标题： 活性布朗粒子在中等密度下的自扩散动力学 显示英文标题

标题： Self-diffusive dynamics of active Brownian particles at moderate densities

摘要： 活性布朗粒子（ABP）模型已成为自推进粒子的原型。 ABP 以恒定速度$V$沿着一个方向移动，该方向通过旋转扩散缓慢变化，由系数$\Dr$表征。 持续运动加上随机重定向在长时间尺度上产生随机行走，对于二维空间中的孤立 ABP，其扩散系数由$D_0=V^2/(2\Dr)$给出。 在这里，我们使用最近提出的 ABP 动力学理论来研究密度对自扩散动力学的影响，在该理论中，持续碰撞被描述为在粒子上产生净位移。 在中间时间尺度上，许多碰撞已经发生，但示踪粒子的方向尚未改变，此时可以求解示踪粒子的洛伦兹动力学方程。 结果表明，由于碰撞，示踪粒子遵循一种有效的随机动力学，其特征是有效减少的流速$V_\text{eff}$和各向异性扩散，其系数显式地依赖于密度。 基于这一结果，提出了一种有效的理论和数值方法，其中浴中的粒子遵循基于局部密度的平均场相互作用的随机动力学。 最后，在大于$\Dr^{-1}$的时间尺度上，研究小波矢量处的范霍夫函数，结果表明示踪粒子表现出有效的扩散运动，其扩散系数为$D=V_\text{eff}^2/(2\Dr)$。 $V_\text{eff}$与密度的依赖关系表明，该动力学理论仅适用于面积分数小于 0.42 的情况，超过此限制会出现不合理的结果。 显示英文摘要

摘要： The Active Brownian Particle (ABP) model has become a prototype of self-propelled particles. ABPs move persistently at a constant speed $V$ along a direction that changes slowly by rotational diffusion, characterized by a coefficient $\Dr$. Persistent motion plus random reorientations generate a random walk at long times with a diffusion coefficient that, for isolated ABPs in two dimensions, is given by $D_0=V^2/(2\Dr)$. Here we study the density effects on the self-diffusive dynamics using a recently proposed kinetic theory for ABPs, in which persistent collisions are described as producing a net displacement on the particles. On intermediate timescales, where many collisions have taken place but the director of the tracer particle has not yet changed, it is possible to solve the Lorentz kinetic equation for a tracer particle. It turns out that, as a result of collisions, the tracer follows an effective stochastic dynamics, characterized by an effective reduced streaming velocity $V_\text{eff}$ and anisotropic diffusion, with coefficients explicitly depending on the density. Based on this result, an effective theoretical and numerical approach is proposed in which the particles in a bath follow stochastic dynamics with mean-field interactions based on the local density. Finally, on time scales larger than $\Dr^{-1}$, studying the van Hove function at small wavevectors, it is shown that the tracer particle presents an effective diffusive motion with a coefficient $D=V_\text{eff}^2/(2\Dr)$. The dependence of $V_\text{eff}$ on the density indicates that the kinetic theory is limited to area fractions smaller than 0.42, and beyond this limit unphysical results appear.