舞蹈团藻的稳定性
Stability of dancing Volvox
摘要：
团藻属的双鞭毛藻细胞形成球形菌落，通过数千个鞭毛的协调跳动，在静止的流体中垂直向上推动自己，这也导致菌落围绕其垂直轴旋转。当它们在有限深度的腔室中游泳时，Drescher等人观察到成对（或更多）的团藻菌落。102，168101（2009）]以在它们接近刚性水平边界时表现出流体动力学束缚态。当边界在上方时，蜂群相互吸引，以“华尔兹”的方式绕着彼此旋转;当边界在下方时，它们会进行更复杂的“小步舞曲”运动。这些舞蹈在本文中模拟，使用一种新的“球形蠕动”模型的殖民地，而不是一个时间无关，但$θ$依赖的切向速度施加在球面上（半径$a$ ; $θ$是极角），将与时间无关的且均匀的切向剪切应力施加到半径为$(1+ε)a, ε\ll 1$的球体上的流体，其中$εa$表示鞭毛的长度。流体必须满足半径为$a$的球体上的无滑移条件。除了剪切应力，运动还取决于两个描述重力对菌落影响的无量纲参数：$F_g$，与非游泳菌落的沉降速度与其游泳速度之比成比例，以及$G_{bh}$，代表菌落底部重的事实。
英文摘要：
Biflagellate algal cells of the genus Volvox form spherical colonies that propel themselves, vertically upwards in still fluid, by the coordinated beating of thousands of flagella, that also cause the colonies to rotate about their vertical axes. When they are swimming in a chamber of finite depth, pairs (or more) of Volvox carteri colonies were observed by Drescher et al. [Phys. Rev. Lett. 102, 168101 (2009)] to exhibit hydrodynamic bound states when they are close to a rigid horizontal boundary. When the boundary is above, the colonies are attracted to each other and orbit around each other in a `waltz'; when the boundary is below they perform more complex `minuet' motions. These dances are simulated in the present paper, using a novel `spherical squirmer' model of a colony in which, instead of a time-independent but $θ$-dependent tangential velocity being imposed on the spherical surface (radius $a$; $θ$ is the polar angle), a time-independent and uniform tangential shear stress is applied to the fluid on a sphere of radius $(1+ε)a, ε\ll 1$, where $εa$ represents the length of the flagella. The fluid must satisfy the no-slip condition on the sphere at radius $a$. In addition to the shear stress, the motions depend on two dimensionless parameters that describe the effect of gravity on a colony: $F_g$, proportional to the ratio of the sedimentation speed of a non-swimming colony to its swimming speed, and $G_{bh}$, that represents the fact that colonies are bottom-heavy...
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