Analysis on singular behavior of interfaces by multiple interface dynamics

• Project/Area Number: 22740109
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: Global analysis
• Research Institution: Gunma University
• Principal Investigator: OHTSUKA Takeshi 群馬大学, 理工学研究院, 講師 (00396847)
• Project Period (FY): 2010-04-01 – 2014-03-31
• Project Status: Completed (Fiscal Year 2013)
• Budget Amount: ¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000); Fiscal Year 2013: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2011: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2010: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
• Keywords: 界面の発展方程式 / 等高線法 / 曲率流方程式 / 粘性解 / 結晶成長 / 退化放物型方程式 / 反応拡散方程式 / 結晶のスパイラル成長 / 拡散方程式 / 機械学習理論 / 画像処理問題 / 界面の発現方程式 / 平均曲率流方程式 / 渦巻曲線の運動

Research Abstract

A level set method for evolving spirals by an eikonal-curvature equation on a crystal surface is studied. A level set equation for interlaced spiral is proposed and examined numerically. The stability of a bunch of spirals evolving with an eikonal-curvature equation is obtained. Growth rate of the crystal surface by a single or multiple spiral steps are estimated and examined numerically. Stationary solution to the level set equation with the situation of an inactive pair is obtained. A priori estimate for Lipschitz continuity of solutions to an approximating equation of the level set equation is obtained. A diffusion method for data separation is proposed as an application of the infinite propagation property on the heat equation.

Research Products

• [Journal Article] On behavior of signs for the heat equation and a diffusion method for data separation (2013)
  • Author(s): M.-H. Giga, Y. Giga, T. Ohtsuka and N. Umeda
  • Journal Title: Communications on Pure and Applied Analysis Volume: 12 Pages: 2277-2296
  • NAID: 120006459690
  • Peer Reviewed
• [Journal Article] On behavior of signs for the heat equation and a diffusion method for data separation (2013)
  • Author(s): M.-H. Giga, Y. Giga, T. Ohtsuka and N. Umeda
  • Journal Title: Comm. Pure Appl. Anal. Volume: 12 Issue: 5 Pages: 2277-2296
  • DOI: 10.3934/cpaa.2013.12.2277
  • NAID: 120006459690
  • Peer Reviewed
• [Journal Article] Optimal control problem for Allen-Cahn type equation associated with total variation energy (2012)
  • Author(s): T. Ohtsuka, K. Shirakawa and N.Yamazaki
  • Journal Title: A special volume of Discrete and Continuous Dynamical Systems - Series S "PDE approximations in Fast reaction - Slow diffusion scenarios" Volume: 5 Pages: 159-181
  • Peer Reviewed
• [Journal Article] Evolution of spirals by an eikonal-curvature flow equation with a single level set formulation (2012)
  • Author(s): T. Ohtsuka
  • Journal Title: Hokkaido University Technical Report Series in Mathematics Volume: 153 Pages: 62-71
• [Journal Article] On behavior of signs for the heat equation and a diffusion method for data separation (2012)
  • Author(s): M.-H.Giga, Y.Giga, T.Ohtsuka, N.Umeda
  • Journal Title: Hokkaido University Preprint Series in Mathematics Volume: #998 Pages: 1-23
  • NAID: 120006459690
• [Journal Article] Optimal control problem for Allen-Cahn type equation associated with total variation energy (2012)
  • Author(s): T.Ohtsuka, K.Shirakawa, N.Yamazaki
  • Journal Title: A special volume of Discrete and Continuous Dynamical Systems-Series S "PDE approximations in Fast reaction-Slow diffusion scenarios" Volume: 5(印刷中,Web上で発表済) Pages: 159-181
  • Peer Reviewed
• [Journal Article] Interface evolution by tristable Allen-Cahn equation with collision free condition (2010)
  • Author(s): T. Ohtsuka
  • Journal Title: 数理解析研究所講究録1693非線形発展方程式と現象の数理 Pages: 168-179
• [Journal Article] Interface evolution by tristable Allen-Cahn equation with collision free condition (2010)
  • Author(s): T.Ohtsuka
  • Journal Title: 数理解析研究所講究録 非線形発展方程式と現象の数理 Volume: 1693 Pages: 168-179
• [Presentation] 符号拡散によるデータ分類法 (2014)
  • Author(s): 大塚岳
  • Organizer: 第15回さいたま数理解析セミナー
  • Place of Presentation: 大宮ソニックシティ
  • Year and Date: 2014-02-20
• [Presentation] 界面の発展現象に対する等高面の方法 (2013)
  • Author(s): 大塚岳
  • Organizer: 応用数学勉強会2013
  • Place of Presentation: 芝浦工業大学
  • Year and Date: 2013-12-16
• [Presentation] 拡散方程式を用いたデータ分類法 (2013)
  • Author(s): 大塚岳
  • Organizer: Joint workshop on pure and applied mathematics
  • Place of Presentation: 東北大学
  • Year and Date: 2013-11-02
• [Presentation] Growth rate of a crystal surface evolving with a pair of screw dislocations (2013)
  • Author(s): T. Ohtsuka
  • Organizer: Mathematical Aspects of Surface and Interface Dynamics VI
  • Place of Presentation: 東京大学大学院数理科学研究科
  • Year and Date: 2013-11-01
• [Presentation] Growth rate of a crystal surface with a co-rotating pair of spiral steps evolving by an eikonal-curvature flow (2013)
  • Author(s): T. Ohtsuka
  • Organizer: RIMS研究集会 「非線形現象に現れるパターン形成の数理解析」
  • Place of Presentation: 京都大学
  • Year and Date: 2013-10-30
• [Presentation] Evolution of a crystal surface by a co-rotating pair of screw dislocations (2013)
  • Author(s): T. Ohtsuka
  • Organizer: Workshop on Free Boundaries in Laplacian Growth Phenomena and Related Topics
  • Place of Presentation: 東北大学
  • Year and Date: 2013-10-14
• [Presentation] Crystal growth by a co-rotating pair of screw dislocations (2013)
  • Author(s): 大塚岳・儀我美一・Y .-H. R. Tsai
  • Organizer: 日本数学会2013年度秋季総合分科会
  • Place of Presentation: 愛媛大学
  • Year and Date: 2013-09-26
• [Presentation] 結晶のスパイラル成長でのインアクティブペアにおける成長上限について (2013)
  • Author(s): 大塚岳
  • Organizer: 第2回岐阜数理科学研究会
  • Place of Presentation: 飛騨高山まちの博物館研修室
  • Year and Date: 2013-09-18
• [Presentation] らせん転位の共回転対による結晶表面の成長速度 (2013)
  • Author(s): 大塚岳
  • Organizer: HMMC セミナー
  • Place of Presentation: 北海道大学電子科学研究所
  • Year and Date: 2013-08-01
• [Presentation] Stability of a bunch of spirals evolving with an eikonal curvature flow equation (2013)
  • Author(s): T. Ohtsuka
  • Organizer: SIAM Conference on Mathematical Aspects of Materials Science
  • Place of Presentation: Philadelphia (USA)
  • Year and Date: 2013-06-12
• [Presentation] スパイラル成長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 (2013)
  • Author(s): 大塚岳
  • Organizer: 表面・界面ダイナミクスの数理V
  • Place of Presentation: 東京大学大学院数理科学研究科
  • Year and Date: 2013-05-28
• [Presentation] Stability of bunched spirals and inactive pair in evolution of spirals with an eikonal-curvature flow (2013)
  • Author(s): T. Ohtsuka
  • Organizer: Oberwolfach Workshop Interfaces and Free Boundaries : Analysis, Control and Simulation
  • Place of Presentation: Mathematisches Forshungsinstitut Oberwolfach gGmbH (Germany)
  • Year and Date: 2013-03-28
• [Presentation] 結晶のスパイラル成長の等高線法による定式化と渦巻ステップの挙動の解析 (2013)
  • Author(s): 大塚岳
  • Organizer: 日本数学会2013年度年会, 応用数学分科会
  • Place of Presentation: 京都大学
  • Year and Date: 2013-03-22
• [Presentation] 曲率流方程式にしたがう渦巻曲線を表す等高線方程式の解のLipschitz連続性について (2013)
  • Author(s): 大塚岳
  • Organizer: 東工大数理解析研究会
  • Place of Presentation: 東京工業大学
  • Year and Date: 2013-02-04
• [Presentation] 曲率流方程式にしたがう渦巻曲線を表す等高線方程式の解のLipschitz連続性について (2013)
  • Author(s): 大塚岳
  • Organizer: 東工大数理解析研究会
  • Place of Presentation: 東京工業大学 大岡山キャンパス
  • Invited
• [Presentation] 結晶のスパイラル成長の等高線法による定式化と渦巻ステッ プの挙動の解析 (2013)
  • Author(s): 大塚岳
  • Organizer: 日本数学会2013年度年会 応用数学分科会 特別講演
  • Place of Presentation: 京都大学吉田キャンパス
  • Invited
• [Presentation] Stability of bunched spirals and inactive pair in evolution of spirals with an eikonal-curvature flow (2013)
  • Author(s): T. Ohtsuka
  • Organizer: Interfaces and Free Boundaries: Analysis, Control and Simulation
  • Place of Presentation: Mathematisches Forschungsinstitut Oberwolfach gGmbH (Germany)
  • Invited
• [Presentation] 駆動力付き曲率流方程式における渦巻曲線の運動での束の安定性およびインアクティブペアにおける定常解について (2012)
  • Author(s): 大塚岳
  • Organizer: 京都駅前セミナー
  • Place of Presentation: キャンパスプラザ京都
  • Year and Date: 2012-10-19
• [Presentation] Lipschitz continuity of solutions to an eikonal-curvature flow equation for spiral evolution (2012)
  • Author(s): 大塚岳
  • Organizer: 東北大学非線形偏微分方程式ワークショップ
  • Place of Presentation: 東北大学
  • Year and Date: 2012-09-27
• [Presentation] Surface evolution by a pair of spiral steps evolving with an eikonal-curvature equation (2012)
  • Author(s): T. Ohtsuka
  • Organizer: ALGORITMY 2012
  • Place of Presentation: Hotel Permon**** (Slovak)
  • Year and Date: 2012-09-10
• [Presentation] Evolution of spirals by an eikonal-curvature flow equation with a single level set formulation (2012)
  • Author(s): T. Ohtsuka
  • Organizer: The 37th Sapporo Symposium on Partial Differential Equations
  • Place of Presentation: 北海道大学
  • Year and Date: 2012-08-27
• [Presentation] 結晶表面上の渦巻模様の運動 (2012)
  • Author(s): 大塚岳
  • Organizer: 渦の特徴付け
  • Place of Presentation: 北海道大学
  • Year and Date: 2012-08-06
• [Presentation] 界面の運動を解析する数学的手法 (2012)
  • Author(s): 大塚岳
  • Organizer: 計算材料科学研究拠点(CMRI)第一回シンポジウム
  • Place of Presentation: 東北大学
  • Year and Date: 2012-06-19
• [Presentation] 複数のスパイラルステップに対する等高線の方法 (2012)
  • Author(s): 大塚岳
  • Organizer: 表面・界面ダイナミクスの数理III
  • Place of Presentation: 東京大学大学院数理科学研究科
  • Year and Date: 2012-05-17
• [Presentation] 駆動力付き曲率流方程式で運動する渦巻曲線の束の安定性 (2012)
  • Author(s): 大塚岳・儀我美一・Y .-H. R. Tsai
  • Organizer: 日本数学会2012年度年会
  • Place of Presentation: 東京理科大学
  • Year and Date: 2012-03-29
• [Presentation] 駆動力つき曲率流方程式で運動する渦巻曲線の束の安定性 (2012)
  • Author(s): 大塚岳, 儀我美一, Y.-H.R.Tsai
  • Organizer: 日本数学会2012年度年会,応用数学分科会
  • Place of Presentation: 東京理科大学
  • Year and Date: 2012-03-29
• [Presentation] 結晶のスパイラル成長におけるインアクティブペアの存在と束状ステップの運動の安定性について (2012)
  • Author(s): 大塚岳
  • Organizer: 非線形現象の数値シミュレーションと解析2012
  • Place of Presentation: 北海道大学
  • Year and Date: 2012-03-08
• [Presentation] 複数のスパイラルステップの等高線法によるシミュレーションと解析 (2012)
  • Author(s): 大塚岳
  • Organizer: ニセコ冬の学校「結晶・物性・素粒子・数学」
  • Place of Presentation: 北海道工業大学ニセコ山荘
  • Year and Date: 2012-01-08
• [Presentation] 複数のスパイラルステップの等高線法によるシミュレーションと解析 (2012)
  • Author(s): 大塚岳
  • Organizer: ニセコ冬の学校「結晶・物性・素粒子・数学」
  • Place of Presentation: 北海道工業大学 ニセコ山荘
  • Year and Date: 2012-01-08
• [Presentation] 界面の運動を解析する数学的手法 (2012)
  • Author(s): 大塚岳
  • Organizer: 計算材料科学研究拠点(CMRI)第一回シンポジウム
  • Place of Presentation: 東北大学金属材料研究所
  • Invited
• [Presentation] 結晶表面上の渦巻模様の運動 (2012)
  • Author(s): 大塚岳
  • Organizer: 渦の特徴付け
  • Place of Presentation: 北海道大学理学部数学科
  • Invited
• [Presentation] Evolution of spirals by an eikonal-curvature flow equation with a single level set formulation (2012)
  • Author(s): T. Ohtsuka
  • Organizer: The 37th Sapporo Symposium on Partial Differential Equations
  • Place of Presentation: 北海道大学理学部数学科
  • Invited
• [Presentation] Surface evolution by a pair of spiral steps evolving with an eikonal-curvature equation (2012)
  • Author(s): T. Ohtsuka
  • Organizer: ALGORITMY 2012 minisymposium
  • Place of Presentation: Hotel Permon**** (Slovak)
  • Invited
• [Presentation] Lipschitz continuity of solutions to an eikonal-curvature flow equation for spiral evolution (2012)
  • Author(s): 大塚岳
  • Organizer: 東北大学非線形偏微分方程式ワークショップ
  • Place of Presentation: 東北大学理学研究科
  • Invited
• [Presentation] 駆動力付き曲率流方程式における渦巻曲線の運動での束の安定性およびインアクティブペアにおける定常解の存在 (2012)
  • Author(s): 大塚岳
  • Organizer: 京都駅前セミナー
  • Place of Presentation: キャンパスプラザ京都
  • Invited
• [Presentation] Stability of bunched steps in spiral crystal growth (2011)
  • Author(s): T. Ohtsuka
  • Organizer: Dutch-Japan Workshop Analysis of non-equilibrium evolution problems : selected topics in material and life sciences
  • Place of Presentation: Technische Universiteit Eindhoven (Netherlands)
  • Year and Date: 2011-11-09
• [Presentation] Stability of bunched steps in spiral crystal growth (2011)
  • Author(s): T.Ohtsuka
  • Organizer: Dutch-Japanese Workshop Analysis of non-equilibrium evolution problems : selected topics in material and life sciences
  • Place of Presentation: Technische Universiteit Eindhoven, Eindhoven (Netherlands)
  • Year and Date: 2011-11-09
• [Presentation] Inactive pair and stability of bunched steps in spiral crystal growth (2011)
  • Author(s): 大塚岳
  • Organizer: N.L.P.M. サマーセミナー
  • Place of Presentation: 料理旅館紅葉屋(愛知県)
  • Year and Date: 2011-08-06
• [Presentation] Inactive pair and stability of bunched steps in spiral crystal growth (2011)
  • Author(s): 大塚岳
  • Organizer: N.L.P.M.サマーセミナー
  • Place of Presentation: 料理旅館紅葉屋(愛知県知多郡)
  • Year and Date: 2011-08-06
• [Presentation] 趣旨と渦巻模様 (2011)
  • Author(s): 儀我美一, 大塚岳
  • Organizer: 渦の特徴付け
  • Place of Presentation: 北海道大学
  • Year and Date: 2011-08-03
• [Presentation] Inactive pair and bunching phenomena in spiral crystal growth (2011)
  • Author(s): T. Ohtsuka
  • Organizer: ICIAM2011
  • Place of Presentation: Vancouver (Canada)
  • Year and Date: 2011-07-18
• [Presentation] Inactive pair and bunching phenomena in spiral crystal growth (2011)
  • Author(s): T.Ohtsuka
  • Organizer: Anisotropic Evolution of Interfaces Part II of II, I CIAM2011 Minisymposium
  • Place of Presentation: Vancouver Convention Centre (Canada)
  • Year and Date: 2011-07-18
• [Presentation] 綾織り模様について (2011)
  • Author(s): 大塚岳
  • Organizer: 表面・界面ダイナミクスの数理 I
  • Place of Presentation: 東京大学大学院数理科学研究科
  • Year and Date: 2011-05-12
• [Presentation] 綾織り模様について (2011)
  • Author(s): 大塚岳
  • Organizer: 表面・界面ダイナミクスの数理I
  • Place of Presentation: 東京大学大学院数理科学研究科
  • Year and Date: 2011-05-12
• [Presentation] A level set method for evolving spirals by the mean curvature flow with driving force, Computing in Image Processing (2011)
  • Author(s): T. Ohtsuka
  • Organizer: Computer Graphics, Virtual Surgery , and Sports
  • Place of Presentation: University of Minnesota (USA)
  • Year and Date: 2011-03-07
• [Presentation] A level set method for evolving spirals by the mean curvature flow with driving force (2011)
  • Author(s): 大塚岳
  • Organizer: Computing in Image Processing, Computer Graphics, Virtual Surgery, and Sports
  • Place of Presentation: University of Minnesota (U.S.A.)
  • Year and Date: 2011-03-07
• [Presentation] スパイラル成長の数理モデルにおけるバンチング現象の安定性, および inactive pairにおける定常解について (2010)
  • Author(s): 大塚岳
  • Organizer: 九州関数方程式セミナー
  • Place of Presentation: 福岡大学セミナーハウス
  • Year and Date: 2010-11-19
• [Presentation] スパイラル成長の数理モデルにおけるバンチング現象の安定性、およびinactive pairにおける定常解について (2010)
  • Author(s): 大塚岳
  • Organizer: 九州関数方程式セミナー
  • Place of Presentation: 福岡大学セミナーハウス
  • Year and Date: 2010-11-19
• [Presentation] Allen-Cahn type equation for multiple or spiral steps and its singular limit (2010)
  • Author(s): 大塚岳
  • Organizer: 第22回CREST セミナー
  • Place of Presentation: 東北大学
  • Year and Date: 2010-10-15
• [Presentation] Allen-Cahn type equation for multiple or spiral steps and its singular limit (2010)
  • Author(s): 大塚岳
  • Organizer: 第22回CRESTセミナー
  • Place of Presentation: 東北大学
  • Year and Date: 2010-10-15
• [Presentation] Level set method for spirals and evolution of crystal surface by a pair of screw dislocations (2010)
  • Author(s): T. Ohtsuka
  • Organizer: Workshop Extrinsic Geometric Flows
  • Place of Presentation: Valencia (Spain)
  • Year and Date: 2010-09-04
• [Presentation] Level set method for spirals and evolution of crystal surface by a pair of screw dislocations (2010)
  • Author(s): T.Ohtsuka
  • Organizer: Workshop Extrinsic Geometric Flows
  • Place of Presentation: University of Valencia
  • Year and Date: 2010-09-04
• [Presentation] A level set method for spiral crystal growth and growth rate of crystal surface (2010)
  • Author(s): T. Ohtsuka
  • Organizer: Tutorial Lectures and Interdisciplinary Conference "Mathematical Aspects of Crystal Growth"
  • Place of Presentation: 北海道大学
  • Year and Date: 2010-07-26
• [Presentation] Numerical simulations for spiral crystal growth with impurity, interlaced spiral and variable step velocity (2010)
  • Author(s): T. Ohtsuka
  • Organizer: Tutorial Lectures and Interdisciplinary Conference "Mathematical Aspects of Crystal Growth"
  • Place of Presentation: 北海道大学
  • Year and Date: 2010-07-26
• [Presentation] Stability of a bunch of spirals evolving with an eikonal-curvature flow equation
  • Author(s): T. Ohtsuka
  • Organizer: Surface Evolution by Geometric Laws Controlling Interfacial Motions: Minisymposium on SIAM Conference on Materials Science
  • Place of Presentation: DoubleTree by Hilton Hotel Philadelphia, Pennsylvania, USA
  • Invited
• [Presentation] らせん転位の共回転対による結晶表面の成長速度
  • Author(s): 大塚岳
  • Organizer: HMMCセミナー
  • Place of Presentation: 北海道大学電子科学研究所
  • Invited
• [Presentation] Crystal growth by a co-rotating pair of screw dislocations
  • Author(s): 大塚岳, 儀我美一, Y.-H. R. Tsai
  • Organizer: 日本数学会2013年度秋季総合分科会 応用数学分科会
  • Place of Presentation: 愛媛大学
• [Presentation] Evolution of a crystal surface by a co-rotating pair of screw dislocations
  • Author(s): T. Ohtsuka
  • Organizer: Workshop on Free Boundaries in Laplacian Growth Phenomena and Related Topics
  • Place of Presentation: 東北大学大学院理学研究科川井ホール
  • Invited
• [Presentation] Growth rate of a crystal surface with a co-rotating pair of spiral steps evolving by an eikonal-curvature flow
  • Author(s): 大塚岳
  • Organizer: RIMS研究集会「非線形現象に現れるパターン形成の数理解析」
  • Place of Presentation: 京都大学数理解析研究所
  • Invited
• [Presentation] 拡散方程式を用いたデータ分類法
  • Author(s): 大塚岳
  • Organizer: Joint workshop on pure and applied mathematics
  • Place of Presentation: 東北大学大学院理学研究科川井ホール
  • Invited
• [Presentation] 符号拡散によるデータ分類法
  • Author(s): 大塚岳
  • Organizer: 第15回さいたま数理解析セミナー
  • Place of Presentation: 大宮ソニックシティ5階（埼玉大学サテライトキャンパス）
  • Invited
• [Remarks] 発表論文についてはCommunication on Pure and Applied Analysisに投稿中。