2016 Fiscal Year Research-status Report
The Interfacial and Free-Boundary Dynamics of Active Matter
| Project/Area Number |
15KT0099
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| Research Institution | Hokkaido University |
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Principal Investigator |
Ginder Elliott 北海道大学, 電子科学研究所, 助教 (30648217)
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| Co-Investigator(Kenkyū-buntansha) |
中田 聡 広島大学, 理学研究科, 教授 (50217741)
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| Project Period (FY) |
2015-07-10 – 2019-03-31
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| Keywords | Active matter / surface activity / filament motion |
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| Outline of Annual Research Achievements |
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.
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| Current Status of Research Progress |
Current Status of Research Progress
2: Research has progressed on the whole more than it was originally planned.
Reason
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.
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| Strategy for Future Research Activity |
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.
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| Causes of Carryover |
Improvements to the algorithms postposed the purchase of computational equipment.
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| Expenditure Plan for Carryover Budget |
We plan to purchase the computational equipment in H29.
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