We study analytically how noninteracting weakly active particles, for which passive Brownian diffusion cannot be neglected and activity can be treated perturbatively, distribute and behave near boundaries in various geometries. In particular, we develop a perturbative approach for the model of active particles driven by an exponentially correlated random force (active Ornstein-Uhlenbeck particles). This approach involves a relatively simple expansion of the distribution in powers of the Péclet number and in terms of Hermite polynomials. We use this approach to cleanly formulate boundary conditions, which allows us to study weakly active particles in several geometries: confinement by a single wall or between two walls in 1D, confinement in a circular or wedge-shaped region in 2D, motion near a corrugated boundary, and, finally, absorption onto a sphere. We consider how quantities such as the density, pressure, and flow of the active particles change as we gradually increase the activity away from a purely passive system. These results for the limit of weak activity help us gain insight into how active particles behave in the presence of various types of boundaries.

中文翻译：

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边界对不同几何形状的非相互作用弱活性颗粒的影响

我们分析性地研究了如何忽略不相互作用的弱活性粒子（对于该粒子而言，不能忽略其被动的布朗扩散，并且可以扰动地处理活性）如何在各种几何形状的边界附近分布和表现。特别是，我们为由指数相关的随机力（活动Ornstein-Uhlenbeck粒子）驱动的活动粒子模型开发了一种摄动方法。这种方法涉及相对简单地扩展Péclet数的幂和Hermite多项式的分布。我们使用这种方法来清晰地制定边界条件，这使我们能够研究几种几何形状中的弱活性颗粒：在一维中由单壁或两壁之间的约束，二维中在圆形或楔形区域中的约束，波纹附近的运动边界，最后，吸收到一个球体上。我们考虑随着逐渐从纯被动系统中逐渐增加活动性，主动颗粒的密度，压力和流量等量如何变化。这些限制弱活性的结果有助于我们洞悉活性颗粒在各种类型的边界存在下的行为。