论文标题
具有分数旋转布朗运动的活性颗粒
Active particles with fractional rotational Brownian motion
论文作者
论文摘要
我们研究了活性粒子的二维超级阻尼运动，其定向动力学会受到分数布朗噪声的影响，而其位置则受自我刺激和布朗尼波动的影响。从具有恒定游泳速度的Langevin类模型的活动运动模型，我们得出了相应的Fokker-Planck方程，从中我们可以从中找到粒子方向的角度概率密度，以表征分数旋转噪声的Hurst指数的任意值。我们为速度自相关函数和平移于点的位移提供了分析表达式，这表明主动扩散有效地出现在Hurst指数的所有值的长期限制中。还得出了活动扩散系数和有效旋转扩散时间的相应表达式。将我们的结果与由分数布朗噪声驱动的旋转运动的活动颗粒的数值模拟进行了比较，我们发现了极好的一致性。
We study the two-dimensional overdamped motion of an active particle whose orientational dynamics is subject to fractional Brownian noise, whereas its position is affected by self-propulsion and Brownian fluctuations. From a Langevin-like model of active motion with constant swimming speed, we derive the corresponding Fokker-Planck equation, from which we find the angular probability density of the particle orientation for arbitrary values of the Hurst exponent that characterizes the fractional rotational noise. We provide analytical expressions for the velocity autocorrelation function and the translational mean-squared displacement, which show that active diffusion effectively emerges in the long-time limit for all values of the Hurst exponent. The corresponding expressions for the active diffusion coefficient and the effective rotational diffusion time are also derived. Our results are compared with numerical simulations of active particles with rotational motion driven by fractional Brownian noise, with which we find an excellent agreement.
