| 研究課題/領域番号 |
15KT0099
|
|---|
| 研究機関 | 北海道大学 |
|---|
研究代表者 |
Ginder Elliott 北海道大学, 電子科学研究所, 助教 (30648217)
|
|---|
| 研究分担者 |
中田 聡 広島大学, 理学研究科, 教授 (50217741)
|
|---|
| 研究期間 (年度) |
2015-07-10 – 2019-03-31
|
| キーワード | Active matter / surface activity / filament motion |
|---|
| 研究実績の概要 |
Experimental results have clarified a mechanism for inducing out of phase filament synchronization. In particular, it has been found that collision or significant approach between the tips of the surfactant strings is important for generating such motions. Moreover, out of phase motions are not observed when the distance between strings exceeds their combined lengths. Pattern formation under the cAMP rules has also be observed.
We have also constructed improved finite element methods for simulating the experimental observations. These techniques alleviate several of the restrictions put on the method of lines approach used in our prior research. The new methods also outperform the previous ones in the sense of their numerical complexity and line-mass values are compatible with the finite element method’s basis function assumptions.
Analysis of the model equation has clarified the structure of jump conditions (which designate free boundary conditions at the location of the filaments). This information allowed us to construct classes of stationary solutions. We were also able to show the existence of traveling solutions under the assumption of periodic boundary conditions. Moreover, we have derived improved functional gradients for including length constraints and curvature effects into the interfacial motions.
|
| 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
The previous methods used in our simulations were computationally heavy. We have created new numerical algorithms for performing simulations of the model equation using both the method of lines and weak couplings. The weak coupling approaches have enabled fast simulations, which enabled us to easily check the behavior of our model equation. We have also
The experimental finding have also illuminated new directions for understanding properties of our model equation and are serving to direct its improvement.
|
| 今後の研究の推進方策 |
Experiments have guided us toward understanding the onset of out of phase filament synchronization. Since the mechanism is observed to be the collision, or significant approach, of the filaments, we would like to implement techniques for treating collision in our simulations in order to see whether our model can reproduce the findings.
Our simulations also suggest the existence of traveling pulse solutions domains with boundary. Mathematical analysis has yet to established their existence, which we will continue to pursue. We will also to search for the appearance of traveling filaments in the experimental setting. Relatedly, we will continue working on the stability analysis of stationary solutions that have been found to exist in our model equation.
|
| 次年度使用額が生じた理由 |
Improvements to the algorithms postposed the purchase of computational equipment.
|
| 次年度使用額の使用計画 |
We plan to purchase the computational equipment in H29.
|
