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Variational approach to collision, detachment and adhesion

Research Project

Project/Area Number 23340024
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionKanazawa 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 *help
¥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.

Report

(5 results)
  • 2014 Annual Research Report   Final Research Report ( PDF )
  • 2013 Annual Research Report
  • 2012 Annual Research Report
  • 2011 Annual Research Report
  • Research Products

    (11 results)

All 2015 2014 2013 2011

All Journal Article (8 results) (of which Peer Reviewed: 8 results,  Acknowledgement Compliant: 3 results) Presentation (3 results) (of which Invited: 3 results)

  • [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

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Physicochemical design and analysis of self-propelled objects that are characteristically sensitive to interfacial environments2015

    • 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

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] A variational method for multiphase volume-preserving interface motions2014

    • Author(s)
      Svadlenka, Karel; Ginder, Elliott; Omata, Seiro
    • Journal Title

      J. Comput. Appl. Math.

      Volume: 257 Pages: 157-179

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] A variational method for multiphase volume-preserving interface motions2014

    • Author(s)
      Svadlenka, Karel; Ginder, Elliott; Omata, Seiro
    • Journal Title

      J. Comput. Appl. Math

      Volume: 257 Pages: 157-179

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A global model for impact of elastic shells and its numerical implementation2013

    • Author(s)
      M.Kazama, S. Omata, T.Nagasawa, A.Kikuta, K. Svadlenka
    • Journal Title

      Adv. Math. Sci. Appl.

      Volume: 23-1 Pages: 93-108

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A global model for impact of elastic shells and its numerical implementation2013

    • Author(s)
      M.Kazama, S. Omata, T.Nagasawa, A.Kikuta, K. Svadlenka
    • Journal Title

      Adv. Math. Sci. Appl

      Volume: 23

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Chaotic motion of propagating pulses in the Gray-Scott model2011

    • 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

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Convergence of the Approximation Scheme to American Option Pricing via the Discrete Morse Semiflow2011

    • Author(s)
      Katsuyuki Ishii, Seiro Omata
    • Journal Title

      Applied Mathematics & Optimization

      Volume: 64 Pages: 364-415

    • Related Report
      2011 Annual Research Report
    • 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
    • Related Report
      2014 Annual Research Report
    • 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
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Mathematical modeling and numerical treatment of adhesion, exfoliation and collision2013

    • Author(s)
      Seiro Omata
    • Organizer
      The 38th Sapporo Symposium on Partial Differential Equation
    • Place of Presentation
      北海道大学
    • Related Report
      2013 Annual Research Report
    • Invited

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Published: 2011-04-06   Modified: 2019-07-29  

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