## Seminar on Mathematics for various disciplines

Seminar information archive ～09/21｜Next seminar｜Future seminars 09/22～

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

**Seminar information archive**

### 2016/11/17

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

Convexity preserving properties for nonlinear evolution equations (English)

**Qing Liu**(Fukuoka University)Convexity preserving properties for nonlinear evolution equations (English)

[ Abstract ]

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.

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.

### 2015/10/06

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

Multi-material phase field approach to structural topology optimization and its relation to sharp interface approach (English)

**Mohammad Hassan Farshbaf Shaker**(Weierstrass Institute, Berlin)Multi-material phase field approach to structural topology optimization and its relation to sharp interface approach (English)

[ Abstract ]

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.

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.

### 2015/09/08

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

Duality based approaches to total variation-like flows with applications to image processing (English)

**Monika Muszkieta**(Wroclaw University of Technology)Duality based approaches to total variation-like flows with applications to image processing (English)

[ Abstract ]

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 differentiability 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.

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 differentiability 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.

### 2015/04/14

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

**Yosuke Hasegawa**### 2015/01/27

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

### 2014/10/14

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

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)

**Tsutomu Kambe**(University of Tokyo)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)

[ Abstract ]

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.

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.

### 2014/06/10

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

The self-similar collapse solution of a point vortex system and complex time singularities (JAPANESE)

**Yoshifumi Kimura**(Graduate School of Mathematics, Nagoya University)The self-similar collapse solution of a point vortex system and complex time singularities (JAPANESE)

[ Abstract ]

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.

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.

### 2013/11/26

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

An immersed boundary method for mass transfer across permeable moving interfaces (ENGLISH)

**Huaxiong Huang**(York University)An immersed boundary method for mass transfer across permeable moving interfaces (ENGLISH)

[ Abstract ]

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.

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.

### 2013/06/11

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

脳の同一源性推定を仮定した聴覚時間知覚のベイズモデル (JAPANESE)

**Ken-ichi SAWAI**(Institute of Industrial Science, the University of Tokyo)脳の同一源性推定を仮定した聴覚時間知覚のベイズモデル (JAPANESE)

### 2013/01/23

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

Ionic Fluids and Their Transport: From Kinetic Descriptions to Continuum Models (ENGLISH)

**Chun Liu**(Pennsylvania State University)Ionic Fluids and Their Transport: From Kinetic Descriptions to Continuum Models (ENGLISH)

[ Abstract ]

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.

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.

### 2011/11/21

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

A convex model for non-negative matrix factorization and dimensionality reduction on physical space (ENGLISH)

**Ernie Esser**(University of California, Irvine)A convex model for non-negative matrix factorization and dimensionality reduction on physical space (ENGLISH)

[ Abstract ]

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.

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.

### 2011/11/08

16:30-17:30 Room #052 (Graduate School of Math. Sci. Bldg.)

Interactive Data Visualization challenges, approaches and examples (ENGLISH)

**Ralph Bruckschen**(ベルリン工科大学、MATHEON)Interactive Data Visualization challenges, approaches and examples (ENGLISH)

[ Abstract ]

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.

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.

### 2011/10/05

10:00-11:00 Room #056 (Graduate School of Math. Sci. Bldg.)

Energetic Variational Approaches for Ionic Fluids (ENGLISH)

**Chun Liu**(University of Tokyo / Pennsylvania State University)Energetic Variational Approaches for Ionic Fluids (ENGLISH)

[ Abstract ]

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.

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.

### 2011/06/29

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

Computational understanding of diverse structures in human anatomy by landmark detection in medical images (JAPANESE)

http://info.ms.u-tokyo.ac.jp/seminar/mathvar/future.html

**Yoshitaka Masutani**(University of Tokyo)Computational understanding of diverse structures in human anatomy by landmark detection in medical images (JAPANESE)

[ Abstract ]

Robust recognition of anatomical structures in medical images is indispensable for clinical support of diagnosis and therapy. In this lecture, the diverse system of human anatomy is shortly introduced first. Then, the overview of detection techniques for such structures in medical images is shown. Finally, our approach of anatomical structure recognition is presented and is discussed, which is realized by a unified framework of landmark detection based on appearance model matching and MAP estimation on inter-landmark distance probabilities.

[ Reference URL ]Robust recognition of anatomical structures in medical images is indispensable for clinical support of diagnosis and therapy. In this lecture, the diverse system of human anatomy is shortly introduced first. Then, the overview of detection techniques for such structures in medical images is shown. Finally, our approach of anatomical structure recognition is presented and is discussed, which is realized by a unified framework of landmark detection based on appearance model matching and MAP estimation on inter-landmark distance probabilities.

http://info.ms.u-tokyo.ac.jp/seminar/mathvar/future.html

### 2011/05/18

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

On the perturbation theory for many-electron systems at positive temperature (JAPANESE)

[ Reference URL ]

http://info.ms.u-tokyo.ac.jp/seminar/mathvar/future.html

**Yohei Kashima**(University of Tokyo)On the perturbation theory for many-electron systems at positive temperature (JAPANESE)

[ Reference URL ]

http://info.ms.u-tokyo.ac.jp/seminar/mathvar/future.html

### 2011/01/19

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

Exploration of essence of Mullins equation (JAPANESE)

**Yoshihito Ogasawara**(Waseda University Faculty of Science and Engineering)Exploration of essence of Mullins equation (JAPANESE)

### 2010/10/20

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

Curvature Dependent Diffusion Flow on Surface with Thickness (JAPANESE)

**Naohisa Ogawa**(Hokkaido Institute of Technology)Curvature Dependent Diffusion Flow on Surface with Thickness (JAPANESE)

[ Abstract ]

Particle diffusion in a two dimensional curved surface with thickness

embedded in $R_3$ is considered.

In addition to the usual diffusion flow, we find a new flow with an explicit

curvature dependence in $\\epsilon$ (thickness of surface) expansion.

As an example, the surface of elliptic cylinder is considered, and curvature

dependent diffusion coefficient is calculated. In addition, we consider the

1 dimensional object in $R_3$ (Tube),

and check the physical meaning of curvature effect.

Particle diffusion in a two dimensional curved surface with thickness

embedded in $R_3$ is considered.

In addition to the usual diffusion flow, we find a new flow with an explicit

curvature dependence in $\\epsilon$ (thickness of surface) expansion.

As an example, the surface of elliptic cylinder is considered, and curvature

dependent diffusion coefficient is calculated. In addition, we consider the

1 dimensional object in $R_3$ (Tube),

and check the physical meaning of curvature effect.

### 2010/07/07

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

Instabilities of steps on a vicinal face induced by the

asymmetry of diffusion field. (JAPANESE)

**Masahide Sato**(Information Media Center, Kanazawa University)Instabilities of steps on a vicinal face induced by the

asymmetry of diffusion field. (JAPANESE)

### 2010/05/19

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

Mathematical sciences collaborating with clinical medicine (JAPANESE)

**Hiroshi Suito**(Okayama University)Mathematical sciences collaborating with clinical medicine (JAPANESE)

### 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.