Study on bunching phenomena of interface motion by combined dynamics

• Project/Area Number: 26400158
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Mathematical analysis
• Research Institution: Gunma University
• Principal Investigator: Ohtsuka Takeshi 群馬大学, 大学院理工学府, 講師 (00396847)
• Project Period (FY): 2014-04-01 – 2017-03-31
• Project Status: Completed (Fiscal Year 2016)
• Budget Amount: ¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000); Fiscal Year 2016: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000); Fiscal Year 2015: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000); Fiscal Year 2014: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
• Keywords: 平均曲率流方程式 / 等高面法 / 特異拡散方程式 / 粘性解 / 異方的曲率流方程式 / 等高線法 / 最適化問題 / 渦巻曲線の運動 / クリスタライン曲率流方程式 / 結晶成長 / 定常解 / 安定性

Outline of Final Research Achievements

Existence and stability or instability of discontinuous stationary solution to the level set equation of eikonal mean curvature flow is proved. For the crystalline motion of spirals, an ODE scheme by evolution equation of each facet length, and two minimizing movement approach for spirals evolving with crystalline eikonal-curvature flow are proposed.

Research Products

• [Journal Article] A level set approach reflecting sheet structure with single auxiliary function for evolving spirals on crystal surfaces (2015)
  • Author(s): T. Ohtsuka, Y.-H. Tsai, Y. Giga
  • Journal Title: J. Sci. Comput. Volume: 62 Issue: 3 Pages: 831-874
  • DOI: 10.1007/s10915-014-9877-2
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Discontinuous stationary solution to generalized eikonal-curvature equation and its stability (2014)
  • Author(s): T. Ohtsuka
  • Journal Title: Commentarii Mathematici Universitatis Sancti Pauli Volume: 63 Pages: 233-260
  • NAID: 120006459748
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] 渦巻成長のインアクティブペアにおける成長上限と定常解の構成について (2014)
  • Author(s): 大塚岳
  • Journal Title: 第36回発展方程式若手セミナー報告集 Pages: 35-43
• [Presentation] 駆動力つきクリスタライン曲率流によるスパイラルの成長に対する最小化問題アプローチ (2017)
  • Author(s): 大塚岳
  • Organizer: 第8-9回神戸大学解析セミナー
  • Place of Presentation: 神戸大学理学部
  • Invited
• [Presentation] Minimizing movement approach for spirals evolving by crystalline curvature using level set functions (2017)
  • Author(s): T. Ohtsuka
  • Organizer: Emerging Developments in Interfaces and Free Boundaries
  • Place of Presentation: Mathematisches Forschunginstitut Oberwolfach(Germany)
  • Int'l Joint Research / Invited
• [Presentation] A level set method for geometric evolution of spirals and its application (2016)
  • Author(s): T. Ohtsuka
  • Organizer: SEMINAR, NUMERICAL ANALYSIS
  • Place of Presentation: KTH Royal Institute of Technology
  • Year and Date: 2016-03-17
  • Invited
• [Presentation] クリスタライン曲率流方程式による渦巻の成長について (2016)
  • Author(s): 大塚岳
  • Organizer: 2016年度第10-12回明治非線形数理セミナー
  • Place of Presentation: 明治大学中野キャンパス
  • Invited
• [Presentation] A level set approach for spirals and its application to spiral crystal growth (2016)
  • Author(s): T. Ohtsuka
  • Organizer: NTT-BRL Seminar
  • Place of Presentation: NTT物性科学基礎研究所
  • Int'l Joint Research / Invited
• [Presentation] Evolution of polygonal spirals by crystalline eikonal-curvature flow with pinned center (2016)
  • Author(s): T. Ishiwata and T. Ohtsuka
  • Organizer: Czech-Japanese-Polish Seminar in Applied Mathematics 2016
  • Place of Presentation: AGH University of Science and Technology(Poland)
  • Int'l Joint Research / Invited
• [Presentation] Optimal control problem for Allen-Cahn type equation associated with total variation energy (2016)
  • Author(s): T. Ohtsuka
  • Organizer: The Fifth International Conference on Continuous Optimization
  • Place of Presentation: 政策研究大学院大学
  • Int'l Joint Research / Invited
• [Presentation] A level set method for evolution of spirals and its numerical simulations for crystal growth with evolving spiral steps (2016)
  • Author(s): T. Ohtsuka
  • Organizer: Shokaku Mathematical Lecture Series by Professor Lawrence C. Evans and Nonlinear PDE satellite Workshop
  • Place of Presentation: 東北大学川井ホール
  • Int'l Joint Research / Invited
• [Presentation] A level set method for evolving spirals and its numerical simulations on the vertical growth rate of crystal surface by several spiral steps (2016)
  • Author(s): T. Ohtsuka
  • Organizer: Karuizawa camp Workshop on interface motions and free boundary problems: mathematical analysis, modellings and experiments
  • Place of Presentation: いするの家, 西原脩三記念館
  • Int'l Joint Research / Invited
• [Presentation] A new level set method for spirals evolving by eikonal-curvature equation and its application to spiral crystal growth (2016)
  • Author(s): T. Ohtsuka
  • Organizer: The 11th AIMS Conference on Dynamical Systems, Differential Equations and Applications
  • Place of Presentation: Hyatt Regency Orland, Florida(USA)
  • Int'l Joint Research / Invited
• [Presentation] 結晶のスパイラル成長におけるインアクティブ・ペアについて (2016)
  • Author(s): 大塚岳
  • Organizer: 表面・界面ダイナミクスの数理11
  • Place of Presentation: 東京大学大学院数理科学研究科
  • Invited
• [Presentation] 中心を固定された多角形型渦巻曲線の駆動力付きクリスタライン曲率流方程式による運動について (2015)
  • Author(s): 石渡哲哉, 大塚岳
  • Organizer: 2016年度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: 2015-12-19
• [Presentation] A level set method for evolution of several spiral steps and its applications to spiral crystal growth (2015)
  • Author(s): T. Ohtsuka
  • Organizer: Mathematical Aspects of Surface and Interface Dynamics X
  • Place of Presentation: 東京大学大学院数理科学研究科
  • Year and Date: 2015-10-28
  • Int'l Joint Research / Invited
• [Presentation] Evolution of spirals by crystalline curvature and eikonal equation (2015)
  • Author(s): T. Ohtsuka
  • Organizer: Mathematics for Nonlinear Phenomena: Analysis and Computation -International Conference in honor of Professor Yoshikazu Giga on his 60th birthday-
  • Place of Presentation: 札幌コンベンションセンター
  • Year and Date: 2015-08-16
  • Int'l Joint Research / Invited
• [Presentation] 異方的曲率流方程式によるスパイラルステップの運動 (2015)
  • Author(s): 大塚岳
  • Organizer: 表面・界面ダイナミクスの数理IX
  • Place of Presentation: 東京大学大学院数理科学研究科
  • Year and Date: 2015-04-22
  • Invited
• [Presentation] Growth rate of a surface by co-rotating pair of spiral steps evolving by an eikonal-curvature equation (2014)
  • Author(s): T. Ohtsuka
  • Organizer: 反応拡散現象に見られる境界層とその周辺の数理
  • Place of Presentation: 明治大学中野キャンパス
  • Year and Date: 2014-11-28
  • Invited
• [Presentation] 渦巻成長のインアクティブペアにおける成長上限と定常解の構成について (2014)
  • Author(s): 大塚岳
  • Organizer: 第36回発展方程式若手セミナー
  • Place of Presentation: 休暇村南阿蘇
  • Year and Date: 2014-08-30
  • Invited
• [Presentation] 複数のらせん転位による結晶表面の成長速度の数値計算シミュレーション (2014)
  • Author(s): 大塚岳
  • Organizer: 表面・界面ダイナミクスの数理VII
  • Place of Presentation: 東京大学大学院数理科学研究科
  • Year and Date: 2014-04-23