论文标题
椭圆形粒子在二维的布朗运动的持久性
Persistence in Brownian motion of an ellipsoidal particle in two dimensions
论文作者
论文摘要
我们研究了具有二维形状不对称的布朗粒子位置的持久性概率$ p（t）$。持久性概率定义为随机变量在给定时间间隔中没有更改其符号的概率。我们明确考虑两种情况 - 自由粒子的扩散和谐波捕获的粒子的扩散。后者在使用陷阱和跟踪技术来测量位移的实验中特别重要。我们为各种情况提供了$ p（t）$的分析表达式，并表明在没有形状不对称的情况下，结果将减少到各向同性粒子的情况下。 $ p（t）$的分析表达式与对基础过度阻尼动力学的数值模拟进行了进一步验证。我们还说明，$ p（t）$可以是确定胶体形状不对称的措施，并且可以从测得的持续性概率中估算转移和旋转扩散率。该方法的优点是它不需要跟踪粒子的方向。
We investigate the persistence probability $p(t)$ of the position of a Brownian particle with shape asymmetry in two dimensions. The persistence probability is defined as the probability that a stochastic variable has not changed it's sign in the given time interval. We explicitly consider two cases -- diffusion of a free particle and that of harmonically trapped particle. The later is particularly relevant in experiments which uses trapping and tracking techniques to measure the displacements. We provide analytical expressions of $p(t)$ for both the scenarios and show that in the absence of the shape asymmetry the results reduce to the case of an isotropic particle. The analytical expressions of $p(t)$ are further validated against numerical simulation of the underlying overdamped dynamics. We also illustrate that $p(t)$ can be a measure to determine the shape asymmetry of a colloid and the translational and rotational diffusivities can be estimated from the measured persistence probability. The advantage of this method is that it does not require the tracking of the orientation of the particle.
