Surface tension and its interaction for non-equilibrium surface phenomena

• Project/Area Number: 17340041
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Global analysis
• Research Institution: Hokkaido University
• Principal Investigator: TONEGAWA Tonegawa Hokkaido University, 大学院理学研究院, 教授 (80296748)
• Co-Investigator(Kenkyū-buntansha): JIMBO Shuichi 北海道大学, 大学院理学研究院, 教授 (80201565) ; YANAGITA Tatsuo 北海道大学, 電子科学研究所, 助教 (80242262)
• Project Period (FY): 2005 – 2008
• Project Status: Completed (Fiscal Year 2008)
• Budget Amount: ¥14,430,000 (Direct Cost: ¥12,600,000、Indirect Cost: ¥1,830,000); Fiscal Year 2008: ¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000); Fiscal Year 2007: ¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000); Fiscal Year 2006: ¥3,000,000 (Direct Cost: ¥3,000,000); Fiscal Year 2005: ¥3,500,000 (Direct Cost: ¥3,500,000)
• Keywords: 相分離 / 表面張力 / フェーズフィールドモデル / 変分問題 / Allen-Cahn方程式 / 非線形偏微分方程式 / 曲率流 / Cahn-Hilliard方程式 / フェーズフイールドモデル / 確率偏微分方程式 / 曲率 / 特異摂動

Research Abstract

フェイズフィールド法は相分離面を含む非一様状態を表すため、理論と数値計算に多用されている. 当該研究では、フェイズフィールド法における内部遷移層のプロファイルについて特別な仮定を置かなくても、エネルギーおよびその第一変分、またはそれに類する積分量が制御されていれば、仮定が結果として自動的に成り立つ構造をもつことを様々な問題設定(De Giorgi問題、流体問題、大偏差原理問題など)で示し、フェイズフィールド法の数学的基礎の解明を進めた.

Research Products

• [Journal Article] Partial regularity of weak solutions to Maxwell's equation in quasi-static electromagnetic field (2008)
  • Author(s): Hong, Ming-Chun, Tonegawa, Yoshihiro, Yassin, Alzubaidi
  • Journal Title: Methods and Applications of Analysis 15, no.2 Pages: 205-222
  • Peer Reviewed
• [Journal Article] Convergence of phase-field approximations to the Gibbs-Thomson law (2008)
  • Author(s): Roger, Matthias, Tonegawa, Yoshihiro
  • Journal Title: Calc. Var. Partial Differential Equations 32, no.1 Pages: 111-136
  • NAID: 120000952615
  • Peer Reviewed
• [Journal Article] Partial regularity of weak solutions to Maxwell' s equations in a quasi-static electromagnetic field (2008)
  • Author(s): Hong, Ming-Chun
  • Journal Title: Methods and applications of analysis 15 Pages: 205-222
  • Peer Reviewed
• [Journal Article] Convergence of phase-field approximations to the Gibbs-Thomson law (2008)
  • Author(s): Roger, Matthias
  • Journal Title: Calculus of variations and partial differential equations 32 Pages: 111-136
  • Peer Reviewed
• [Journal Article] Higher multiplicities in the one-dimensional Allen-Cahn action functional, Indiana University Math (2007)
  • Author(s): Westdickenberg, Maria, Tonegawa, Yoshihiro
  • Journal Title: Journal 56, no6 Pages: 2935-2989
  • Peer Reviewed
• [Journal Article] A singular perturbation problem with integral curvature bound (2007)
  • Author(s): Nagase, Yuko, Tonegawa, Yoshihiro
  • Journal Title: Hiroshima Math J. 37, no.3 Pages: 455-489
  • NAID: 110006455963
  • Peer Reviewed
• [Journal Article] Magnetic clusters and fold energies (2007)
  • Author(s): Giga, Yoshikazu, Kubo, Motohiko, Tonegawa, Yoshihiro
  • Journal Title: Proc. Roy. Soc. Edinburgh Sect A 137, no.1 Pages: 23-40
  • NAID: 120006459377
  • Peer Reviewed
• [Journal Article] Higher multiplicities in the one-dimensional Allen-Cahn action functional (2007)
  • Author(s): Westdickenberg, Maria
  • Journal Title: Indiana University Math. Journal 56 Pages: 2935-2989
  • Peer Reviewed
• [Journal Article] A singular perturbation problem with integral curvature bound (2007)
  • Author(s): Nagase, Yuko
  • Journal Title: Hiroshima Math. Journal 37 Pages: 455-489
  • Peer Reviewed
• [Journal Article] Magnetic clusters and fold energies (2007)
  • Author(s): Giga, Yoshikazu
  • Journal Title: Proc. Roy. Soc. Edinburgh Sect. A 137 Pages: 23-40
  • Peer Reviewed
• [Journal Article] Sharp-interface limit of the action functional for Allen Cahn in one space dimension (2006)
  • Author(s): Kohn, Robert, Reznikoff, Maria, Tonegawa, Yoshihiro
  • Journal Title: Calc. Var. Partial Differential Equations 25 25 no.4 Pages: 503-534
  • NAID: 120006459416
  • Peer Reviewed
• [Journal Article] Sharp-interface limit of the action functional for Allen Cahn in one space dimension (2006)
  • Author(s): Kohn, Robert
  • Journal Title: Calc. Var. Partial Differential Equations 25・4 Pages: 503-534
• [Journal Article] A transition from ascending flight to vertical hovering : a study of a symmetric flapping model (2006)
  • Author(s): Iima, Makoto
  • Journal Title: Europhys. Lett 74・1 Pages: 55-61
• [Journal Article] Interior gradient estimate for 1-D anisotropic curvature flow (2005)
  • Author(s): Nagase, Yuko, Tonegawa, Yoshihiro
  • Journal Title: Boletim da Sociedade Paranaense de Matematica 23 no.1-2 Pages: 93-98
  • NAID: 120006459360
  • Peer Reviewed
• [Journal Article] Evaluation of data in terms of two-dimensional random walk model : Interaction between NADH-cytochrome b5 reductase and cytochrome b5 (2005)
  • Author(s): Tonegawa, Yoshihiro, Umeda, Noriaki, Hayakawa, Tohru, Ishibashi, Teruo
  • Journal Title: Biomedical Research 26(5) Pages: 207-212
  • NAID: 130004470653
  • Peer Reviewed
• [Journal Article] A diffused interface whose chemical potential lies in Sobolev spaces (2005)
  • Author(s): Tonegawa, Yoshihiro
  • Journal Title: Ann. Scuola Norm. Sup. Pisa Cl. Sci. 5(4) Pages: 487-510
  • Peer Reviewed
• [Journal Article] Partial regularity for a selective smoothing functional for image restoration in BV space (2005)
  • Author(s): Chen, Yunmei, Rao, M., Tonegawa, Y., Wunderli, T.
  • Journal Title: SIAM Journal on Mathematical Analysis 37, no.4 Pages: 1098-1116
  • NAID: 120006459404
  • Peer Reviewed
• [Journal Article] On stable critical points for a singular perturbation problem (2005)
  • Author(s): Tonegawa, Yoshihiro
  • Journal Title: Comm. Analysis and Geometry 13 no.2 Pages: 439-459
  • Peer Reviewed
• [Journal Article] A diffused interface whose chemical potential lies in Sobolev spaces (2005)
  • Author(s): Tonegawa, Yoshihiro
  • Journal Title: Ann.Scuola Norm.Sup.Pisa Cl.Sci.(5) 4・3 Pages: 487-510
• [Journal Article] Partial regularity for a selective smoothing functional for image restoration in BV space (2005)
  • Author(s): Chen, Yunmei
  • Journal Title: SIAM Journal on Mathematical Analysis 37・4 Pages: 1098-1116
• [Journal Article] Evaluation of data in terms of two-dimensional random walk model : Interaction between NADH-cytochrome b5 reductase and cytochrome b5 (2005)
  • Author(s): Tonegawa, Yoshihiro
  • Journal Title: Biomedical Research 26・5 Pages: 207-212
  • NAID: 130004470653
• [Journal Article] A pair of excitable FitzHugh-Nagumo elements : Synchronization, Multistability and Chaos (2005)
  • Author(s): Yanagita, Tetsuo
  • Journal Title: Physical Review E 72・5
  • NAID: 120000962943
• [Journal Article] Signal propagation and failure in one-dimensional FitzHugh-Nagumo equations with periodic stimuli (2005)
  • Author(s): Yanagita, Tetsuo
  • Journal Title: Physical Review E 71・3
  • NAID: 120000949935
• [Journal Article] Asymmetric motion of a two-dimensional symmetric flapping model (2005)
  • Author(s): Iima, Makoto
  • Journal Title: Fluid Dynamics Research 36・(4-6) Pages: 407-425
• [Presentation] Two-phase non-Newtonian fluid flow with surface tension (2008)
  • Author(s): 利根川吉廣
  • Organizer: 第6回浜松偏微分方程式研究集会
  • Place of Presentation: 静岡大学
  • Year and Date: 2008-12-23
• [Presentation] On some regularity issues of stable critical points for phase boundary problems (2008)
  • Author(s): 利根川吉廣
  • Organizer: 熊本における偏微分方程式研究集会
  • Place of Presentation: 熊本大学
  • Year and Date: 2008-10-25
• [Presentation] Existence of measure-valued solutions for two-phase non-Newtonian fluid flow with surface tension (2008)
  • Author(s): 利根川吉廣
  • Organizer: 研究集会「第四回非線型の諸問題」
  • Place of Presentation: 佐賀大学
  • Year and Date: 2008-09-21
• [Presentation] Phase field model and the generalized Gibbs-Thomson law (2008)
  • Author(s): 利根川吉廣
  • Organizer: Recent Progress on Pattern Formation and Dynamics in Mathematical Sciences
  • Place of Presentation: 龍谷大学
  • Year and Date: 2008-06-13
• [Presentation] Phase field model and the generalized Gibbs-Thomson law (2008)
  • Author(s): 利根川吉廣
  • Organizer: Workshop on Nonlinear PDEs related to physical models
  • Place of Presentation: 国立台湾大学
  • Year and Date: 2008-05-31
• [Presentation] Various mathematial questions arising in phase separation problem,Geometry of singularities via PDE's (2007)
  • Author(s): 利根川吉廣
  • Organizer: GMT and Diff. Geometry
  • Place of Presentation: 東北大学
  • Year and Date: 2007-01-10
• [Presentation] Allen-Cahn action functional and its singular perturbation (2006)
  • Author(s): 利根川吉廣
  • Organizer: SNP2006
  • Place of Presentation: 京都
  • Year and Date: 2006-12-04
• [Presentation] A singular perturbation problem motivated by larege deviation theory (2005)
  • Author(s): 利根川吉廣
  • Organizer: SNP2005
  • Place of Presentation: 京都
  • Year and Date: 2005-11-28
• [Presentation] A singular perturbation problem motivated by larege deviation theory (2005)
  • Author(s): 利根川吉廣
  • Organizer: PDE and applications
  • Place of Presentation: University of Florida
  • Year and Date: 2005-11-14
• [Presentation] Singular perturbation limit of phase separation problem (2005)
  • Author(s): 利根川吉廣
  • Organizer: PDE
  • Place of Presentation: Oberwolfach
  • Year and Date: 2005-07-25
• [Remarks]
  • URL: http://www.math.sci.hokudai.ac.jp/~tonegawa/toppagejp.htm
• [Remarks]
  • URL: http://www.math.sci.hokudai.ac.jp/~tonegawa/toppagejp.htm