A variational approach to the modeling and analysis of droplet and bubble motions

• Project/Area Number: 25800087
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Foundations of mathematics/Applied mathematics
• Research Institution: Hokkaido University
• Principal Investigator: Ginder Elliott 北海道大学, 電子科学研究所, 助教 (30648217)
• Project Period (FY): 2013-04-01 – 2016-03-31
• Project Status: Completed (Fiscal Year 2015)
• Budget Amount: ¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000); Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2014: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000); Fiscal Year 2013: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
• Keywords: droplet motion / threshold dynamics / free boundary problems / variational methods / numerical algorithm / Threshold dynamics / approximation scheme

Outline of Final Research Achievements

This research analyzed and simulated a mathematical model which describes the motion of droplets and bubbles. We used a variational method known as minimizing movements to treat our equation from the point of view of energy. Droplet contact angle dynamics were also incorporated by using techniques from the calculus of variations, and we built numerical methods for simulating the droplet motions (including coalesce and division). We also discovered a threshold dynamical algorithm for approximating interface motion by hyperbolic mean curvature flow. This research was awarded the Mathematical Society of Japan’s 2013 Prize for Excellent Young Applied Mathematicians.

Research Products

• [Journal Article] Wave-type threshold dynamics and the hyperbolic mean curvature flow (2016)
  • Author(s): Elliott Ginder, Karel Svadlenka
  • Journal Title: Japan Journal of Industrial and Applied Mathematics Volume: (Submitted) Pages: 1-22
  • NAID: 120006414206
  • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
• [Journal Article] On an approximation method for hyperbolic mean curvature lfow (2016)
  • Author(s): Elliott Ginder, Ayumu Katayama, Karel Svadlenka
  • Journal Title: Rims Kokyuroku Volume: TBD Pages: 1-8
• [Journal Article] On an approximation scheme for oscillatory interfacial motions (2015)
  • Author(s): Elliott Ginder, Karel Svadlenka
  • Journal Title: Proceedings of the 40th Sapporo Symposium on Partial Differential Equations Volume: 40 Pages: 90-96
• [Journal Article] Wave-type threshold dynamics and the hyperbolic mean curvature flow (2015)
  • Author(s): Elliott Ginder, Karel Svadlenka
  • Journal Title: arXiv Volume: 1505.01963 Pages: 1-17
  • NAID: 120006414206
• [Journal Article] 変分法による界面運動のシミュレーション (2015)
  • Author(s): Elliott Ginder, Karel Svadlenka
  • Journal Title: 計算工学 Volume: 20 No. 3 Pages: 17-20
  • Acknowledgement Compliant
• [Journal Article] On an algorithm for curvature-dependent interfacial acceleration (2014)
  • Author(s): Elliott Ginder, Karel Svadlenka
  • Journal Title: JSCES Volume: 19 Pages: 1-5
  • NAID: 40020116818
  • 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
  • DOI: 10.1016/j.cam.2013.08.027
  • Peer Reviewed
• [Presentation] On an approximation method for hyperbolic mean curvature flow (2015)
  • Author(s): Elliott Ginder
  • Organizer: RIMS研究集会：現象解明に向けた数値解析の新発展
  • Place of Presentation: 京都大学（京都府京都市）
  • Year and Date: 2015-11-20
  • Invited
• [Presentation] On an approximation scheme for oscillatory interfacial motions (2015)
  • Author(s): Elliott Ginder
  • Organizer: The 40th Sapporo Symposium on PDE
  • Place of Presentation: 北海道大学（北海道札幌市）
  • Year and Date: 2015-08-20
  • Int'l Joint Research / Invited
• [Presentation] On the use of minimizing movements in applications (2015)
  • Author(s): Elliott Ginder
  • Organizer: 数学と現象 in 伊豆大島
  • Place of Presentation: 伊豆大島（東京都大島町）
  • Year and Date: 2015-07-30
  • Invited
• [Presentation] A minimizing movement approach to constrained distributed parameter systems (2015)
  • Author(s): Elliott Ginder
  • Organizer: Hokkaido University PDE Seminar
  • Place of Presentation: 北海道大学（北海道札幌市）
  • Year and Date: 2015-04-20
  • Invited
• [Presentation] Methods for approximation of constrained interfacial dynamics (2015)
  • Author(s): Elliott Ginder
  • Organizer: 日本数学会 2015 年度年会
  • Place of Presentation: 明治大学（東京都千代田区神保町）
  • Year and Date: 2015-03-23
  • Invited
• [Presentation] Threshold dynamics generating curvature dependent interfacial acceleration (2014)
  • Author(s): Elliott Ginder
  • Organizer: 日本応用数理学会2014年度年会
  • Place of Presentation: 政策研究大学院大学（東京都港区六本木）
  • Year and Date: 2014-09-03
  • Invited
• [Presentation] On an algorithm for curvature-dependent interfacial acceleration (2014)
  • Author(s): Elliott Ginder
  • Organizer: 第19回計算工学講演会
  • Place of Presentation: 広島国際会議場（広島市中区中島町）
  • Year and Date: 2014-06-13
• [Presentation] The hyperbolic BMO algorithm (2014)
  • Author(s): Elliott Ginder
  • Organizer: 日本数学会 2014 年度年会
  • Place of Presentation: 学習院大学（東京都）
• [Presentation] A numerical method for curvature dependent acceleration (2014)
  • Author(s): Elliott Ginder
  • Organizer: 北陸応用数理研究会2014
  • Place of Presentation: 金沢大学サトライトプラザ（石川県）
• [Presentation] On the hyperbolic BMO algorithm (2014)
  • Author(s): Elliott Ginder
  • Organizer: Kunitachi One-Day Symposium
  • Place of Presentation: 一橋大学（東京都）
  • Invited
• [Presentation] Droplets and Bubbles: the Free Boundary and Interfacial Dynamics (2014)
  • Author(s): Elliott Ginder
  • Organizer: The 17th Sanken International Symposium
  • Place of Presentation: 大阪大学（大阪府）
• [Presentation] Droplet and bubble motion: a hyperbolic free boundary problem approach (2013)
  • Author(s): Elliott Ginder
  • Organizer: 2013年度応用数学合同研究集会
  • Place of Presentation: 龍谷大学（滋賀県）
• [Presentation] Interfacial dynamics and free boundary problems for oscillating membrane motions (2013)
  • Author(s): Elliott Ginder
  • Organizer: Kyoto University Applied Mathematics Seminar
  • Place of Presentation: 京都大学（京都府）
  • Invited
• [Presentation] A variational approach to droplet motion (2013)
  • Author(s): Elliott Ginder
  • Organizer: The 9th East Asia Siam Conference
  • Place of Presentation: Istitut Teknologi Bandung, Indonesia
• [Presentation] A variational approach to volume-constrained membrane motions (2013)
  • Author(s): Elliott Ginder
  • Organizer: Institute for Mathematics and its Applications
  • Place of Presentation: University of Minnesota, USA
  • Invited
• [Presentation] Droplets and bubbles: a variational approach (2013)
  • Author(s): Elliott Ginder
  • Organizer: International Symposium on Complex Chemical Systems
  • Place of Presentation: University of Glasgow, UK
  • Invited
• [Remarks] 2013年度応用数学研究奨励賞
  • URL: http://mathsoc.jp/publicity/appmath2013.html