微生物台球
Microorganism Billiards
摘要：
最近的实验和数值模拟表明，某些类型的微生物以临界角从平坦表面“反射”，而与入射角无关。反射的性质可以是主动的（细胞和鞭毛与表面接触）或被动的（流体动力学）相互作用。我们利用规则多边形内的经验反射定律探索了物体的台球式运动，并表明动力学可以稳定在稳定的周期轨道上，也可以是混乱的，具体取决于游泳者的出发角和域几何形状。动态往往被发现是强大的弱随机波动的引入。游泳者轨迹的李雅普诺夫指数可以是正的或负的，可以具有极值，并且可以具有取决于多边形的度的不连续性。提出了一种被动分选装置，其将不同离去角度的游泳者捕获到单独的箱中。我们还研究了在方形障碍物的图案化环境中游泳的微生物的外部问题，其中的离去角决定了捕获或扩散轨迹的可能性。
英文摘要：
Recent experiments and numerical simulations have shown that certain types of microorganisms "reflect" off of a flat surface at a critical angle of departure, independent of the angle of incidence. The nature of the reflection may be active (cell and flagellar contact with the surface) or passive (hydrodynamic) interactions. We explore the billiard-like motion of a body with this empirical reflection law inside a regular polygon and show that the dynamics can settle on a stable periodic orbit or can be chaotic, depending on the swimmer's departure angle and the domain geometry. The dynamics are often found to be robust to the introduction of weak random fluctuations. The Lyapunov exponent of swimmer trajectories can be positive or negative, can have extremal values, and can have discontinuities depending on the degree of the polygon. A passive sorting device is proposed that traps swimmers of different departure angles into separate bins. We also study the external problem of a microorganism swimming in a patterned environment of square obstacles, where the departure angle dictates the possibility of trapping or diffusive trajectories.
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