Theory of synchronization and cooperative dynamics in active fluid systems

在本计画中，我们建立了纤毛与鞭毛在流体动力相互作用下集体运动的数学模型，并得到下列结果。我们建立了ciia的刚体转子模型，并分析了它们在一对和一维和二维阵列中的动力学。我们发现，各种同步状态和行波图案的出现取决于模式的驱动力，距离基板，轨道形状和倾斜度，以及纤毛的灵活性。我们还数值分析了由于细菌地毯中的许多鞭毛的集体传输现象，并澄清了集体同步过渡的性质，由于一般类的长程相互作用的场论方法。

In this project we constructed mathematical models of collective motion of cilia and flagella due to hydrodynamic interactions, and obtained the following results. We constructed a rigid-body rotor model of ciia and analyzed their dynamics in a pair and in one- and two-dimensional arrays. We showed that various synchronized states and traveling wave patterns arise depending on the pattern of the driving force, distance from the substrate, orbital shape and inclination, and flexibility of the cilia. We also numerically analyzed the collective transport phenomena due to many flagella in a bacterial carpet, and clarified the properties of collective synchronization transition due to a general class of long-range interactions by a field-theoretic method.