期刊
EUROPEAN PHYSICAL JOURNAL E
卷 35, 期 12, 页码 -出版社
SPRINGER
DOI: 10.1140/epje/i2012-12135-5
关键词
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资金
- JSPS KAKENHI [23740286]
- JSPS Core-to-Core Program International research network for non-equilibrium dynamics of soft matter
- Grants-in-Aid for Scientific Research [23740286] Funding Source: KAKEN
Synchronization induced by long-range hydrodynamic interactions is attracting attention as a candidate mechanism behind coordinated beating of cilia and flagella. Here we consider a minimal model of hydrodynamic synchronization in the low Reynolds number limit. The model consists of rotors, each of which assumed to be a rigid bead making a fixed trajectory under periodically varying driving force. By a linear analysis, we derive the necessary and sufficient conditions for a pair of rotors to synchronize in phase. We also derive a non-linear evolution equation for their phase difference, which is reduced to minimization of an effective potential. The effective potential is calculated for a variety of trajectory shapes and geometries (either bulk or substrated), for which the stable and metastable states of the system are identified. Finite size of the trajectory induces asymmetry of the potential, which also depends sensitively on the tilt of the trajectory. Our results show that flexibility of cilia or flagella is not a requisite for their synchronized motion, in contrast to previous expectations. We discuss the possibility to directly implement the model and verify our results by optically driven colloids.
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