论文标题
跳舞的稳定性Volvox
Stability of dancing Volvox
论文作者
论文摘要
Volvox属的双晶酸盐藻类细胞形成球形菌落，它们通过数以千计的鞭毛的协调跳动在静态流体中垂直向上向上，这也导致菌落围绕其垂直轴旋转。当他们在有限深度的腔室中游泳时，Drescher等人观察到了volvox Carteri菌落的对（或更多）。 [物理。莱特牧师。 102，168101（2009）]在接近刚性水平边界时表现出流体动力结合状态。当边界上方时，殖民地将彼此吸引，并在“华尔兹”中互相绕；当边界低于下方时，它们执行更复杂的“ minuet”运动。 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 $，其中$εa$表示鞭毛的长度。流体必须满足半径$ a $的球体上的无滑状条件。除剪切应力外，这些动作还取决于描述重力对菌落的影响的两个无量纲参数：$ f_g $，与非变速菌落与游泳速度的沉积速度和$ g_ {bh} $相称的比例成正比，这代表了殖民地的最低水平...
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...
