract ]

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.

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**(Fudan University) 13:00-14:00On mixed and componentwise condition numbers for Moore-Penrose inverse and linear least squares problems

[ Abstract ]

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.

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.

### 2008/01/07

13:30-14:30 Room #056 (Graduate School of Math. Sci. Bldg.)

An Optimal Feedback Solution to Quantum Control Problems.

http://coe.math.sci.hokudai.ac.jp/sympo/various/index.html

**伊藤一文**(North Carolina State University)An Optimal Feedback Solution to Quantum Control Problems.

[ Abstract ]

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.

[ Reference URL ]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.

http://coe.math.sci.hokudai.ac.jp/sympo/various/index.html

### 2007/12/04

15:00-17:15 Room #122 (Graduate School of Math. Sci. Bldg.)

Quasilinear hyperbolic equations with hysteresis

http://coe.math.sci.hokudai.ac.jp/sympo/various/index.html

Carleman estimates for second order operators with two large parameters

http://coe.math.sci.hokudai.ac.jp/sympo/various/index.html

**Pavel Krejci**(Weierstrass Institute for Applied Analysis and Stochastics) 15:00-16:00Quasilinear hyperbolic equations with hysteresis

[ Abstract ]

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.

[ Reference URL ]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.

http://coe.math.sci.hokudai.ac.jp/sympo/various/index.html

**Victor Isakov**(Wichita State University) 16:15-17:15Carleman estimates for second order operators with two large parameters

[ Abstract ]

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.

[ Reference URL ]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.

http://coe.math.sci.hokudai.ac.jp/sympo/various/index.html

### 2007/04/12

16:30-17:30 Room #056 (Graduate School of Math. Sci. Bldg.)

Dynamics on diffeomorphism groups: shocks of the Burgers equation and hydrodynamical instability

http://coe.math.sci.hokudai.ac.jp/

**Boris Khesin**(University of Toronto)Dynamics on diffeomorphism groups: shocks of the Burgers equation and hydrodynamical instability

[ Abstract ]

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.

[ Reference URL ]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.

http://coe.math.sci.hokudai.ac.jp/

### 2007/04/11

10:30-11:30 Room #056 (Graduate School of Math. Sci. Bldg.)

The numerical treatment of pricing early exercise options under L'evy processes

http://coe.math.sci.hokudai.ac.jp/

**C. W. Oosterlee**(Delft University of Technology)The numerical treatment of pricing early exercise options under L'evy processes

[ Abstract ]

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.

[ Reference URL ]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.

http://coe.math.sci.hokudai.ac.jp/

### 2007/03/07

14:00-15:00 Room #056 (Graduate School of Math. Sci. Bldg.)

Stability theory in L^p for the space-inhomogeneous Boltzmann equation

http://coe.math.sci.hokudai.ac.jp/index.html.en

**Seung Yeal Ha**(Seoul National University)Stability theory in L^p for the space-inhomogeneous Boltzmann equation

[ Abstract ]

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.)

[ Reference URL ]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.)

http://coe.math.sci.hokudai.ac.jp/index.html.en

### 2007/01/31

10:30-11:30 Room #123 (Graduate School of Math. Sci. Bldg.)

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――

http://coe.math.sci.hokudai.ac.jp/sympo/various/index.html

**小谷正博**(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――

[ Abstract ]

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。

[ Reference URL ]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。

http://coe.math.sci.hokudai.ac.jp/sympo/various/index.html

### 2006/12/13

10:30-11:30 Room #056 (Graduate School of Math. Sci. Bldg.)

Computational Methods for Geometric PDEs

http://coe.math.sci.hokudai.ac.jp/sympo/various/index.html

**C. M. Elliott**(University of Sussex)Computational Methods for Geometric PDEs

[ Abstract ]

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.

[ Reference URL ]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.

http://coe.math.sci.hokudai.ac.jp/sympo/various/index.html

### 2006/12/06

10:30-11:30 Room #056 (Graduate School of Math. Sci. Bldg.)

Formation of rims surrounding a chondrule during solidification in 3- dimensions using the phase field model

http://coe.math.sci.hokudai.ac.jp/sympo/various/index.html

**横山悦郎**(学習院大学)Formation of rims surrounding a chondrule during solidification in 3- dimensions using the phase field model

[ Abstract ]

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.

[ Reference URL ]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.

http://coe.math.sci.hokudai.ac.jp/sympo/various/index.html

### 2006/11/29

10:30-11:30 Room #056 (Graduate School of Math. Sci. Bldg.)

Atomistic view of InAs quantum dot self-assembly from inside the growth chamber

http://coe.math.sci.hokudai.ac.jp/sympo/various/index.html

**塚本 史郎**(東京大学生産技術研究所)Atomistic view of InAs quantum dot self-assembly from inside the growth chamber

[ Abstract ]

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.

[ Reference URL ]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.

http://coe.math.sci.hokudai.ac.jp/sympo/various/index.html

### 2006/11/08

10:30-11:30 Room #056 (Graduate School of Math. Sci. Bldg.)

Crystal growth in dry deposited snow: experiment, theoretical modeling and simulation

http://coe.math.sci.hokudai.ac.jp/sympo/various/index.html

**Fredric Flin**(Hokkaido University)Crystal growth in dry deposited snow: experiment, theoretical modeling and simulation

[ Abstract ]

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.

[ Reference URL ]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.

http://coe.math.sci.hokudai.ac.jp/sympo/various/index.html

### 2006/10/05

16:30-17:30 Room #123 (Graduate School of Math. Sci. Bldg.)

Global existence and asymptotic behavior of Gowdy symmetric spacetimes with nonlinear scalar field

http://coe.math.sci.hokudai.ac.jp/sympo/various/index.html

**成田誠**(Department of Mathematics, National Taiwan University)Global existence and asymptotic behavior of Gowdy symmetric spacetimes with nonlinear scalar field

[ Abstract ]

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.

[ Reference URL ]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.

http://coe.math.sci.hokudai.ac.jp/sympo/various/index.html

### 2006/07/05

10:30-11:30 Room #056 (Graduate School of Math. Sci. Bldg.)

Level Set Methods and Multi-valued solutions

http://coe.math.sci.hokudai.ac.jp/sympo/various/index.html

**Y. H. Richard Tsai**(University of Texas)Level Set Methods and Multi-valued solutions

[ Abstract ]

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.

[ Reference URL ]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.

http://coe.math.sci.hokudai.ac.jp/sympo/various/index.html

### 2006/04/19

10:30-11:30 Room #056 (Graduate School of Math. Sci. Bldg.)

Oscillatory growth of a crystal controlled by interface kinetics and transport process

http://coe.math.sci.hokudai.ac.jp/sympo/various/005.html

**横山 悦郎**(学習院大学)Oscillatory growth of a crystal controlled by interface kinetics and transport process

[ Abstract ]

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.

[ Reference URL ]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.

http://coe.math.sci.hokudai.ac.jp/sympo/various/005.html

### 2006/04/04

16:30-17:30 Room #128 (Graduate School of Math. Sci. Bldg.)

Thermally-Driven Rare Events and Action Minimization

[ Reference URL ]

http://coe.math.sci.hokudai.ac.jp/sympo/various/004.html

**Maria Reznikoff**(Department of Mathematics, Princeton University)Thermally-Driven Rare Events and Action Minimization

[ Reference URL ]

http://coe.math.sci.hokudai.ac.jp/sympo/various/004.html

### 2005/11/22

16:30-17:30 Room #128 (Graduate School of Math. Sci. Bldg.)

Mathematics in the epidemiology and control of infectious diseases

http://coe.math.sci.hokudai.ac.jp/sympo/various/index.html

**Hans Heesterbeek**(University of Utrecht)Mathematics in the epidemiology and control of infectious diseases

[ Abstract ]

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.

[ Reference URL ]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.

http://coe.math.sci.hokudai.ac.jp/sympo/various/index.html