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Mathematical analysis related to a model of droplet motion

Research Project

Project/Area Number 22740102
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeSingle-year Grants
Research Field Global analysis
Research InstitutionKanazawa University

Principal Investigator

SVADLENKA Karel  金沢大学, 数物科学系, 准教授 (60572188)

Project Period (FY) 2010 – 2012
Project Status Completed (Fiscal Year 2012)
Budget Amount *help
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2011: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2010: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Keywords界面運動 / 自由境界問題 / 平均曲率流 / 体積保存 / 関数方程式論
Research Abstract

A model was developed for the motion of droplets on surfaces including the dynamics of contact angle, and mathematical analysis of the problem was performed. It was found that the evolution of the contact angle depends on the mode of motion of the droplet surface, and for two basic modes of motion some of the properties of solutions to the corresponding problem were derived. Moreover, a numerical approximation method was introduced for the problem of several interfaces with junctions, which has been considered as difficult to treat mathematically, and it was shown that the suggested method has a perspective to be extended as a tool of mathematical analysis.

Report

(4 results)
  • 2012 Annual Research Report   Final Research Report ( PDF )
  • 2011 Annual Research Report
  • 2010 Annual Research Report
  • Research Products

    (35 results)

All 2013 2012 2011 2010 Other

All Journal Article (14 results) (of which Peer Reviewed: 12 results) Presentation (21 results) (of which Invited: 3 results)

  • [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

      Advances in Mathematical Sciences and Applications

      Volume: Vol. 23 No. 1(in press)

    • Related Report
      2012 Annual Research Report 2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] On a minimizing movement for diffusiongenerated interfacial motions2012

    • Author(s)
      E. Ginder, S. Omata, K. Svadlenka
    • Journal Title

      数理解析研究所講究録

      Volume: 1791 Pages: 189-195

    • URL

      http://repository.kulib.kyoto-u.ac.jp/dspace/bitstream/2433/172824/1/1791-22.pdf

    • Related Report
      2012 Final Research Report
  • [Journal Article] Diffusion-generatedvolume-preserving motions: A comparison of MBO-variant algorithms2012

    • Author(s)
      R. Z. Mohammad, K. Svadlenka
    • Journal Title

      Proceedings of Computational Engineering Conference JSCES

      Volume: Vol. 17

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] The discrete Morse flow for volume-constrained membrane motions2012

    • Author(s)
      E. Ginder, K. Svadlenka
    • Journal Title

      Advances in Mathematical Sciences and Applications

      Volume: Vol. 22, No. 1 Pages: 205-223

    • Related Report
      2012 Annual Research Report 2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Diffusion-generated volume-preserving motions: A comparison of MBO-variant algorithms2012

    • Author(s)
      R. Z. Mohammad, K. Svadlenka
    • Journal Title

      Proceedings of Computational Engineering Conference JSCES

      Volume: 17

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On a minimizing movement for diffusion-generated interfacial motions2012

    • Author(s)
      E. Ginder, S. Omata, K. Svadlenka
    • Journal Title

      数理解析研究所講究録

      Volume: 1791 Pages: 189-195

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Diffusion-generated volume-preserving motions : A comparison of MBO-variant algorithms2012

    • Author(s)
      R.Z.Mohammad, K.Svadlenka
    • Journal Title

      Proceedings of Computational Engineering Conference JSCES

      Volume: 17(CD ROM)

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Numerical computation of volume preserving multiphase mean curvature flow2011

    • Author(s)
      E. Ginder, S. Omata, K. Svadlenka
    • Journal Title

      Proceedings of Computational Engineering Conference JSCES

      Volume: Vol. 16

    • NAID

      40019581840

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] A variational method for diffusiongenerated area preserving interface motion2011

    • Author(s)
      E. Ginder, S. Omata, K. Svadlenka
    • Journal Title

      Theoretical and Applied Mechanics Japan

      Volume: Vol. 60 Pages: 265-270

    • URL

      https://www.jstage.jst.go.jp/article/nctam/60/0/60_265/_pdf

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] A variational method for diffusion-generated area-preserving interface motion2011

    • Author(s)
      E.Ginder, S.Omata, K.Svadlenka
    • Journal Title

      Theoretical and Applied Mechanics Japan

      Volume: 60 Pages: 265-270

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] 体積を保存する多相平均曲率流の数値計算2011

    • Author(s)
      E.Ginder, S.Omata, K.Svadlenka
    • Journal Title

      Proceedings of Computational Engineering Conference JSCES

      Volume: 16(CD ROM)

    • NAID

      40019581840

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A thresholding variational method for area preserving interface motion2011

    • Author(s)
      E.Ginder, S.Omata, K.Svadlenka
    • Journal Title

      The 60^<th> Nat.Congress of Theoretical & Applied Mechanics

      Volume: OS08-02

    • NAID

      130004604648

    • Related Report
      2010 Annual Research Report
  • [Journal Article] Numerical computation of coupled problems comprising elastic membrane2010

    • Author(s)
      S. Omata, M. Kazama, K. Svadlenka
    • Journal Title

      Proceedings of Computational Engineering Conference JSCES

      Volume: Vol. 15, No. 2 Pages: 697-700

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Numerical computation of coupled problems comprising elastic membrane2010

    • Author(s)
      S.Omata, M.Kazama, K.Svadlenka
    • Journal Title

      Proceedings of Computational Engineering Conference JSCES

      Volume: Vol.15 No.2 Pages: 697-700

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Presentation] Approximations for constrained motion of multiple interfaces2012

    • Author(s)
      K. Svadlenka
    • Organizer
      5thPolish-Japanese Days on Nonlinear Analysis in Interdisciplinary Sciences
    • Place of Presentation
      Kyoto, Japan
    • Year and Date
      2012-11-08
    • Related Report
      2012 Final Research Report
  • [Presentation] Numerical computation of multiple interface motion with constraints2012

    • Author(s)
      K. Svadlenka
    • Organizer
      Current Problems in Numerical Analysis
    • Place of Presentation
      Czech Academy of Sciences, Prague, Czech Republic
    • Year and Date
      2012-10-19
    • Related Report
      2012 Final Research Report
  • [Presentation] A numerical scheme for constrained motion of multiple interfaces2012

    • Author(s)
      K. Svadlenka
    • Organizer
      4th China-Japan-Korea Conference on Numerical Mathematics
    • Place of Presentation
      Otsu, Japan
    • Related Report
      2012 Annual Research Report 2012 Final Research Report
  • [Presentation] On a new numerical method for multiphase area-preserving mean curvature motion of interfaces2012

    • Author(s)
      K. Svadlenka
    • Organizer
      International Symposium on Computational Science 2012
    • Place of Presentation
      University Gadjah Mada, Yogyakarta, Indonesia
    • Related Report
      2012 Annual Research Report 2012 Final Research Report
  • [Presentation] Numerical computation of multiple interface motion with constraints2012

    • Author(s)
      K. Svadlenka
    • Organizer
      Current Problems in Numerical Analysis
    • Place of Presentation
      Czech Academy of Sciences, Prague
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Approximations for constrained motion of multiple interfaces2012

    • Author(s)
      K. Svadlenka
    • Organizer
      5th Polish-Japanese Days on Nonlinear Analysis in Interdisciplinary Sciences
    • Place of Presentation
      Kyoto, Japan
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Vector-valued BMO algorithm for approximation of multiphase mean-curvature flow2012

    • Author(s)
      K. Svadlenka
    • Organizer
      研究集会「界面の数理と幾何解析」
    • Place of Presentation
      芝浦工業大学、日本
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] On a constrained multiphase mean curvature flow2011

    • Author(s)
      K.Svadlenka
    • Organizer
      Emerging Topics on Differential Equations and their Applications
    • Place of Presentation
      南開大学(天津・中国)(招待講演)
    • Year and Date
      2011-12-05
    • Related Report
      2011 Annual Research Report
  • [Presentation] Mean curvature flow with volume constraint2011

    • Author(s)
      K.Svadlenka
    • Organizer
      SIAM Conference on Analysis of PDEs
    • Place of Presentation
      San Diego (USA) San Diego Marriott Mission Vallry(招待講演)
    • Year and Date
      2011-11-14
    • Related Report
      2011 Annual Research Report
  • [Presentation] 体積を保存する多相平均曲率流の数値計算2011

    • Author(s)
      K.Svadlenka
    • Organizer
      第16回計算工学会講演会
    • Place of Presentation
      東京大学(千葉県)(招待講演)
    • Year and Date
      2011-05-25
    • Related Report
      2011 Annual Research Report
  • [Presentation] On a constrained multiphase mean curvature flow2011

    • Author(s)
      University Gadjah Mada, Yogyakarta, Indonesia
    • Organizer
      Emerging Topics on Differential Equations and their Applications
    • Place of Presentation
      Nankai University, China
    • Related Report
      2012 Final Research Report
  • [Presentation] Mean Curvature Flow With Volume Constraint2011

    • Author(s)
      K. Svadlenka
    • Organizer
      SIAM Conference on Analysis of PDEs
    • Place of Presentation
      San Diego Marriott Mission Valley, USA
    • Related Report
      2012 Final Research Report
  • [Presentation] 体積を保存する多相平均曲率流の数値計2011

    • Author(s)
      K. Svadlenka
    • Organizer
      算第16回計算工学会講演会
    • Place of Presentation
      東京大学柏キャンパス
    • Related Report
      2012 Final Research Report
  • [Presentation] Theoretical and computational aspects of global constraints in evolutionary problems2010

    • Author(s)
      Svadlenka Karel
    • Organizer
      Czech Japanese Seminar in Applied Mathematics 2010
    • Place of Presentation
      Czech Technical University (Czech Republic)
    • Year and Date
      2010-08-31
    • Related Report
      2010 Annual Research Report
  • [Presentation] Analysis of the motion of a membrane touching a solid plane2010

    • Author(s)
      Svadlenka Karel
    • Organizer
      第35回偏微分方程式論札幌シンポジウム
    • Place of Presentation
      北海道大学(北海道)(招待講演)
    • Year and Date
      2010-08-23
    • Related Report
      2010 Annual Research Report
  • [Presentation] On a volume preserving free boundary problem2010

    • Author(s)
      Svadlenka Karel
    • Organizer
      RIMS研究集会「保存則と幾何学的偏微分方程式とその応用」
    • Place of Presentation
      京都大学数理解析研究所(京都府)(招待講演)
    • Year and Date
      2010-06-10
    • Related Report
      2010 Annual Research Report
  • [Presentation] Numerical computation of coupled problems comprising elastic membrane2010

    • Author(s)
      Svadlenka Karel
    • Organizer
      第15回計算工学会講演会
    • Place of Presentation
      九州大学(福岡県)(招待講演)
    • Year and Date
      2010-05-26
    • Related Report
      2010 Annual Research Report
  • [Presentation] Theoretical and computational aspects of global constraints in evolutionary problems2010

    • Author(s)
      K. Svadlenka
    • Organizer
      Czech Japanese Seminar in Applied Mathematics 2010
    • Place of Presentation
      Czech Technical University in Prague, Prague, Czech Republic
    • Related Report
      2012 Final Research Report
  • [Presentation] Analysis of the motion of a membrane touching a solid plane2010

    • Author(s)
      K. Svadlenka
    • Organizer
      第35回偏微分方程式論札幌シンポジウム(The 35th Sapporo Symposium on Partial Differential Equations)
    • Place of Presentation
      北海道大学
    • Related Report
      2012 Final Research Report
  • [Presentation] On a volume-preserving free boundary problem2010

    • Author(s)
      K. Svadlenka
    • Organizer
      RIMS Workshop: Geometric aspects of partial differential equations and conservation laws
    • Place of Presentation
      京都大学
    • Related Report
      2012 Final Research Report
  • [Presentation] Numerical computation of coupled problems comprising elastic membrane

    • Author(s)
      K. Svadlenka
    • Organizer
      第15回計算工学会講演会
    • Related Report
      2012 Final Research Report

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Published: 2010-08-23   Modified: 2019-07-29  

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