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

2015 Fiscal Year Final Research Report

• 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
• Keywords: droplet motion / threshold dynamics / free boundary problems / variational methods / numerical algorithm

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.

Free Research Field

Applied Mathematics