论文标题
活性布朗粒子的定向分布：分析研究
Orientational Distribution of an Active Brownian Particle: an analytical study
论文作者
论文摘要
我们使用Fokker Planck方程作为研究活性Brownian粒子（ABP）在$（D+1）$尺寸中的定向概率分布的起点。这个Fokker Planck方程在串联形式中接受了精确的解决方案，但是，由于短时间和中间时间收敛性不佳，因此可以使用笨拙的使用。该系列的截断版本是长期合理的近似值。在本文中，我们提出了一个分析封闭形式的表达式，该表达式提供了良好的近似定向概率分布，该分布是在短时间内使用鞍点方法得出的。但是，它即使在中间时间也很好。因此，我们为$ {\ it整个} $范围的时间尺度提供了简单的分析形式，用于ABP的定向概率分布。我们的预测可以根据未来的实验和模拟探测ABP的定向概率分布进行测试。
We use the Fokker Planck equation as a starting point for studying the orientational probability distribution of an Active Brownian Particle (ABP) in $(d+1)$ dimensions. This Fokker Planck equation admits an exact solution in series form which is, however, unwieldly to use because of poor convergence for short and intermediate times. A truncated version of this series is a reasonable approximation for long times. In this paper, we present an analytical closed form expression, which gives a good approximate orientational probability distribution, which is derived using saddle point methods for short times. However, it works well even for intermediate times. Thus, we have simple analytical forms for the ${\it entire}$ range of time scales for the orientational probability distribution of an ABP. Our predictions can be tested against future experiments and simulations probing orientational probability distribution of an ABP.
