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Mathematical Study of Renormalization Groups and applications to Dynamical System

Research Project

Project/Area Number 20540221
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Global analysis
Research InstitutionSetsunan University

Principal Investigator

ITO KeiichiR.  Setsunan University, 理工学部, 教授 (50268489)

Co-Investigator(Kenkyū-buntansha) TERAMOTO Yoshiaki  摂南大学, 理工学部, 教授 (40237011)
SHIMADA ShinーIchi  摂南大学, 理工学部, 准教授 (40196481)
Co-Investigator(Renkei-kenkyūsha) HIROKAWA Masao  岡山大学, 自然科学研究科, 教授 (70282788)
HIROSHIMA Humio  九州大学, 数理科学研究科, 准教授 (00330358)
TAMURA Hiroshi  金沢大学, 理工学部, 教授 (80188440)
Project Period (FY) 2008 – 2010
Project Status Completed (Fiscal Year 2010)
Budget Amount *help
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2010: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2009: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2008: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Keywords繰りこみ群 / 相転移 / 臨界現象 / 非線形方程式 / 流体 / 乱流 / リッチ・フロウ / スピンモデル / ナヴィエ・ストークス方程式 / リッチフロウ / シグマ模型 / パターシ形成 / ベルナール流 / アンダーソン局在 / クオーク幽閉 / アハラノフーボーム効果 / ソレノイド
Research Abstract

Ito studied applications of renormalization group method in mathematical sciences from various points of view. He investigates the Ricci flows from statistical mechanics point of view, and suggested that the transformation of manifolds by the flow is strongly related to the Pirogov-Sinai theory of phase transitions.
He also reconsidered the paper by Ya Sinai and D.Li on the constructions of (complex) turbulent solution of Navier-Stokes equation of fluid, using the renormalization group type argument. It seems that the paper needed some calculations to be understood. Ito studied quark confinement problem some decades ago, and established confinement in the hierarchical approximation of the Migdal-Kadanov type. However there appeared a misleading paper in which the author claimed that he established the confinement.
Ito and Prof.E.Seiler of MaxPlanck Institute argued how and why he made mistakes in his arguments.

Report

(4 results)
  • 2010 Annual Research Report   Final Research Report ( PDF )
  • 2009 Annual Research Report
  • 2008 Annual Research Report
  • Research Products

    (27 results)

All 2011 2010 2009 2008 Other

All Journal Article (17 results) (of which Peer Reviewed: 6 results) Presentation (5 results) Book (2 results) Remarks (3 results)

  • [Journal Article] 数理物理学(繰りこみ群)から見たペレルマン理論2010

    • Author(s)
      伊東恵一
    • Journal Title

      数理物理学への誘い(河東康之編)(遊星社) vol.7

      Pages: 53-100

    • Related Report
      2010 Final Research Report
  • [Journal Article] Large Deviation principle for noninteracting boson random point processes2010

    • Author(s)
      H.Tamura, V.Zagrevnov
    • Journal Title

      J.Math.Phys. 51

      Pages: 23528-23528

    • NAID

      120002165231

    • Related Report
      2010 Final Research Report
  • [Journal Article] 数理物理学(繰りこみ群)からみたペレルマン理論2010

    • Author(s)
      伊東恵一
    • Journal Title

      数理物理学への誘い

      Volume: 7 Pages: 53-100

    • Related Report
      2010 Annual Research Report
  • [Journal Article] 数理物理学(繰りこみ群)からみたペレルマン理論2010

    • Author(s)
      伊東恵一
    • Journal Title

      数理物理への誘い(遊星社) 7

      Pages: 53-100

    • Related Report
      2009 Annual Research Report
  • [Journal Article] Pattern Formations in Heat Convection Problems2010

    • Author(s)
      Y.Teramoto, T.Nishida
    • Journal Title

      Chinese Annals of Mathematics 30

      Pages: 769-784

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Pattern Formationin Heat Convection Problems2009

    • Author(s)
      Y.Teramoto, T.Nishida
    • Journal Title

      Chinese Annals of Mathematics 30

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] 繰りこみ群とリッチフロウ2009

    • Author(s)
      伊東恵一
    • Journal Title

      数理科学(サイエンス社) No.550

      Pages: 36-37

    • Related Report
      2010 Final Research Report
  • [Journal Article] Bifurcation Theorems for the Model Sysytem of Bernard-<arangoni Convection2009

    • Author(s)
      Y.Teramoto, T.Nishida
    • Journal Title

      Journal of Math.Fluid Mechanics 11

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Infrared Divergence of a scalar quantum field model on a pseudo Riemannian manifold2009

    • Author(s)
      F.Hiroshima, C.Gerald, A.Panati, A.Suzuki
    • Journal Title

      Interdiciplinary Inf.Sci. 15

      Pages: 399-421

    • NAID

      130000120888

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] 繰りこみ群とリッチフロウ2009

    • Author(s)
      伊東恵一
    • Journal Title

      数理科学 550

      Pages: 36-37

    • Related Report
      2009 Annual Research Report
  • [Journal Article] Critical Discussion of Tomboulis's Approach to the Confinement Problem2009

    • Author(s)
      Keiichi R. Ito
    • Journal Title

      PoS (Proceedings of Science) "Confinement 8 (Mainz)"

      Pages: 1-5

    • Related Report
      2008 Annual Research Report
  • [Journal Article] 繰りこみ群とリッチフロウ2009

    • Author(s)
      伊東恵一
    • Journal Title

      数理科学“現代数学はいかに使われているか「幾何篇」" No. 550

      Pages: 36-37

    • Related Report
      2008 Annual Research Report
  • [Journal Article] Norm resolvent convergence to Schroedinger operators with infinitely thin toroidal magnetic field2008

    • Author(s)
      H.Tamura, V.Zagrevnov
    • Journal Title

      Contemporary Mathematics AMS, 500

      Pages: 139-151

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Norm resolvent convergence to Schroedinger operators with infinitely thin toroidal magnetic field2008

    • Author(s)
      Shin-ichi Shimada, Akira Iwatsuka, Takuya Mine
    • Journal Title

      Contemporary Mathematics AMS, 500

      Pages: 139-151

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] PoS (Proceedings of Sciences)2008

    • Author(s)
      伊東恵一
    • Journal Title

      Critical Discussion of Tomboulis' Approachto the Confinement Problem

      Pages: 1-4

    • Related Report
      2010 Final Research Report
  • [Journal Article] One-Dimensional Schroedinger Equations And Renormalization Group of Wegner-Houghton-Aoki type2008

    • Author(s)
      伊東恵一
    • Journal Title

      数理解析研究所講究録 No.1600

      Pages: 204-218

    • Related Report
      2010 Final Research Report
  • [Journal Article] One-Dimensional Schroedinger Equations and Renormalizations Groups of Wegner-Houghton-Aoki type2008

    • Author(s)
      伊東恵一
    • Journal Title

      数理解析研究所講究録 1600

      Pages: 204-218

    • Related Report
      2008 Annual Research Report
  • [Presentation] Navier-Stokes flow down a vertical wall , Mathematical fluid dynamics2011

    • Author(s)
      Y.Teramoto, T.Nishida, K.Tomoeda
    • Organizer
      Darmsstad-Tokyo Spring School 2011
    • Year and Date
      2011-03-02
    • Related Report
      2010 Final Research Report
  • [Presentation] Navier-Stokes flow down a vertical wall, Mathematical fluid dynamics2011

    • Author(s)
      Y.Teramoto
    • Organizer
      Darmstadt-Tokyo Spring School 2011
    • Place of Presentation
      Darmstadt Univ.of Tech.
    • Year and Date
      2011-03-02
    • Related Report
      2010 Annual Research Report
  • [Presentation] New and old unsolved problems in mathematical physics and Renormalization group method2009

    • Author(s)
      Keiichi R.Ito
    • Organizer
      数理解析研究所共同研究集会
    • Place of Presentation
      京都大学
    • Year and Date
      2009-09-11
    • Related Report
      2009 Annual Research Report
  • [Presentation] 数理物理学(繰りこみ群)的視点からみたペレルマンの論文について2008

    • Author(s)
      伊東恵一
    • Organizer
      数理物理2008
    • Place of Presentation
      東京大学
    • Related Report
      2010 Final Research Report
  • [Presentation] 数理物理学(繰り込み群)的視点からみたペレルマンの論文について2008

    • Author(s)
      伊東恵一
    • Organizer
      数理物理2008リッチフロウの微分幾何と位相幾何
    • Place of Presentation
      東京大学
    • Related Report
      2008 Annual Research Report
  • [Book] SGCライブラリーvol.81繰りこみ群の物理と数理2011

    • Author(s)
      伊東恵一
    • Total Pages
      160
    • Publisher
      サイエンス社
    • Related Report
      2010 Final Research Report
  • [Book] 繰りこみ群の物理と数理2010

    • Author(s)
      伊東恵一
    • Total Pages
      160
    • Publisher
      サイエンス社
    • Related Report
      2010 Annual Research Report
  • [Remarks] ホームページ等

    • URL

      http://www.setsunan.ac.jp/mpg/

    • Related Report
      2010 Final Research Report
  • [Remarks]

    • URL

      http://www.setsunan.ac.jp/mpg/

    • Related Report
      2010 Annual Research Report
  • [Remarks]

    • URL

      http://www.setsunan.ac.jp/mpg/

    • Related Report
      2009 Annual Research Report

URL: 

Published: 2008-04-01   Modified: 2016-04-21  

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