Mathematical analysis for interface dynamics of crystal

• Project/Area Number: 21740068
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Shibaura Institute of Technology
• Principal Investigator: ISHIWATA Tetsuya 芝浦工業大学, システム理工学部, 准教授 (50334917)
• Project Period (FY): 2009 – 2011
• Project Status: Completed (Fiscal Year 2011)
• Budget Amount: ¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000); Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2010: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000); Fiscal Year 2009: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
• Keywords: 界面ダイナミクス / 結晶界面 / 曲率流 / 解の挙動 / 進行波 / 非線形現象 / 数理モデル / 結晶成長 / 形状単調化 / 非平面進行波 / 応用数学

Research Abstract

In this research, we consider some crystalline motions : a kind of interface motion of crystal. In particular, we mainly treat 2 types of crystalline motion : crystalline curvature flow with bulk effect and area-preserving crystalline curvature flow. We discuss the behavior of solution curves, not asymptotic behavior, and classify the extinction patterns of a line-segment of the interface completely and obtain the deformation process of solution curve under the conditions for no self-intersection of the interface.

Research Products

• [Journal Article] Motion of essentially admissible V-shaped polygonal curves governed by generalized crystalline motion with a driving force (2011)
  • Author(s): T. Ishiwata
  • Journal Title: Journal of Math-for-Industry Volume: Vol.3 Pages: 21-25
  • URL: http://gcoe-mi.jp/english/temp/publish/098d0a97160e4eacbdcfe54542c293c3.pdf
• [Journal Article] Asymptotic behavior of blow-up solutions to a degenerate parabolic equation (2011)
  • Author(s): K. Anada and T. Ishiwata
  • Journal Title: Journal of Math-for-Industry Volume: Vol.3 Pages: 1-8
  • URL: http://gcoe-mi.jp/english/temp/publish/b381507677a68af7d14357dba61a72a4.pdf
• [Journal Article] Motion of polygonal curved fronts by crystalline motion : V-shaped solutions and eventual monotonicity (2011)
  • Author(s): T. Ishiwata
  • Journal Title: Discrete and Continuous Dynamical Systems, Supplement Volume: Volume 1 Pages: 717-726
• [Journal Article] On the motion of polygonal curves with asymptotic lines by crystalline curvature flow with bulk effect (2011)
  • Author(s): T. Ishiwata
  • Journal Title: Discrete and Continuous Dynamical Systems Series S Volume: vol.4, no.4 Pages: 865-873
  • URL: http://aimsciences.org/journals/displayArticles.jsp?paperID=5705
• [Journal Article] Motion of polygonal curved fronts by crystalline motion : V-shaped solutions and eventual monotonicity (2011)
  • Author(s): T.Ishiwata
  • Journal Title: Discrete and Continuous Dynamical Systems, Suplement Pages: 717-726
  • Peer Reviewed
• [Journal Article] Asymptotic behavior of blow-up solutions to a degenerate parabolic equation (2011)
  • Author(s): K.Anada, T.Ishiwata
  • Journal Title: Journal of Math-for-Industry Volume: 3 Pages: 1-8
  • Peer Reviewed
• [Journal Article] Motion of essentially admissible V-shaped polygonal curves governed by generalized crystalline motion with a driving force (2011)
  • Author(s): T.Ishiwata
  • Journal Title: Journal of Math-for-Industry Volume: 3 Pages: 21-25
  • Peer Reviewed
• [Journal Article] On the motion of polygonal curves with asymptotic lines by crystalline curvature flow with bulk effect (2011)
  • Author(s): T.Ishiwata
  • Journal Title: Discrete and Continuous Dynamical Systems Series S Volume: 4 Pages: 865-873
  • Peer Reviewed
• [Journal Article] On the motion of polygonal curves with asymptotic lines by crystalline curvature flow with bulk effect (2010)
  • Author(s): T.Ishiwata
  • Journal Title: Discrete and Continuous Dynamical Systems, Series S (掲載予定)
  • 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
• [Presentation] クリスタライン曲率流による開曲線の運動 (2012)
  • Author(s): 石渡哲哉
  • Organizer: 北陸応用数理研究会2012
  • Place of Presentation: 金沢大学サテライトプラザ
  • Year and Date: 2012-02-19
• [Presentation] Behavior of polygonal curves by crystalline curvature flow (2011)
  • Author(s): T.Ishiwata
  • Organizer: Dutch-Japanese Workshop
  • Place of Presentation: Eindhoven University of Technology, Netherlands
  • Year and Date: 2011-11-08
• [Presentation] Behavior of Polygonal Curves by Crystalline Curvature Flow (2011)
  • Author(s): T.Ishiwata
  • Organizer: Workshop on Nonlinear Partial Differential Equations
  • Place of Presentation: East China Normal University,上海
  • Year and Date: 2011-11-03
• [Presentation] Behavior of polygonal curves by crystalline curvature flow with a driving force (2011)
  • Author(s): T. Ishiwata
  • Organizer: East Asia section of SIAM 2011
  • Place of Presentation: Waseda Univ. Kita-Kyushu campus
  • Year and Date: 2011-07-29
• [Presentation] Crystalline motion and eventual monotonicity of the shape, The 7th International Congress on Industrial and Applied Mathematics (2011)
  • Author(s): T. Ishiwata
  • Organizer: Vancouver Convention Centre
  • Place of Presentation: Vancouver, BC, Canada
  • Year and Date: 2011-07-19
• [Presentation] Crystalline motion and eventual monotonicity of the shape (2011)
  • Author(s): T.Ishiwata
  • Organizer: ICIAM 2011
  • Place of Presentation: Vancouver Convention Centre, Canada
  • Year and Date: 2011-07-19
• [Presentation] Behavior of polygonal curves by crystalline curvature flow with a driving force (2011)
  • Author(s): T.Ishiwata
  • Organizer: East Aisa SIAM 2011
  • Place of Presentation: 早稲田大学北九州キャンパス
  • Year and Date: 2011-06-29
• [Presentation] Motion of infinite length polygonal curves by crystalline curvature flow with a driving force (2011)
  • Author(s): 石渡哲哉
  • Organizer: 東工大数理解析小研究会
  • Place of Presentation: 東京工業大学(日本)
  • Year and Date: 2011-02-07
• [Presentation] Motion of non-closed planar polygonal curves by crystalline curvature flow with a driving force (2011)
  • Author(s): T.Ishiwata
  • Organizer: Far-From-Equilibrium Dynamics 2011
  • Place of Presentation: 京都大学(日本)
  • Year and Date: 2011-01-06
• [Presentation] Behavior of polygonal curves by crystalline curvature flow, Dutch-Japanese Workshop, Analysis of non-equilibrium evolution problems : selected topics in material and life sciences (2011)
  • Author(s): T. Ishiwata
  • Organizer: Eindhoven University of Technology
  • Place of Presentation: Netherlands
• [Presentation] Behavior of Polygonal Curves by Crystalline Curvature Flow, Workshop on Nonlinear Partial Differential Equations (2011)
  • Author(s): T. Ishiwata
  • Organizer: Dept of Math and Center of PDE
  • Place of Presentation: East China Normal University,上海
• [Presentation] Motion of non-closed planar polygonal curves by crystalline curvature flow with a driving force (2011)
  • Author(s): T. Ishiwata
  • Organizer: From-Equilibrium Dynamics 2011
  • Place of Presentation: Kyoto, Japan
• [Presentation] クリスタライン運動による解形状の単調化 (2010)
  • Author(s): 石渡哲哉
  • Organizer: 岐阜数理科学セミナー
  • Place of Presentation: 岐阜大学(日本)
  • Year and Date: 2010-12-27
• [Presentation] Motion of non-closed planar polygonal curves by crystalline motion (2010)
  • Author(s): 石渡哲哉
  • Organizer: 応用数学合同研究集会
  • Place of Presentation: 龍谷大学瀬田キャンパス
  • Year and Date: 2010-12-17
• [Presentation] Motion of non-closed planar polygonal curves by crystalline motion (2010)
  • Author(s): 石渡哲哉
  • Organizer: 応用数学合同研究集会
  • Place of Presentation: 龍谷大学(日本)
  • Year and Date: 2010-12-17
• [Presentation] Crystalline motion and eventual monotonicity of the shape (2010)
  • Author(s): T. Ishiwata
  • Organizer: Czech-Japanese Semilar in Applied Mathematics
  • Place of Presentation: Czech Technical University, Prague, Czech Republic
  • Year and Date: 2010-08-30
• [Presentation] Crystalline motion and eventual monotonicity of the shape (2010)
  • Author(s): T.Ishiwata
  • Organizer: Czech-Japanese Semilar in Applied Mathematics
  • Place of Presentation: チェコ工科大学(チェコ)
  • Year and Date: 2010-08-30
• [Presentation] Motion of polygonal curved fronts by crystalline motion : V-shaped solutions and eventual monotonicity (2010)
  • Author(s): T. Ishiwata
  • Organizer: The 8th AIMS Conference on Dynamical Systems, Differential Equations and Applications
  • Place of Presentation: Dresden University of Technology, Dresden, Germany
  • Year and Date: 2010-05-26
• [Presentation] Motion of polygonal curved fronts by crystalline motion : V-shaped solutions and eventual monotonicity (2010)
  • Author(s): T.Ishiwata
  • Organizer: The 8th AIMS Conference on Dynamical Systems, Differential Equations and Applications
  • Place of Presentation: ドレスデン大学(ドイツ)
  • Year and Date: 2010-05-26
• [Presentation] On the motion of polygonal curves by crystalline curvature flow with bulk effect (2009)
  • Author(s): T. Ishiwata
  • Organizer: 1st Italian-Japanese workshop on geometric properties for parabolic and elliptic PDE's
  • Place of Presentation: Tohoku University, Sendai, Japan
  • Year and Date: 2009-06-16
• [Presentation] On the motion of polygonal curves by crystalline curvature flow with bulk effect (2009)
  • Author(s): T.Ishiwata
  • Organizer: 1st Italian-Japanese workshop on geometric properties for parabolic and elliptic PDE's
  • Place of Presentation: 東北大学(仙台)
  • Year and Date: 2009-06-16