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過去の記録
過去の記録 ～05/22｜本日 05/23 | 今後の予定 05/24～
2012年04月04日(水)
PDE実解析研究会
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(2004年9月29日)～第38回(2008年10月15日)までの情報が掲載されております。
Jens Hoppe 氏 (Sogang University / KTH Royal Institute of Technology)
Multi linear formulation of differential geometry and matrix regularizations (ENGLISH)
北海道大学のHPには、第1回(2004年9月29日)～第38回(2008年10月15日)までの情報が掲載されております。
Jens Hoppe 氏 (Sogang University / KTH Royal Institute of Technology)
Multi linear formulation of differential geometry and matrix regularizations (ENGLISH)
[ 講演概要 ]
We prove that many aspects of the differential geometry of embedded Riemannian manifolds can be formulated in terms of multi linear algebraic structures on the space of smooth functions. In particular, we find algebraic expressions for Weingarten's formula, the Ricci curvature and the Codazzi-Mainardi equations.
For matrix analogues of embedded surfaces we define discrete curvatures and Euler characteristics, and a non-commutative Gauss–Bonnet theorem is shown to follow. We derive simple expressions for the discrete Gauss curvature in terms of matrices representing the embedding coordinates, and a large class of explicit examples is provided.
We prove that many aspects of the differential geometry of embedded Riemannian manifolds can be formulated in terms of multi linear algebraic structures on the space of smooth functions. In particular, we find algebraic expressions for Weingarten's formula, the Ricci curvature and the Codazzi-Mainardi equations.
For matrix analogues of embedded surfaces we define discrete curvatures and Euler characteristics, and a non-commutative Gauss–Bonnet theorem is shown to follow. We derive simple expressions for the discrete Gauss curvature in terms of matrices representing the embedding coordinates, and a large class of explicit examples is provided.
2012年04月03日(火)
保型形式の整数論月例セミナー
13:30-16:00 数理科学研究科棟(駒場) 123号室
刈山和俊 氏 (尾道市立大学経済情報学部
) 13:30-14:30
GL_m(D)の離散系列表現の形式次数に関する明示公式 (JAPANESE)
宗野恵樹 氏 (東京大学数理科学研究科) 15:00-16:00
Moments of the derivatives of the Riemann zeta function (JAPANESE)
刈山和俊 氏 (尾道市立大学経済情報学部
) 13:30-14:30
GL_m(D)の離散系列表現の形式次数に関する明示公式 (JAPANESE)
宗野恵樹 氏 (東京大学数理科学研究科) 15:00-16:00
Moments of the derivatives of the Riemann zeta function (JAPANESE)
[ 講演概要 ]
In my talk, we consider the integral moments of the derivatives of the Riemann zeta function on the critical line. We give certain lower bounds for these moments under the assumption of the Riemann hypothesis.
In my talk, we consider the integral moments of the derivatives of the Riemann zeta function on the critical line. We give certain lower bounds for these moments under the assumption of the Riemann hypothesis.
2012年03月23日(金)
作用素環セミナー
16:30-18:00 数理科学研究科棟(駒場) 117号室
Alex Kumjian 氏 (University of Nevada, Reno)
Higher Rank Graph $C^*$-algebras (ENGLISH)
Alex Kumjian 氏 (University of Nevada, Reno)
Higher Rank Graph $C^*$-algebras (ENGLISH)
講演会
10:30-11:30 数理科学研究科棟(駒場) 117号室
R. Penner 氏 (Aarhus/Caltech)
Cell decomposition of homotopy Deligne-Mumford. (ENGLISH)
R. Penner 氏 (Aarhus/Caltech)
Cell decomposition of homotopy Deligne-Mumford. (ENGLISH)
[ 講演概要 ]
A long-standing problem has been to extend the ideal cell decomposition of Riemann's moduli space to its compactification by stable curves. In joint work with Doug LaFountain, we have solved this problem with an explicit generalization of fatgraphs. The solution immediately provides a construction of odd-degree cycles, which are conjectured to be non-trivial, thus addressing yet another long-standing issue.
A long-standing problem has been to extend the ideal cell decomposition of Riemann's moduli space to its compactification by stable curves. In joint work with Doug LaFountain, we have solved this problem with an explicit generalization of fatgraphs. The solution immediately provides a construction of odd-degree cycles, which are conjectured to be non-trivial, thus addressing yet another long-standing issue.
2012年03月21日(水)
講演会
10:15-12:00 数理科学研究科棟(駒場) 123号室
R. Penner 氏 (Aarhus/Caltech)
Geochemical structure of biological macromolecules (ENGLISH)
R. Penner 氏 (Aarhus/Caltech)
Geochemical structure of biological macromolecules (ENGLISH)
[ 講演概要 ]
This first of two lectures will explain the basic combinatorial and geometrical structures of both protein and RNA. It is intended to set the stage of subsequent discussions for an audience with mathematical background.
This first of two lectures will explain the basic combinatorial and geometrical structures of both protein and RNA. It is intended to set the stage of subsequent discussions for an audience with mathematical background.
講演会
15:15-17:00 数理科学研究科棟(駒場) 123号室
R. Penner 氏 (Aarhus/Caltech)
Moduli space techniques in computational biology
(ENGLISH)
R. Penner 氏 (Aarhus/Caltech)
Moduli space techniques in computational biology
(ENGLISH)
[ 講演概要 ]
Basic fatgraph models of RNA and protein will be discussed, where edges are associated with base pairs in the former case and with hydrogen bonds between backbone atoms in the latter. For RNA, this leads to new methods described by context-free grammars of RNA folding prediction including certain classes of pseudo-knots. For protein, beyond these discrete invariants lie continuous ones which associate a rotation of
3-dimensional space to each hydrogen bond linking a pair of peptide units. Histograms of these rotations over the entire database of proteins exhibit a small number of "peptide unit legos" which can be used to advantage for the protein folding problem.
Basic fatgraph models of RNA and protein will be discussed, where edges are associated with base pairs in the former case and with hydrogen bonds between backbone atoms in the latter. For RNA, this leads to new methods described by context-free grammars of RNA folding prediction including certain classes of pseudo-knots. For protein, beyond these discrete invariants lie continuous ones which associate a rotation of
3-dimensional space to each hydrogen bond linking a pair of peptide units. Histograms of these rotations over the entire database of proteins exhibit a small number of "peptide unit legos" which can be used to advantage for the protein folding problem.
PDE実解析研究会
10:00-11:00 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(2004年9月29日)～第38回(2008年10月15日)までの情報が掲載されております。
Chiun-Chang Lee 氏 (National Taiwan University)
The asymptotic behaviors of the solutions of Poisson-Boltzmann type of equations (ENGLISH)
北海道大学のHPには、第1回(2004年9月29日)～第38回(2008年10月15日)までの情報が掲載されております。
Chiun-Chang Lee 氏 (National Taiwan University)
The asymptotic behaviors of the solutions of Poisson-Boltzmann type of equations (ENGLISH)
[ 講演概要 ]
Understanding the existence of electrical double layers around particles in the colloidal dispersion (system) is a crucial phenomenon of the colloid science. The Poisson-Boltzmann (PB) equation is one of the most widely used models to describe the equilibrium phenomenon of an electrical double layer in colloidal systems. This motivates us to study the asymptotic behavior for the boundary layer of the solutions of the PB equation. In this talk, we introduce the precise asymptotic formulas for the slope of the boundary layers with the exact leading order term and the second-order term. In particular, these formulas show that the mean curvature of the boundary exactly appears in the second-order term. This part is my personal work.
On the other hand, to study how the ionic concentrations and ionic valences affect the difference between the boundary and interior potentials in an electrolyte solution, we also introduce a modified PB equation - New Poisson-Boltzmann (PB_n) equation - joint works with Prof. Tai-Chia Lin and Chun Liu and YunKyong Hyon. We give a specific formula showing the influence of these crucial physical quantities on the potential difference in an electrolyte solution. This cannot be found in the PB equation.
Understanding the existence of electrical double layers around particles in the colloidal dispersion (system) is a crucial phenomenon of the colloid science. The Poisson-Boltzmann (PB) equation is one of the most widely used models to describe the equilibrium phenomenon of an electrical double layer in colloidal systems. This motivates us to study the asymptotic behavior for the boundary layer of the solutions of the PB equation. In this talk, we introduce the precise asymptotic formulas for the slope of the boundary layers with the exact leading order term and the second-order term. In particular, these formulas show that the mean curvature of the boundary exactly appears in the second-order term. This part is my personal work.
On the other hand, to study how the ionic concentrations and ionic valences affect the difference between the boundary and interior potentials in an electrolyte solution, we also introduce a modified PB equation - New Poisson-Boltzmann (PB_n) equation - joint works with Prof. Tai-Chia Lin and Chun Liu and YunKyong Hyon. We give a specific formula showing the influence of these crucial physical quantities on the potential difference in an electrolyte solution. This cannot be found in the PB equation.
2012年03月16日(金)
談話会・数理科学講演会
16:30-17:30 数理科学研究科棟(駒場) 123号室
旧記録は、上記セミナーURLにあります。
お茶&Coffee&お菓子: 16:00～16:30 (コモンルーム)。
柳 春（LIU, Chun） 氏 (東京大学大学院数理科学研究科／ペンシルバニア州立大学)
複雑流体について (ENGLISH)
旧記録は、上記セミナーURLにあります。
お茶&Coffee&お菓子: 16:00～16:30 (コモンルーム)。
柳 春（LIU, Chun） 氏 (東京大学大学院数理科学研究科／ペンシルバニア州立大学)
複雑流体について (ENGLISH)
[ 講演概要 ]
この講演では、タンパク質と生体液における粘弾性材料、液晶、イオン流体といった異方的複雑流体のエネルギー的な変分法手法の数学理論について取 り上げる。
混合液や溶液などの複雑流体は我々の日常生活にあふれている。これらの材料が示す複雑な現象や特性は、微視的相互作用と巨視的動力学の間の結合と 競合を反映している。我々はこれらのあらゆるマルチスケール・マルチフィジックスシステムに共通する基本的なエネルギー的変分構造を研究する。
この講演では、さまざまな複雑流体についてのモデリングに加えて、数学解析や数値計算まで触れたい。
この講演では、タンパク質と生体液における粘弾性材料、液晶、イオン流体といった異方的複雑流体のエネルギー的な変分法手法の数学理論について取 り上げる。
混合液や溶液などの複雑流体は我々の日常生活にあふれている。これらの材料が示す複雑な現象や特性は、微視的相互作用と巨視的動力学の間の結合と 競合を反映している。我々はこれらのあらゆるマルチスケール・マルチフィジックスシステムに共通する基本的なエネルギー的変分構造を研究する。
この講演では、さまざまな複雑流体についてのモデリングに加えて、数学解析や数値計算まで触れたい。
2012年03月14日(水)
PDE実解析研究会
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(2004年9月29日)～第38回(2008年10月15日)までの情報が掲載されております。
Jürgen Saal 氏 (Technische Universität Darmstadt)
Exponential convergence to equilibria for a general model in hydrodynamics (ENGLISH)
北海道大学のHPには、第1回(2004年9月29日)～第38回(2008年10月15日)までの情報が掲載されております。
Jürgen Saal 氏 (Technische Universität Darmstadt)
Exponential convergence to equilibria for a general model in hydrodynamics (ENGLISH)
[ 講演概要 ]
We present a thorough analysis of the Navier-Stokes-Nernst-Planck-Poisson equations. This system describes the dynamics of charged particles dispersed in an incompressible fluid.
In contrast to existing literature and in view of its physical relevance, we also allow for different diffusion coefficients of the charged species.
In addition, the commonly assumed electro-neutrality condition is not required by our approach.
Our aim is to present results on local and global well-posedness as well as exponential stability of equilibria. The results are obtained jointly with Dieter Bothe and Andre Fischer at the Center of Smart Interfaces at TU Darmstadt.
We present a thorough analysis of the Navier-Stokes-Nernst-Planck-Poisson equations. This system describes the dynamics of charged particles dispersed in an incompressible fluid.
In contrast to existing literature and in view of its physical relevance, we also allow for different diffusion coefficients of the charged species.
In addition, the commonly assumed electro-neutrality condition is not required by our approach.
Our aim is to present results on local and global well-posedness as well as exponential stability of equilibria. The results are obtained jointly with Dieter Bothe and Andre Fischer at the Center of Smart Interfaces at TU Darmstadt.
2012年03月13日(火)
談話会・数理科学講演会
15:00-16:00 数理科学研究科棟(駒場) 050号室
旧記録は、上記セミナーURLにあります。
お茶&Coffee&お菓子: 14:30～15:00 (コモンルーム)。
Aleksandar Ivic 氏 (University of Belgrade, the Serbian Academy of Science and Arts)
Problems and results on Hardy's Z-function (JAPANESE)
旧記録は、上記セミナーURLにあります。
お茶&Coffee&お菓子: 14:30～15:00 (コモンルーム)。
Aleksandar Ivic 氏 (University of Belgrade, the Serbian Academy of Science and Arts)
Problems and results on Hardy's Z-function (JAPANESE)
[ 講演概要 ]
The title is self-explanatory: G.H. Hardy first used the function
$Z(t)$ to show that there are infinitely many zeta-zeros on the
critical line $\\Re s = 1/2$. In recent years there is a revived
interest in this function, with many results and open problems.
The title is self-explanatory: G.H. Hardy first used the function
$Z(t)$ to show that there are infinitely many zeta-zeros on the
critical line $\\Re s = 1/2$. In recent years there is a revived
interest in this function, with many results and open problems.
数理人口学・数理生物学セミナー
14:00-15:00 数理科学研究科棟(駒場) 154号室
梶原毅 氏 (岡山大学環境理工学部)
リアプノフ関数および汎関数の構成について (JAPANESE)
梶原毅 氏 (岡山大学環境理工学部)
リアプノフ関数および汎関数の構成について (JAPANESE)
[ 講演概要 ]
常微分方程式、遅れのある微分方程式などの大域安定性の判定において有用なLyapunov 関数、Lyapunov 汎関数をシステマティックに構成する一つの方法について報告する。また、齢構造を持つモデルへの拡張についても触れたい。
常微分方程式、遅れのある微分方程式などの大域安定性の判定において有用なLyapunov 関数、Lyapunov 汎関数をシステマティックに構成する一つの方法について報告する。また、齢構造を持つモデルへの拡張についても触れたい。
2012年03月09日(金)
東京無限可積分系セミナー
13:30-14:30 数理科学研究科棟(駒場) 002号室
柳田 伸太郎 氏 (神戸大理)
On Hall algebra of complexes (JAPANESE)
柳田 伸太郎 氏 (神戸大理)
On Hall algebra of complexes (JAPANESE)
[ 講演概要 ]
The topic of my talk is the Hall algebra of complexes,
which is recently introduced by T. Bridgeland.
I will discuss its properties and relation to
auto-equivalences of derived category.
If I have enough time,
I will also discuss the relation
of this Hall algebra to the so-called Ding-Iohara algebra.
The topic of my talk is the Hall algebra of complexes,
which is recently introduced by T. Bridgeland.
I will discuss its properties and relation to
auto-equivalences of derived category.
If I have enough time,
I will also discuss the relation
of this Hall algebra to the so-called Ding-Iohara algebra.
2012年03月07日(水)
GCOEセミナー
17:00-18:00 数理科学研究科棟(駒場) 370号室
Kazufumi Ito 氏 (North Carolina State Univ.)
Nonsmooth Optimization, Theory and Applications. (ENGLISH)
Kazufumi Ito 氏 (North Carolina State Univ.)
Nonsmooth Optimization, Theory and Applications. (ENGLISH)
[ 講演概要 ]
We develop a Lagrange multiplier theory for Nonsmooth optimization, including $L^¥infty$ and $L^1$ optimizations, $¥ell^0$ (counting meric) and $L^0$ (Ekeland mertic), Binary and Mixed integer optimizations and Data mining. A multitude of important problems can be treated by our approach and numerical algorithms are developed based on the Lagrange multiplier theory.
We develop a Lagrange multiplier theory for Nonsmooth optimization, including $L^¥infty$ and $L^1$ optimizations, $¥ell^0$ (counting meric) and $L^0$ (Ekeland mertic), Binary and Mixed integer optimizations and Data mining. A multitude of important problems can be treated by our approach and numerical algorithms are developed based on the Lagrange multiplier theory.
2012年03月06日(火)
GCOEセミナー
16:00-17:00 数理科学研究科棟(駒場) 370号室
Dietmar Hoemberg 氏 (Weierstrass Institute, Berlin)
On the phase field approach to shape and topology optimization (ENGLISH)
Dietmar Hoemberg 氏 (Weierstrass Institute, Berlin)
On the phase field approach to shape and topology optimization (ENGLISH)
[ 講演概要 ]
Owing to different densities of the respective phases, solid-solid phase transitions often are accompanied by (often undesired) changes in workpiece size and shape. In my talk I will address the reverse question of finding an optimal phase mixture in order to accomplish a desired workpiece shape.
From mathematical point of view this corresponds to an optimal shape design problem subject to a static mechanical equilibrium problem with phase dependent stiffness tensor, in which the two phases exhibit different densities leading to different internal stresses. Our goal is to tackle this problem using a phasefield relaxation.
To this end we first briefly recall previous works regarding phasefield approaches to topology optimization (e.g. by Bourdin ¥& Chambolle, Burger ¥& Stainko and Blank, Garcke et al.).
We add a Ginzburg-Landau term to our cost functional, derive an adjoint equation for the displacement and choose a gradient flow dynamics with an articial time variable for our phasefield variable. We discuss well-posedness results for the resulting system and conclude with some numerical results.
Owing to different densities of the respective phases, solid-solid phase transitions often are accompanied by (often undesired) changes in workpiece size and shape. In my talk I will address the reverse question of finding an optimal phase mixture in order to accomplish a desired workpiece shape.
From mathematical point of view this corresponds to an optimal shape design problem subject to a static mechanical equilibrium problem with phase dependent stiffness tensor, in which the two phases exhibit different densities leading to different internal stresses. Our goal is to tackle this problem using a phasefield relaxation.
To this end we first briefly recall previous works regarding phasefield approaches to topology optimization (e.g. by Bourdin ¥& Chambolle, Burger ¥& Stainko and Blank, Garcke et al.).
We add a Ginzburg-Landau term to our cost functional, derive an adjoint equation for the displacement and choose a gradient flow dynamics with an articial time variable for our phasefield variable. We discuss well-posedness results for the resulting system and conclude with some numerical results.
GCOEセミナー
17:00-18:00 数理科学研究科棟(駒場) 370号室
Thomas Petzold 氏 (Weierstrass Institute, Berlin)
Finite element simulations of induction hardening of steel parts (ENGLISH)
Thomas Petzold 氏 (Weierstrass Institute, Berlin)
Finite element simulations of induction hardening of steel parts (ENGLISH)
[ 講演概要 ]
Induction hardening is a modern method for the heat treatment of steel parts.
A well directed heating by electromagnetic waves and subsequent quenching of the workpiece increases the hardness of the surface layer.
The process is very fast and energy efficient and plays a big role in modern manufacturing facilities in many industrial application areas.
In this talk a model for induction hardening of steel parts is presented. It consist of a system of partial differential equations including Maxwell's equations and the heat equation.
The finite element method is used to perform numerical simulations in 3D.
This requires a suitable discretization of Maxwell's equations leading to so called edge-finite-elements.
We will give a short overview of edge elements and present numerical simulations of induction hardening.
We will address some of the difficulties arising when solving the large system of non-linear coupled PDEs in three space dimensions.
Induction hardening is a modern method for the heat treatment of steel parts.
A well directed heating by electromagnetic waves and subsequent quenching of the workpiece increases the hardness of the surface layer.
The process is very fast and energy efficient and plays a big role in modern manufacturing facilities in many industrial application areas.
In this talk a model for induction hardening of steel parts is presented. It consist of a system of partial differential equations including Maxwell's equations and the heat equation.
The finite element method is used to perform numerical simulations in 3D.
This requires a suitable discretization of Maxwell's equations leading to so called edge-finite-elements.
We will give a short overview of edge elements and present numerical simulations of induction hardening.
We will address some of the difficulties arising when solving the large system of non-linear coupled PDEs in three space dimensions.
2012年02月29日(水)
GCOEセミナー
16:00-17:00 数理科学研究科棟(駒場) 270号室
Johannes Elschner 氏 (Weierstrass Institute, Germany)
Direct and inverse scattering of elastic waves by diffraction gratings (ENGLISH)
Johannes Elschner 氏 (Weierstrass Institute, Germany)
Direct and inverse scattering of elastic waves by diffraction gratings (ENGLISH)
[ 講演概要 ]
The talk presents joint work with Guanghui Hu on the scattering of time-harmonic plane elastic waves by two-dimensional periodic structures. The first part presents existence and uniqueness results for the direct problem , using a variational approach. For the inverse problem, we discuss global uniqueness results with a minimal number of incident pressure or shear waves under the boundary conditions of the third and fourth kind. Generalizations to biperiodic elastic diffraction gratings in 3D are also mentioned. Finally we consider a reconstruction method applied to the inverse Dirichlet problem for the quasi-periodic 2D Navier equation.
The talk presents joint work with Guanghui Hu on the scattering of time-harmonic plane elastic waves by two-dimensional periodic structures. The first part presents existence and uniqueness results for the direct problem , using a variational approach. For the inverse problem, we discuss global uniqueness results with a minimal number of incident pressure or shear waves under the boundary conditions of the third and fourth kind. Generalizations to biperiodic elastic diffraction gratings in 3D are also mentioned. Finally we consider a reconstruction method applied to the inverse Dirichlet problem for the quasi-periodic 2D Navier equation.
2012年02月22日(水)
代数学コロキウム
18:00-19:00 数理科学研究科棟(駒場) 056号室
望月拓郎 氏 (京都大学数理解析研究所)
Twistor $D$-module and harmonic bundle (ENGLISH)
望月拓郎 氏 (京都大学数理解析研究所)
Twistor $D$-module and harmonic bundle (ENGLISH)
[ 講演概要 ]
Abstract:
We shall overview the theory of twistor $D$-modules and
harmonic bundles. I am planning to survey the following topics,
motivated by the Hard Lefschetz Theorem for semisimple holonomic
$D$-modules:
1. What is a twistor $D$-module?
2. Local structure of meromorphic flat bundles
3. Wild harmonic bundles from local and global viewpoints
(本講演は「東京パリ数論幾何セミナー」として、インターネットによる東大数理とIHESとの双方向同時中継で行います。)
Abstract:
We shall overview the theory of twistor $D$-modules and
harmonic bundles. I am planning to survey the following topics,
motivated by the Hard Lefschetz Theorem for semisimple holonomic
$D$-modules:
1. What is a twistor $D$-module?
2. Local structure of meromorphic flat bundles
3. Wild harmonic bundles from local and global viewpoints
(本講演は「東京パリ数論幾何セミナー」として、インターネットによる東大数理とIHESとの双方向同時中継で行います。)
GCOEセミナー
15:00-16:00 数理科学研究科棟(駒場) 270号室
Bernadette Miara 氏 (Université Paris-Est, ESIEE, France)
Justification of a Shallow Shell Model in Unilateral Contact with an Obstacle (ENGLISH)
Bernadette Miara 氏 (Université Paris-Est, ESIEE, France)
Justification of a Shallow Shell Model in Unilateral Contact with an Obstacle (ENGLISH)
[ 講演概要 ]
We consider a three-dimensional elastic shell in unilateral contact with a plane. This lecture aims at justifying the asymptotic limit of the set of equilibrium equations of the structure when the thickness of the shell goes to zero. More precisely, we start with the 3D Signorini problem (with finite thickness) and obtain at the limit an obstacle 2D problem. This problem has already been studied [4] in the Cartesian framework on the basis of the bi-lateral problem [3]. The interest and the difficulty of the approach in the curvilinear framework (more appropriate to handle general shells) is due to the coupling between the tangential and transverse covariant components of the elastic field in the expression of the nonpenetrability conditions.
The procedure is the same as the one used in the asymptotic analysis of 3D bilateral structures [1, 2]: assumptions on the data, (loads and geometry of the middle surface of the shell) and re-scalling of the unknowns (displacement field or stress tensor); the new feature is the special handling of the components coupling.
The main result we obtain is as follows:
i) Under the assumption of regularity of the external volume and surface loads, and of the mapping that defines the middle surface of the shell, we establish that the family of elastic displacements converges strongly as the thickness tends to zero in an appropriate set which is a convex cone.
ii) The limit elastic displacement is a Kirchhoff-Love field given by a variational problem which will be analysed into details. The contact conditions are fully explicited for any finite thickness and at the limit.
This is a joint work with Alain L´eger, CNRS, Laboratoire de M´ecanique et d’Acoustique, 13402, Marseille, France.
We consider a three-dimensional elastic shell in unilateral contact with a plane. This lecture aims at justifying the asymptotic limit of the set of equilibrium equations of the structure when the thickness of the shell goes to zero. More precisely, we start with the 3D Signorini problem (with finite thickness) and obtain at the limit an obstacle 2D problem. This problem has already been studied [4] in the Cartesian framework on the basis of the bi-lateral problem [3]. The interest and the difficulty of the approach in the curvilinear framework (more appropriate to handle general shells) is due to the coupling between the tangential and transverse covariant components of the elastic field in the expression of the nonpenetrability conditions.
The procedure is the same as the one used in the asymptotic analysis of 3D bilateral structures [1, 2]: assumptions on the data, (loads and geometry of the middle surface of the shell) and re-scalling of the unknowns (displacement field or stress tensor); the new feature is the special handling of the components coupling.
The main result we obtain is as follows:
i) Under the assumption of regularity of the external volume and surface loads, and of the mapping that defines the middle surface of the shell, we establish that the family of elastic displacements converges strongly as the thickness tends to zero in an appropriate set which is a convex cone.
ii) The limit elastic displacement is a Kirchhoff-Love field given by a variational problem which will be analysed into details. The contact conditions are fully explicited for any finite thickness and at the limit.
This is a joint work with Alain L´eger, CNRS, Laboratoire de M´ecanique et d’Acoustique, 13402, Marseille, France.
GCOEセミナー
16:15-17:15 数理科学研究科棟(駒場) 270号室
Oleg Emanouilov 氏 (Colorado State University)
Determination of first order coefficient in semilinear elliptic equation by partial Cauchy data. (ENGLISH)
Oleg Emanouilov 氏 (Colorado State University)
Determination of first order coefficient in semilinear elliptic equation by partial Cauchy data. (ENGLISH)
[ 講演概要 ]
In a bounded domain in $R^2$, we consider a semilinear elliptic equation $¥Delta u +qu +f(u)=0$.
Under some conditions on $f$, we show that the coefficient $q$ can be uniquely determined by the following partial data
$$
{¥mathcal C}_q=¥{(u,¥frac{¥partial u}{¥partial¥nu})¥vert_{\\\\tilde Gamma}¥vert
- ¥Delta u +qu +f(u)=0, ¥,¥,¥, u¥vert_{¥Gamma_0}=0,¥,¥, u¥in H^1(¥Omega)¥}
$$
where $¥tilde ¥Gamma$ is an arbitrary fixed open set of
$¥partial¥Omega$ and $¥Gamma_0=¥partial¥Omega¥setminus¥tilde¥Gamma$.
In a bounded domain in $R^2$, we consider a semilinear elliptic equation $¥Delta u +qu +f(u)=0$.
Under some conditions on $f$, we show that the coefficient $q$ can be uniquely determined by the following partial data
$$
{¥mathcal C}_q=¥{(u,¥frac{¥partial u}{¥partial¥nu})¥vert_{\\\\tilde Gamma}¥vert
- ¥Delta u +qu +f(u)=0, ¥,¥,¥, u¥vert_{¥Gamma_0}=0,¥,¥, u¥in H^1(¥Omega)¥}
$$
where $¥tilde ¥Gamma$ is an arbitrary fixed open set of
$¥partial¥Omega$ and $¥Gamma_0=¥partial¥Omega¥setminus¥tilde¥Gamma$.
2012年02月21日(火)
トポロジー火曜セミナー
16:30-18:00 数理科学研究科棟(駒場) 056号室
Tea: 16:00 - 16:30 コモンルーム
見村 万佐人 氏 (東京大学大学院数理科学研究科)
Property (TT)/T and homomorphism superrigidity into mapping class groups (JAPANESE)
Tea: 16:00 - 16:30 コモンルーム
見村 万佐人 氏 (東京大学大学院数理科学研究科)
Property (TT)/T and homomorphism superrigidity into mapping class groups (JAPANESE)
[ 講演概要 ]
コンパクトで向きづけられた曲面(パンクがあってもよい)の写像類群には,多くの謎めいた性質があることが知られている:写像類群はある場合には高ランク格子(つまり,高ランク代数群の既約格子)に近いふるまいをするが,別の場合にはランク1格子に近いふるまいをする.次に述べる定理はFarb--Kaimanovich--Masur超剛性と呼ばれており,写像類群のランク1格子に近いふるまいの顕著な例である:「高ランク格子(例えばSL(3,Z)や,SL(3,R)の余コンパクト格子など)から写像類群への任意の群準同型は有限の像をもつ.」
本講演では,この超剛性の以下のような拡張を証明する:「高ランク格子を(算術的とは限らない)一般の環上の適切な行列群に置き換えた時でも,上の定理が成り立つ.」考える群の主な例は「普遍格子」と呼ばれる群であり,これは整係数有限生成可換多項式環上の特殊線型群(SL(3,Z[x])など)のことを指す.この定理を示すために,群の"性質(TT)/T"という,Kazhdanの性質(T)を強めた性質を導入する.
以上の2性質を紹介し,群の(ユニタリ表現で捻じれた係数の)コホモロジー・有界コホモロジーとの関係を説明したい.その上で, 本講演の定理の証明の概略を述べたい.
コンパクトで向きづけられた曲面(パンクがあってもよい)の写像類群には,多くの謎めいた性質があることが知られている:写像類群はある場合には高ランク格子(つまり,高ランク代数群の既約格子)に近いふるまいをするが,別の場合にはランク1格子に近いふるまいをする.次に述べる定理はFarb--Kaimanovich--Masur超剛性と呼ばれており,写像類群のランク1格子に近いふるまいの顕著な例である:「高ランク格子(例えばSL(3,Z)や,SL(3,R)の余コンパクト格子など)から写像類群への任意の群準同型は有限の像をもつ.」
本講演では,この超剛性の以下のような拡張を証明する:「高ランク格子を(算術的とは限らない)一般の環上の適切な行列群に置き換えた時でも,上の定理が成り立つ.」考える群の主な例は「普遍格子」と呼ばれる群であり,これは整係数有限生成可換多項式環上の特殊線型群(SL(3,Z[x])など)のことを指す.この定理を示すために,群の"性質(TT)/T"という,Kazhdanの性質(T)を強めた性質を導入する.
以上の2性質を紹介し,群の(ユニタリ表現で捻じれた係数の)コホモロジー・有界コホモロジーとの関係を説明したい.その上で, 本講演の定理の証明の概略を述べたい.
2012年02月20日(月)
関数解析セミナー
16:30-17:30 数理科学研究科棟(駒場) 128号室
Jan Philip SOLOVEJ 氏 (コペンハーゲン大学)
Microscopic derivation of the Ginzburg-Landau model (ENGLISH)
Jan Philip SOLOVEJ 氏 (コペンハーゲン大学)
Microscopic derivation of the Ginzburg-Landau model (ENGLISH)
[ 講演概要 ]
I will discuss how the \\emph{Ginzburg-Landau} (GL) model of superconductivity arises as an asymptotic limit of the microscopic Bardeen-Cooper-Schrieffer (BCS) model. The asymptotic limit may be seen as a semiclassical limit and one of the main difficulties is to derive a semiclassical expansion with minimal regularity assumptions. It is not rigorously understood how the BCS model approximates the underlying many-body quantum system. I will formulate the BCS model as a variational problem, but only heuristically discuss its relation to quantum mechanics.
I will discuss how the \\emph{Ginzburg-Landau} (GL) model of superconductivity arises as an asymptotic limit of the microscopic Bardeen-Cooper-Schrieffer (BCS) model. The asymptotic limit may be seen as a semiclassical limit and one of the main difficulties is to derive a semiclassical expansion with minimal regularity assumptions. It is not rigorously understood how the BCS model approximates the underlying many-body quantum system. I will formulate the BCS model as a variational problem, but only heuristically discuss its relation to quantum mechanics.
2012年02月14日(火)
解析学火曜セミナー
16:30-18:00 数理科学研究科棟(駒場) 128号室
Michael Loss 氏 (Georgia Institute of Technology)
Symmetry results for Caffarelli-Kohn-Nirenberg inequalities (ENGLISH)
Michael Loss 氏 (Georgia Institute of Technology)
Symmetry results for Caffarelli-Kohn-Nirenberg inequalities (ENGLISH)
2012年02月07日(火)
GCOEセミナー
14:00-15:00 数理科学研究科棟(駒場) 370号室
Piermarco Cannarsa 氏 (Mat. Univ. Roma "Tor Vergata")
Controllability results for degenerate parabolic operators (ENGLISH)
Piermarco Cannarsa 氏 (Mat. Univ. Roma "Tor Vergata")
Controllability results for degenerate parabolic operators (ENGLISH)
[ 講演概要 ]
UnlikeCuniformly parabolic equations, parabolic operators that degenerate on subsets of the space domain exhibit very different behaviors from the point of view of controllability. For instance, null controllability in arbitrary time may be true or false according to the degree of degeneracy, and there are also examples where a finite time is needed to ensure such a property. This talk will survey most of the theory that has been established so far for operators with boundary degeneracy, and discuss recent results for operators of Grushin type which degenerate in the interior.
UnlikeCuniformly parabolic equations, parabolic operators that degenerate on subsets of the space domain exhibit very different behaviors from the point of view of controllability. For instance, null controllability in arbitrary time may be true or false according to the degree of degeneracy, and there are also examples where a finite time is needed to ensure such a property. This talk will survey most of the theory that has been established so far for operators with boundary degeneracy, and discuss recent results for operators of Grushin type which degenerate in the interior.
2012年02月03日(金)
博士論文発表会
09:45-11:00 数理科学研究科棟(駒場) 118号室
伊藤 敦 氏 (大学院数理科学研究科)
How to estimate Seshadri constants（セシャドリ定数を評価する方法）
(JAPANESE)
伊藤 敦 氏 (大学院数理科学研究科)
How to estimate Seshadri constants（セシャドリ定数を評価する方法）
(JAPANESE)
博士論文発表会
11:00-12:15 数理科学研究科棟(駒場) 118号室
宗野 惠樹 氏 (東京大学大学院数理科学研究科)
Spherical functions associated to the principal series representations of SL(3,R) and higher rank Epstein zeta functions（SL(3,R)の主系列表現に付随する球関数，及び高階Epsteinゼータ関数について）
(JAPANESE)
宗野 惠樹 氏 (東京大学大学院数理科学研究科)
Spherical functions associated to the principal series representations of SL(3,R) and higher rank Epstein zeta functions（SL(3,R)の主系列表現に付随する球関数，及び高階Epsteinゼータ関数について）
(JAPANESE)
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