标题： 趋化带的精确模型：从福克-普朗克方程到带结构和流体流动 显示英文标题

标题： Exact model of aerotactic band: From Fokker-Planck equation to band structure and fluid flow

摘要： 多种细菌种类自发地在趋气带中组装，在气-水界面固定距离处局部积累。 尽管这一现象早已为人所知，但其建模迄今为止仅限于介观、一维或数值描述。 我们使用福克-普朗克方程的精确解，在微观尺度上研究带状特性。 首先，我们表明氧气消耗与翻转调制之间的相互作用由一个将氧气浓度与趋气响应相关联的三阶非线性微分方程控制。 对于两种模型趋气行为，我们给出了解析解并讨论了由此产生的带状结构。 其次，我们研究了在磁场中趋磁细菌的趋气带如何诱导自发流体流动，如实验中观察到的[Marmol等人，arXiv 2025]。 在低场极限下，我们确定了细菌分布和活性应力张量。 利用流体力学问题的格林函数，我们得到了一个既简单又与观测一致的流体流动预测。 总的来说，我们的结果提供了一个趋气带的模型系统，并为分析由趋气性驱动的自组织提供了坚实的基础。 显示英文摘要

摘要： A variety of bacterial species spontaneously assemble in aerotactic band, local accumulation at a fixed distance from the air-water interface. Although the phenomenon is long known, its modelling is so far limited to mesoscopic, one-dimensional or numerical descriptions. We investigate band properties at the microscopic scale using exact solutions to the Fokker-Planck equation. First, we show that the interplay between oxygen consumption and tumbling modulation is governed by a third-order nonlinear differential equation relating the oxygen concentration to the aerotactic response. For two model aerotactic behaviors, we present analytical solutions and discuss the resulting band structure. Second, we investigate how an aerotactic band of magnetotactic bacteria in a magnetic field induces a spontaneous fluid flow, as observed in experiments [Marmol et al, arXiv 2025]. In the low field limit, we determine the bacterial distribution and the active stress tensor. Using the Green function of the hydrodynamic problem, we obtain a prediction for the fluid flow that is both simple and consistent with observations. Altogether, our results provide a model system of aerotactic band and solid ground to analyze aerotaxis-driven self-organization.