2018 Fiscal Year Annual Research Report
The Interfacial and Free-Boundary Dynamics of Active Matter
| Project/Area Number |
15KT0099
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| Research Institution | Meiji University |
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Principal Investigator |
Ginder Elliott 明治大学, 総合数理学部, 専任准教授 (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 / interfacial motion / physical chemistry / mathematical modeling |
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| Outline of Annual Research Achievements |
In 2018, simulations for investigating the behavior of filament groups were performed. Our results showed the existence of preferred distances between filaments near stationary solutions. Special parameter ranges also revealed intermittent filament motions. In these motions, the filaments appear to approach a stationary group configuration, but some members are eventually excited into motion again. Motions occurring at irregular intervals are also observed in chemical systems and this suggests that our model equation is able to capture an interesting feature of the physical chemistry.
Regarding the mathematical analysis, we were able to show the existence of stationary solutions to our model equation in the two dimensional setting. This was done by reducing the model equation to a coupled free boundary problem. We were able to show that the solution of the free boundary problem is composed of solutions to Bessel differential equations, with prescribed jump and continuity conditions. Stationary solutions were constructed for the Cauchy problem, as well as the problem under periodic boundary conditions. In addition, we were able to construct the numerical realization of the stationary solutions and view their structure.
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Research Products
(1 results)
