Multiscale Modeling &Simulation, Volume 18, Issue 1, Page 1-20, January 2020.
The study of active matter consisting of many self-propelled (active) swimmers in an imposed flow is important for many applications. Self-propelled swimmers may represent both living and artificial ones such as bacteria and chemically driven bimetallic nanoparticles. In this work we focus on a kinetic description of active matter represented by self-propelled rods swimming in a viscous fluid confined by a wall. It is well known that walls may significantly affect the trajectories of active rods in contrast to unbounded or periodic containers. Among such effects are accumulation at walls and upstream motion (also known as negative rheotaxis). Our first main result is the rigorous derivation of boundary conditions for the active rods' probability distribution function in the limit of vanishing inertia. Finding such a limit is important because (i) in many examples of active matter inertia is negligible, since swimming occurs in the low Reynolds number regime, and (ii) this limit allows us to reduce the dimension---and so computational complexity---of the kinetic description. For the resulting model, we derive the system in the limit of vanishing translational diffusion which is also typically negligible for active particles. This system allows for tracking separately active particles accumulated at walls and active particles swimming in the bulk of the fluid.

中文翻译：

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有限域中主动杆动力学的动力学方法

多尺度建模与仿真，第18卷，第1期，第1-20页，2020年1月。
对强加气流中由许多自走式（主动）游泳者组成的活动物质的研究对于许多应用而言都很重要。自走游泳者可能代表活的和人工的游泳者，例如细菌和化学驱动的双金属纳米粒子。在这项工作中，我们专注于以自驱动棒在由壁限制的粘性流体中游动为代表的活性物质的动力学描述。众所周知，与无边界的或周期性的容器相比，壁可显着影响主动杆的轨迹。在这些影响中，有在壁处的积累和上游运动（也称为负流变）。我们的第一个主要结果是在消失的惯性极限内严格推导了主动杆的概率分布函数的边界条件。找到这样的限制很重要，因为（i）在许多活动物质惯性的例子中，由于游动发生在低雷诺数体系中，因此在许多例子中微不足道，并且（ii）此限制允许我们减小尺寸-从而降低了计算复杂度- -动力学的描述。对于生成的模型，我们在消失的平移扩散极限内派生了该系统，对于活性颗粒而言，平移扩散通常也可以忽略不计。该系统允许分别跟踪聚集在壁上的活性颗粒和游动在大部分流体中的活性颗粒。我们在消失的平移扩散极限范围内得出了该系统，对于活性颗粒而言，平移扩散通常也可以忽略不计。该系统允许分别跟踪聚集在壁上的活性颗粒和游动在大部分流体中的活性颗粒。我们在消失的平移扩散极限范围内得出了该系统，对于活性颗粒而言，平移扩散通常也可以忽略不计。该系统允许分别跟踪聚集在壁上的活性颗粒和游动在大部分流体中的活性颗粒。