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Mathematical model for the oil droplet motion on the water surface, and its analysis

Research Project

Project/Area Number 18684002
Research Category

Grant-in-Aid for Young Scientists (A)

Allocation TypeSingle-year Grants
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionKanazawa University

Principal Investigator

NAGAYAMA Masaharu  Kanazawa University, 数物科学系, 教授 (20314289)

Research Collaborator OMATA Seiro  金沢大学, 数物科学系, 教授 (20214223)
KITAHATA Hiroyuki  千葉大学, 理学研究科, 講師 (20378532)
Project Period (FY) 2006 – 2008
Project Status Completed (Fiscal Year 2008)
Budget Amount *help
¥14,040,000 (Direct Cost: ¥10,800,000、Indirect Cost: ¥3,240,000)
Fiscal Year 2008: ¥2,860,000 (Direct Cost: ¥2,200,000、Indirect Cost: ¥660,000)
Fiscal Year 2007: ¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000)
Fiscal Year 2006: ¥8,450,000 (Direct Cost: ¥6,500,000、Indirect Cost: ¥1,950,000)
Keywords数理モデル / 反応拡散系 / 離散変分法 / 液滴運動 / 表面張力 / 分裂と融合, 反射 / 離散勾配流法 / 計算機支援解析 / 回転波 / 分裂と合体 / 応用数学
Research Abstract

分裂や融合を伴いながら並進運動する液滴に対する数理的機構を明きからにすることを目的に研究を推進した. 本研究では, 液滴の高さを表す関数を導入し, 表面エネルギー最小原理によって液滴運動を記述する数理モデルを得た. また, 初期体積の保存条件を満足する数値計算法として離散勾配流法を採用し数値計算を行った. この結果, 液滴の初期体積が小さい場合は並進運動すること, 初期体積が大きい場合は, 液滴が分裂し, 分裂した液滴が併進運動を行い, 衝突する角度に依存して反射と融合が起こることを明らかにした.

Report

(4 results)
  • 2008 Annual Research Report   Final Research Report ( PDF )
  • 2007 Annual Research Report
  • 2006 Annual Research Report
  • Research Products

    (18 results)

All 2009 2008 2007 2006 Other

All Journal Article (7 results) (of which Peer Reviewed: 5 results) Presentation (8 results) Book (1 results) Remarks (2 results)

  • [Journal Article] 反応拡散系に対する大域的分岐構造の数値計算法とその応用2009

    • Author(s)
      矢留雅亮, 長山雅晴, 上田肇一
    • Journal Title

      京都大学数理解析研究所講究録 1633

      Pages: 39-61

    • Related Report
      2008 Final Research Report
  • [Journal Article] Bifurcation of self-motion depending on the reaction order2009

    • Author(s)
      M.Nagayama, M.Yadome, N.Kato, J.Kirisaka, M.Murakami and S.Nakata
    • Journal Title

      Physical Chemistry Chemical Physics 11

      Pages: 1085-1090

    • NAID

      120001249805

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Bifurcation of self-motion depending on the reaction order2009

    • Author(s)
      M. NAGAYAMA
    • Journal Title

      Physical Chemistry Chemical Physics 11

      Pages: 1085-1090

    • NAID

      120001249805

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Periodic transition sequences of scattering patterns in a three-component reaction-diffusion system2008

    • Author(s)
      M.Yadome, K.-I.Ueda, T.Teramoto, M.Nagayama and Y.Nishiura
    • Journal Title

      Bulletin of the Institute of Mathematics, Academia Sinica New Series 3(4)

      Pages: 585-602

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Periodic transition sequences of scattering patterns in a three-component reaction-diffusion system2008

    • Author(s)
      M. YADOME
    • Journal Title

      Bulletin of the Institute of Mathematics, Academia Sinica New Series 4

      Pages: 589-602

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Numerical simulation of motion of a bubble restrained to water surface2006

    • Author(s)
      T.Yamazaki, S.Omata and M.Nagayama
    • Journal Title

      京都大学数理解析研究所講究録 1522

      Pages: 111-119

    • Related Report
      2008 Final Research Report
  • [Journal Article] Interacting spots in reaction diffusion systems2006

    • Author(s)
      S.-I.Ei, M.Mimura and M.Nagayama
    • Journal Title

      Discrete and Continuous Dynamical Systems 14(1)

      Pages: 31-62

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Presentation] 双安定反応拡散系に現れるパルス波の遷移ダイナミクスについて2009

    • Author(s)
      矢留雅亮
    • Organizer
      日本数学会
    • Place of Presentation
      東京大学
    • Year and Date
      2009-03-28
    • Related Report
      2008 Annual Research Report
  • [Presentation] 液滴運動の数理モデルとその数値シミュレーション2009

    • Author(s)
      長山 雅晴
    • Organizer
      非線形現象の数値シミュレーションと解析2009
    • Place of Presentation
      北海道大学
    • Year and Date
      2009-03-07
    • Related Report
      2008 Final Research Report
  • [Presentation] 反応拡散系に対する大域的分岐構造の数値計算法2008

    • Author(s)
      長山 雅晴
    • Organizer
      日本数理生物学会企画シンポジウム
    • Place of Presentation
      同志社大学
    • Year and Date
      2008-09-18
    • Related Report
      2008 Final Research Report
  • [Presentation] 現象の数理モデル2008

    • Author(s)
      長山雅晴
    • Organizer
      日本数学会(応用数学分科会特別講演)
    • Place of Presentation
      近畿大学
    • Year and Date
      2008-03-25
    • Related Report
      2008 Final Research Report
  • [Presentation] 現象の数理モデルとその計算機支援解析2008

    • Author(s)
      長山 雅晴
    • Organizer
      数学会 応用数学分科会 特別講演
    • Place of Presentation
      近畿大学
    • Year and Date
      2008-03-25
    • Related Report
      2007 Annual Research Report
  • [Presentation] Traveling Spots Dynamics in Reaction-Diffusion Systems2007

    • Author(s)
      M. Nagayama
    • Organizer
      International Conference on Computational Science 2007(招待講演)
    • Place of Presentation
      Institut Teknologi Bandung
    • Year and Date
      2007-12-03
    • Related Report
      2008 Final Research Report
  • [Presentation] 液滴運動のモデル方程式とその数値計算法2007

    • Author(s)
      長山 雅晴
    • Organizer
      日本物理学会(ポスター講演)
    • Place of Presentation
      鹿児島大学
    • Year and Date
      2007-03-21
    • Related Report
      2008 Final Research Report
  • [Presentation] Mathematical modeling for the motion of oil droplet2006

    • Author(s)
      M. Nagayama
    • Organizer
      East-Asia Workshop on Pattern Formations and Reaction-Diffusion Systems(招待講演)
    • Place of Presentation
      Chinese University of Hong Kong
    • Year and Date
      2006-12-14
    • Related Report
      2008 Final Research Report
  • [Book] パターン形成とダイナミクス(非線形・非平衡現象の数理4)第3章 : 発熱反応拡散系に現われる時空間パターン2006

    • Author(s)
      三村 昌泰, 長山 雅晴
    • Publisher
      東京大学出版会
    • Related Report
      2008 Final Research Report
  • [Remarks] ホームページアドレス

    • URL

      http://blossom1.s.kanazawa-u.ac.jp/professor/research.html

    • Related Report
      2008 Final Research Report
  • [Remarks]

    • URL

      http://blossoml.s.kanazawa-u.ac.jp/professor/research.html

    • Related Report
      2008 Annual Research Report

URL: 

Published: 2006-04-01   Modified: 2016-04-21  

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