论文标题
形状很重要：通道中的布朗微型威格斯
Shape matters: A Brownian microswimmer in a channel
论文作者
论文摘要
我们考虑了具有固定速度的二维微型游泳器的活性布朗粒子（ABP）模型，其游泳方向根据布朗工艺而变化。游泳者的概率密度根据在配置空间上定义的Fokker-Planck方程而演变，其结构取决于游泳者的形状，旋转中心和游泳的域。我们在配置空间的边界上执行零概率通量。我们在无限通道中的游泳器中得出了一个降低的方程，在较小的旋转扩散率的极限下，发现不变密度在很大程度上取决于游泳者的精确形状和旋转中心。我们还为平均反转时间提供了一个公式：游泳者完全逆转通道中的预期时间。使用均质化理论，我们找到了游泳者在通道中有效的纵向扩散率的表达，并表明它受平均反转时间的界定。
We consider the active Brownian particle (ABP) model for a two-dimensional microswimmer with fixed speed, whose direction of swimming changes according to a Brownian process. The probability density for the swimmer evolves according to a Fokker-Planck equation defined on the configuration space, whose structure depends on the swimmer's shape, center of rotation and domain of swimming. We enforce zero probability flux at the boundaries of configuration space. We derive a reduced equation for a swimmer in an infinite channel, in the limit of small rotational diffusivity, and find that the invariant density depends strongly on the swimmer's precise shape and center of rotation. We also give a formula for the mean reversal time: the expected time taken for a swimmer to completely reverse direction in the channel. Using homogenization theory, we find an expression for the effective longitudinal diffusivity of a swimmer in the channel, and show that it is bounded by the mean reversal time.
