| 研究課題/領域番号 |
15KT0099
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| 研究機関 | 北海道大学 |
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研究代表者 |
Ginder Elliott 北海道大学, 電子科学研究所, 助教 (30648217)
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| 研究分担者 |
中田 聡 広島大学, 理学(系)研究科(研究院), 教授 (50217741)
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| 研究期間 (年度) |
2015-07-10 – 2019-03-31
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| キーワード | 動く界面 / Active matter / Physical chemistry |
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| 研究実績の概要 |
We have constructed analytic and computational techniques for applying the Galerkin method to model the motion of thin interface active matter. The interfacial motions that we have modeled correspond to experimental observations of a surface tension driven phenomena involving adhesive filaments (cemedine) on water. The phenomena have been found to display a variety of motions, including propagating (traveling-wave type), periodic, and oscillatory behaviors and we have aimed to understand their origins through the analysis of the mathematical model.
We have also established a framework for expressing interfaces using a line-mass approach, and we have built model equations for prescribing their evolutions. Investigation into the the behavior of line-masses in relation to well-known active matter (esp., cAMP gradient bion motions) has begun, and computational aspects related to treating line-masses have been addressed. We are continuing research here to effectively express interfacial geometry in active matter systems. Our mathematical analyses have also allowed us to show the existence of special classes of solutions to our model equations.
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| 現在までの達成度 (区分) |
現在までの達成度 (区分)
2: おおむね順調に進展している
理由
New techniques for visualizing the motion of interfaces have also been developed, and A large set of new experimental data have been obtained. The observable phenomena display a diverse range of behaviors that we now aim to reproduce using our mathematical model. The finite element methods for approximating the model equation’s solution have been constructed. and this approach have been found to successfully treat interfaces as co-dimension 1 objects. This permits us to easily handle curvature dependent quantities, which we expect to play a vital role in the simulations.
We have also be able to formulate and construct certain traveling wave solutions to the model equation, which has provided us with a good candidate for comparison with experiments, and for investigating the solutions’ stability.
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| 今後の研究の推進方策 |
The finite element method provides us with a means to compute the exact motion of interfaces (within the finite element space), but this requires one to construct a special purpose interface tracking algorithm. This algorithm is nearly complete and a next step will be to incorporate it into the current numerical simulations. The resulting framework will allow us to inquire into reproducing interfacial motions that are observed in experiments in a mathematically rigorous fashion. We would also like to begin analyzing the stability of traveling wave solutions and to develop means for incorporating interfacial collision into our model equation.
Regarding the experiments, it is necessary to continue to simplify the system. As the current experiments correspond to open curves in the simulations, we would also like design an experimental setting where the motion of closed curves can be observed.
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| 次年度使用額が生じた理由 |
広島大学への旅費がかからなかったため．
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| 次年度使用額の使用計画 |
「Active matter」に関する教科書を購入する予定です．
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