边界对不同几何非相互作用弱活性粒子的影响
On the effect of boundaries on noninteracting weakly active particles in different geometries
摘要：
我们研究分析如何非相互作用的弱活性粒子，被动布朗扩散不能被忽略，活动可以被微扰处理，分布和行为在各种几何形状的边界附近。特别是，我们开发了一种微扰方法的模型驱动的指数相关的随机力（主动Ornstein-Uhlenbeck粒子）的活性粒子。这种方法涉及一个相对简单的扩展的权力的分布的佩克莱数和厄米多项式。我们使用这种方法来干净地制定边界条件，这使我们能够研究弱活性粒子在几个几何形状：限制由一个单一的墙壁或两个墙壁之间的一维，限制在一个圆形或楔形区域的二维，运动附近的波纹边界，并最终吸收到一个球体。我们考虑的数量，如密度，压力和流动的活性粒子的变化，我们逐渐增加的活动远离一个纯粹的被动系统。这些弱活动极限的结果有助于我们深入了解在各种类型的边界存在下活动粒子的行为。
英文摘要：
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.
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