论文标题
在二维中跑步颗粒的长时间行为
Long time behavior of run-and-tumble particles in two dimensions
论文作者
论文摘要
我们研究了在二维中运行式粒子（RTP）的位置分布的长期渐近行为，并表明一个时间$ t $的分布可以表示为$（γt）^{ - 1} $的扰动序列，其中$γ^{ - 1} $是RTP的持久时间。我们表明，对领先顺序高斯分布的高阶校正通常满足不均匀的扩散方程，其中源项取决于先前的订单解决方案。不均匀方程的明确解需要位置力矩，我们开发出一种递归形式主义来计算相同的形式。
We study the long-time asymptotic behavior of the position distribution of a run-and-tumble particle (RTP) in two dimensions and show that the distribution at a time $t$ can be expressed as a perturbative series in $(γt)^{-1}$, where $γ^{-1}$ is the persistence time of the RTP. We show that the higher order corrections to the leading order Gaussian distribution generically satisfy an inhomogeneous diffusion equation where the source term depends on the previous order solutions. The explicit solution of the inhomogeneous equation requires the position moments, and we develop a recursive formalism to compute the same.
