固定鱼群的集体定向对趋流性的影响
Collective orientation of an immobile fish school, effect on rheotaxis
摘要：
我们研究一个固定鱼群的定向顺序。从牛顿第二定律出发，我们证明了定向的惯性动力学是由一个Ornstein-Uhlenbeck过程所决定的。这个过程描述了在一个浅滩，动力学已经在文献中使用的移动鱼群相邻的鱼之间的对齐的动态。首先，在静止的流体中，我们计算全局极化（即鱼的平均方向），其作为噪声的函数迅速减小。我们表明，更快的鱼是能够重新定位自己，更学校可以负担得起的重要噪音值重新排序。第二，在溪流中，每条鱼都倾向于确定自己的方向，逆流而游：所谓的趋流性。所以即使有水流，也会导致鱼群无法移动。通过添加一个单独的趋流性的影响，鱼之间的对齐相互作用，我们表明，在嘈杂的环境中，个人趋流性增强鱼之间的对齐相互作用。
英文摘要：
We study the orientational order of an immobile fish school. Starting from the second Newton's law, we show that the inertial dynamics of orientations is ruled by an Ornstein-Uhlenbeck process. This process describes the dynamics of alignment between neighboring fish in a shoal, a dynamics already used in the literature for mobile fish schools. Firstly, in a fluid at rest, we calculate the global polarization (i.e. the mean orientation of the fish) which decreases rapidly as a function of the noise. We show that the faster a fish is able to reorient itself, the more the school can afford to reorder itself for important noise values. Secondly, in the prescence of a stream, each fish tends to orient itself and swims against the flow: the so-called rheotaxis. So even in the presence of a flow, it results in an immobile fish school. By adding an individual rheotaxis effect to alignment interaction between fish, we show that in a noisy environment, individual rheotaxis is enhanced by alignment interactions between fish.
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