Kawamura Yoji, Tsubaki Remi
Department of Mathematical Science and Advanced Technology, Japan Agency for Marine-Earth Science and Technology, Yokohama 236-0001, Japan.
Research and Development Center for Marine Biosciences, Japan Agency for Marine-Earth Science and Technology, Yokosuka 237-0061, Japan.
Phys Rev E. 2018 Feb;97(2-1):022212. doi: 10.1103/PhysRevE.97.022212.
We formulate a theory for the phase reduction of a beating flagellum. The theory enables us to describe the dynamics of a beating flagellum in a systematic manner using a single variable called the phase. The theory can also be considered as a phase reduction method for the limit-cycle solutions in infinite-dimensional dynamical systems, namely, the limit-cycle solutions to partial differential equations representing beating flagella. We derive the phase sensitivity function, which quantifies the phase response of a beating flagellum to weak perturbations applied at each point and at each time. Using the phase sensitivity function, we analyze the phase synchronization between a pair of beating flagella through hydrodynamic interactions at a low Reynolds number.
我们为摆动鞭毛的相位约化建立了一个理论。该理论使我们能够用一个称为相位的单一变量以系统的方式描述摆动鞭毛的动力学。该理论也可被视为一种针对无限维动力系统中极限环解的相位约化方法，即代表摆动鞭毛的偏微分方程的极限环解。我们推导了相位敏感性函数，它量化了摆动鞭毛在每个点和每个时刻对施加的微弱扰动的相位响应。利用相位敏感性函数，我们通过低雷诺数下的流体动力相互作用分析了一对摆动鞭毛之间的相位同步。
