Variational approach to collision, detachment and adhesion

• Project/Area Number: 23340024
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Kanazawa University
• Principal Investigator: OMATA Seiro 金沢大学, 数物科学系, 教授 (20214223)
• Co-Investigator(Kenkyū-buntansha): 長山 雅晴 北海道大学, 電子科学研究所, 教授 (20314289)
• Project Period (FY): 2011-04-01 – 2015-03-31
• Project Status: Completed (Fiscal Year 2014)
• Budget Amount: ¥17,810,000 (Direct Cost: ¥13,700,000、Indirect Cost: ¥4,110,000); Fiscal Year 2014: ¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000); Fiscal Year 2013: ¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000); Fiscal Year 2012: ¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000); Fiscal Year 2011: ¥7,540,000 (Direct Cost: ¥5,800,000、Indirect Cost: ¥1,740,000)
• Keywords: 偏微分方程式 / 変分問題 / 数値解析 / 双曲型自由境界問題 / 自由境界問題 / 離散勾配流 / 双曲型 / 自由境界 / 剥離 / 付着

Outline of Final Research Achievements

We have studied the motion of elastic body, fluid and their interaction. We used energy formula and variational method for solving these problems. The main target was hyperbolic free boundary problems which can be treated the motion of bubble even with junctions.Our method is based on the discrete Morse flow, which is defined by "time difference space differential" type functionals. We have constructed approximate solutions for hyperbolic free boundary problems and in easy cases we could show the existence of the solution.
The other feature of this problem is that we can add global constraints such as volume preserving constraint.We also developed numerical algorithm based on this idea.

Research Products

• [Journal Article] 双曲型自由境界問題の数理解析及び数値解析 (2015)
  • Author(s): 小俣正朗
  • Journal Title: 数学 Volume: 68
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Physicochemical design and analysis of self-propelled objects that are characteristically sensitive to interfacial environments (2015)
  • Author(s): S. Nakata, M. Nagayama, H. Kitahata, N. J. Suematsu and T. Hasegawa
  • Journal Title: Physical Chemistry Chemical Physics Volume: 7 Issue: 16 Pages: 10326-10338
  • DOI: 10.1039/c5cp00541h
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] A variational method for multiphase volume-preserving interface motions (2014)
  • Author(s): Svadlenka, Karel; Ginder, Elliott; Omata, Seiro
  • Journal Title: J. Comput. Appl. Math. Volume: 257 Pages: 157-179
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] A variational method for multiphase volume-preserving interface motions (2014)
  • Author(s): Svadlenka, Karel; Ginder, Elliott; Omata, Seiro
  • Journal Title: J. Comput. Appl. Math Volume: 257 Pages: 157-179
  • Peer Reviewed
• [Journal Article] A global model for impact of elastic shells and its numerical implementation (2013)
  • Author(s): M.Kazama, S. Omata, T.Nagasawa, A.Kikuta, K. Svadlenka
  • Journal Title: Adv. Math. Sci. Appl. Volume: 23-1 Pages: 93-108
  • Peer Reviewed
• [Journal Article] A global model for impact of elastic shells and its numerical implementation (2013)
  • Author(s): M.Kazama, S. Omata, T.Nagasawa, A.Kikuta, K. Svadlenka
  • Journal Title: Adv. Math. Sci. Appl Volume: 23
  • Peer Reviewed
• [Journal Article] Chaotic motion of propagating pulses in the Gray-Scott model (2011)
  • Author(s): M. Yadome, K. Ueda, M. Nagayama
  • Journal Title: Physical Review E Volume: Vol.83, Issue 5 Issue: 5 Pages: 83-83
  • DOI: 10.1103/physreve.83.056207
  • Peer Reviewed
• [Journal Article] Convergence of the Approximation Scheme to American Option Pricing via the Discrete Morse Semiflow (2011)
  • Author(s): Katsuyuki Ishii, Seiro Omata
  • Journal Title: Applied Mathematics & Optimization Volume: 64 Pages: 364-415
  • Peer Reviewed
• [Presentation] 液滴・泡の数理 (2014)
  • Author(s): 小俣正朗
  • Organizer: 日本数学会秋期総合分科会
  • Place of Presentation: 広島大学
  • Year and Date: 2014-09-25
  • Invited
• [Presentation] 粘着と剥離の数理モデルについて (2014)
  • Author(s): 小俣正朗
  • Organizer: 数学協働プログラム主催ワークショップ 「表面微細構造の学理の探求：低環境負荷材料の創造に向けて」
  • Place of Presentation: 北海道大学
  • Invited
• [Presentation] Mathematical modeling and numerical treatment of adhesion, exfoliation and collision (2013)
  • Author(s): Seiro Omata
  • Organizer: The 38th Sapporo Symposium on Partial Differential Equation
  • Place of Presentation: 北海道大学
  • Invited