• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to previous page

A study of direct methods for moving boundary problems and its applications

Research Project

Project/Area Number 19540147
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionTokyo University of Science

Principal Investigator

USHIJIMA Takeo  Tokyo University of Science, 理工学部, 准教授 (30339113)

Co-Investigator(Kenkyū-buntansha) ISHIWATA Tetsuya  芝浦工業大学, システム理工学部, 准教授 (50334917)
YAZAKI Shigetoshi  宮崎大学, 工学部, 准教授 (00323874)
YAMAZAKI Taeko  東京理科大学, 理工学部, 教授 (60220315)
OGAWA Masao  東京理科大学, 理工学部, 助教 (50408704)
WATANABE Michiyuki  新潟大学, 教育学部, 准教授 (90374181)
Project Period (FY) 2007 – 2009
Project Status Completed (Fiscal Year 2009)
Budget Amount *help
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2009: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2008: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2007: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Keywords移動境界問題 / 直接法 / 数値解析 / クリスタライン・アルゴリズム / クリスタライン曲率流
Research Abstract

Interfaces or moving boundaries among several phases often arise in many important physical phenomena like bubble motion in fluid, melting ice, crystal growth, and so on. To study such phenomena, numerical simulation is an indispensable tool. We investigated so-called crystalline algorithm, which is one of direct numerical methods for moving boundary problems. We generalized this method and as a result obtained a powerful numerical tool for moving boundary problem. We also solved several related problems. Moreover, we studied their applications.

Report

(4 results)
  • 2009 Annual Research Report   Final Research Report ( PDF )
  • 2008 Annual Research Report
  • 2007 Annual Research Report
  • Research Products

    (23 results)

All 2009 2008 2007

All Journal Article (12 results) (of which Peer Reviewed: 9 results) Presentation (9 results) Book (2 results)

  • [Journal Article] Second order numerical scheme for motion of polygonal curves with constant area speed2009

    • Author(s)
      M. Beness, M. Kimura, S. Yazaki
    • Journal Title

      Interfaces and Free Boundaries 11

      Pages: 515-536

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] あるクリスタライン運動の多角形解の挙動について2009

    • Author(s)
      石渡哲哉
    • Journal Title

      京都大学数理解析研究所講究録 1633

      Pages: 1-10

    • Related Report
      2009 Annual Research Report 2009 Final Research Report
  • [Journal Article] Second order numerical scheme for motion of polygonal curves with constant area speed2009

    • Author(s)
      M.Bene\vs M.Kimura, S.Yazaki
    • Journal Title

      Interfaces and Free Boundaries 11

      Pages: 515-536

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Motion of non-convex polygons by crystalline curvature and almost convexity phenomena2008

    • Author(s)
      石渡哲哉
    • Journal Title

      Japan Journal of Industrial and Applied Mathematics 25

      Pages: 233-253

    • NAID

      10021073169

    • Related Report
      2009 Final Research Report 2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Interface motion of a negative crystal and its analysis2008

    • Author(s)
      石渡哲哉, 矢崎成俊
    • Journal Title

      数理解析研究所講究録 1588

      Pages: 23-29

    • Related Report
      2009 Final Research Report
  • [Journal Article] Application of a curvature adjusted method in image segmentation2008

    • Author(s)
      M. Benes, M. Kimura, P. Paus, D. Sevcovic, T. Tsujikawa, S. Yazaki
    • Journal Title

      Bull. Inst. Math. Acad. Sin. 3

      Pages: 509-523

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Interface motion of a negative crystal and its analysis2008

    • Author(s)
      石渡 哲哉矢崎 成俊
    • Journal Title

      数理解析研究所講究録 1588

      Pages: 23-29

    • Related Report
      2008 Annual Research Report
  • [Journal Article] Application of a curvature adjusted method in image segmentation2008

    • Author(s)
      矢崎 成俊, 他
    • Journal Title

      Bull. Inst. Math. Acad. Sin. 3

      Pages: 509-523

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On the tangential velocity arising in a crystalline approximation of evolving plane curves2007

    • Author(s)
      S. Yazaki
    • Journal Title

      Kybernetika 43

      Pages: 913-918

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Asymptotic behavior of solutions to an area-preserving motion by crystalline curvature2007

    • Author(s)
      S. Yazaki
    • Journal Title

      Kybernetika 43

      Pages: 903-912

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Motion of nonadmissible convex polygons by crystalline curvature2007

    • Author(s)
      S. Yazaki
    • Journal Title

      Publ. Res. Inst. Math. Sci. 43

      Pages: 155-170

    • NAID

      110006202840

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Numerical Study and examples on singularities of solutions to anisotropic crystalline curvature flows of nonconvex polygonal curves, Asymptotic analysis and singularities-elliptic and parabolic PDEs and related problems2007

    • Author(s)
      C. Hirota, T. Ishiwata, S. Yazaki
    • Journal Title

      Adv. Stud. Pure Math 17199

      Pages: 543-563

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Presentation] 曲率流方程式の数値計算について2009

    • Author(s)
      矢崎成俊
    • Organizer
      日本数学会2009年度秋季総合分科会(応用数学分科会)
    • Place of Presentation
      大阪大学豊中キャンパス
    • Year and Date
      2009-09-27
    • Related Report
      2009 Annual Research Report 2009 Final Research Report
  • [Presentation] On the motion of polygonal curves by crystalline flow with bulk effect2009

    • Author(s)
      石渡哲哉
    • Organizer
      1st Italian-Japanese workshop on geometric properties for parabolic and elliptic PDE's
    • Place of Presentation
      東北大学
    • Year and Date
      2009-06-16
    • Related Report
      2009 Final Research Report
  • [Presentation] On the motion of polygonal curves by crystalline curvature flow with bulk effect2009

    • Author(s)
      石渡哲哉
    • Organizer
      1st Italian-Japanese workshop on geometric properties for parabolic and elliptic PDE's
    • Place of Presentation
      東北大学
    • Year and Date
      2009-06-16
    • Related Report
      2009 Annual Research Report
  • [Presentation] Evolution of plane curves and its numerical computations2009

    • Author(s)
      矢崎成俊
    • Organizer
      Algorithmy 2009
    • Place of Presentation
      Podbanske
    • Year and Date
      2009-03-17
    • Related Report
      2009 Final Research Report
  • [Presentation] Evolution of plane curves and its numerical computations2009

    • Author(s)
      矢崎 成俊
    • Organizer
      Algoritmy 2009
    • Place of Presentation
      Podbanske
    • Year and Date
      2009-03-17
    • Related Report
      2008 Annual Research Report
  • [Presentation] On the motion of polygons by crystalline curvature2008

    • Author(s)
      石渡哲哉
    • Organizer
      Third Euro-Japanese Workshop on Blow-up
    • Place of Presentation
      仙台
    • Related Report
      2009 Final Research Report
  • [Presentation] On the motion of polygons by crystalline curvature2008

    • Author(s)
      石渡 哲哉
    • Organizer
      THIRD EURO-JAPANESE WORKSHOP ON BLOW-UP
    • Place of Presentation
      仙台
    • Related Report
      2008 Annual Research Report
  • [Presentation] D. Seccovic, A redistribution method of points taking into account the shape of curve by using crystalline tangential velocity in curvature flow equations2007

    • Author(s)
      矢崎成俊
    • Organizer
      Equadiff 07, Minisymposia: PDE models of interface evolution and applications
    • Place of Presentation
      Vienna University of Technology
    • Year and Date
      2007-08-10
    • Related Report
      2009 Final Research Report
  • [Presentation] Motion of polygonal curves by crystalline curvature flow and its generalization2007

    • Author(s)
      石渡哲哉
    • Organizer
      The 6th ICIAM (International Congress on Industrial and Applied mathematics)
    • Place of Presentation
      Zurich
    • Year and Date
      2007-07-18
    • Related Report
      2009 Final Research Report
  • [Book] 数理科学2008

    • Author(s)
      牛島健夫, 矢崎成俊, 泡の動きを視る
    • Publisher
      サイエンス社
    • Related Report
      2009 Final Research Report
  • [Book] これからの非線形微分方程式2007

    • Author(s)
      矢崎成俊
    • Publisher
      日本評論社
    • Related Report
      2009 Final Research Report

URL: 

Published: 2007-04-01   Modified: 2016-04-21  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi