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

2009 Fiscal Year Final Research Report

• Project/Area Number: 19540147
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Tokyo 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 (50408704) ; WATANABE Michiyuki 新潟大学, 教育学部, 准教授 (90374181)
• Project Period (FY): 2007 – 2009
• 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.

Research Products

• [Journal Article] Second order numerical scheme for motion of polygonal curves with constant area speed (2009)
  • Author(s): M. Beness, M. Kimura, S. Yazaki
  • Journal Title: Interfaces and Free Boundaries 11 Pages: 515-536
  • 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
• [Journal Article] Motion of non-convex polygons by crystalline curvature and almost convexity phenomena (2008)
  • Author(s): 石渡哲哉
  • Journal Title: Japan Journal of Industrial and Applied Mathematics 25 Pages: 233-253
  • Peer Reviewed
• [Journal Article] Interface motion of a negative crystal and its analysis (2008)
  • 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
• [Journal Article] Application of a curvature adjusted method in image segmentation (2008)
  • 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
  • Peer Reviewed
• [Journal Article] On the tangential velocity arising in a crystalline approximation of evolving plane curves (2007)
  • Author(s): S. Yazaki
  • Journal Title: Kybernetika 43 Pages: 913-918
  • Peer Reviewed
• [Journal Article] Asymptotic behavior of solutions to an area-preserving motion by crystalline curvature (2007)
  • Author(s): S. Yazaki
  • Journal Title: Kybernetika 43 Pages: 903-912
  • Peer Reviewed
• [Journal Article] Motion of nonadmissible convex polygons by crystalline curvature (2007)
  • Author(s): S. Yazaki
  • Journal Title: Publ. Res. Inst. Math. Sci. 43 Pages: 155-170
  • 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 problems (2007)
  • Author(s): C. Hirota, T. Ishiwata, S. Yazaki
  • Journal Title: Adv. Stud. Pure Math 17199 Pages: 543-563
  • 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
• [Presentation] On the motion of polygonal curves by crystalline flow with bulk effect (2009)
  • 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
• [Presentation] Evolution of plane curves and its numerical computations (2009)
  • Author(s): 矢崎成俊
  • Organizer: Algorithmy 2009
  • Place of Presentation: Podbanske
  • Year and Date: 2009-03-17
• [Presentation] On the motion of polygons by crystalline curvature (2008)
  • Author(s): 石渡哲哉
  • Organizer: Third Euro-Japanese Workshop on Blow-up
  • Place of Presentation: 仙台
  • Year and Date: 20080900
• [Presentation] D. Seccovic, A redistribution method of points taking into account the shape of curve by using crystalline tangential velocity in curvature flow equations (2007)
  • 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
• [Presentation] Motion of polygonal curves by crystalline curvature flow and its generalization (2007)
  • 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
• [Book] 数理科学 (2008)
  • Author(s): 牛島健夫, 矢崎成俊, 泡の動きを視る
  • Total Pages: 18-22
  • Publisher: サイエンス社
• [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