封闭平面曲线中的微生物台球
Microorganism billiards in closed plane curves
摘要：
最近的实验表明，许多种类的微生物离开固体表面在一个固定的角度确定的空间相互作用和近场流体动力学。这个角度与入射角完全无关。对于封闭体中的几次碰撞，这决定了一种独特类型的台球系统，即一种出射角对于所有碰撞都是固定的反分子台球。我们分析这样一个系统，使用数值模拟的台球桌和出射角度的变化，并利用一维映射和波前动力学的理论。在适用的情况下，我们引用的结果，并比较我们的系统在文献中类似的台球系统。我们专注于从三个广泛的类的例子：椭圆，Bunimovich台球，和西奈台球。噪声出射角的影响也进行了讨论。
英文摘要：
Recent experiments have shown that many species of microorganisms leave a solid surface at a fixed angle determined by steric interactions and near-field hydrodynamics. This angle is completely independent of the incoming angle. For several collisions in a closed body this determines a unique type of billiard system, an aspecular billiard in which the outgoing angle is fixed for all collisions. We analyze such a system using numerical simulation of this billiard for varying tables and outgoing angles, and also utilize the theory of one-dimensional maps and wavefront dynamics. When applicable we cite results from and compare our system to similar billiard systems in the literature. We focus on examples from three broad classes: the ellipse, the Bunimovich billiards, and the Sinai billiards. The effect of a noisy outgoing angle is also discussed.
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