论文标题
自由活性粒子长期位置分布的通用框架
Universal framework for the long-time position distribution of free active particles
论文作者
论文摘要
主动粒子以随机发展的速度自行自行，产生持续运动，导致位置分布的非扩散行为。然而，有效的扩散行为有时比持续时间大得多。在这里，我们开发了一个一般框架，用于研究一类活动粒子动力学的长时间行为，并使用跑步粒子的示例，活跃的Ornstein-Uhlenbeck粒子，活动性的Brownian粒子和方向逆转活跃的Brownian粒子进行说明。将持久时间与观察时间的比率视为小参数，我们表明位置分布通常满足领先顺序的扩散方程。我们进一步表明，在每个顺序上，子领先的贡献都满足不均匀的扩散方程，其中源项取决于先前的顺序解决方案。我们明确地为高斯位置分布获得了一些子领先贡献。作为我们框架的一部分，我们还规定了一种递归找到位置矩的方法，并明确计算每个模型的前几个。
Active particles self-propel themselves with a stochastically evolving velocity, generating a persistent motion leading to a non-diffusive behavior of the position distribution. Nevertheless, an effective diffusive behavior emerges at times much larger than the persistence time. Here we develop a general framework for studying the long-time behaviour for a class of active particle dynamics and illustrate it using the examples of run-and-tumble particle, active Ornstein-Uhlenbeck particle, active Brownian particle, and direction reversing active Brownian particle. Treating the ratio of the persistence-time to the observation time as the small parameter, we show that the position distribution generically satisfies the diffusion equation at the leading order. We further show that the sub-leading contributions, at each order, satisfies an inhomogeneous diffusion equation, where the source term depends on the previous order solutions. We explicitly obtain a few sub-leading contributions to the Gaussian position distribution. As a part of our framework, we also prescribe a way to find the position moments recursively and compute the first few explicitly for each model.
