Fitting an active Brownian particle?s mean-squared displacement with improved parameter estimation
Fitting an active Brownian particle?s mean-squared displacement with improved parameter estimation
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DOI：
10.1103/physreve.106.l052602
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发表时间：
2022-11-22
影响因子：
2.4
通讯作者：
Isa, Lucio
中科院分区：
文献类型：
--
作者：
Bailey, Maximilian R.;Sprenger, Alexander R.;Isa, Lucio
活性布朗粒子（ABP）模型被广泛用于描述诸如Janus微泳者等活性物质系统的动力学行为。特别是，ABP的均方位移（MSD）的解析表达式是有用的，因为它提供了一种手段来描述一个自推进的，球形布朗粒子的基本物理。然而，MSD方程的截断或“短时”形式通常是拟合的，这可能导致参数估计中的重大问题。此外，异方差性和ABP的MSD的统计依赖性观察导致标准普通最小二乘回归导致有偏估计和不可靠的置信区间的情况。相反，我们建议在这里恢复到总是拟合ABP的MSD在短时间尺度的完整表达，使用自举构建拟合参数的置信区间。此外，在不同的拟合策略之间的比较，我们建议提取的ABP的物理参数，使用其平均对数平方位移。这些步骤提高了ABP的物理特性的估计，并提供更可靠的置信区间，这是至关重要的，在不断增长的兴趣的背景下，在相互作用的microswimmer与限制边界和对他们的运动的影响。
The active Brownian particle (ABP) model is widely used to describe the dynamics of active matter systems, such as Janus microswimmers. In particular, the analytical expression for an ABP's mean-squared displacement (MSD) is useful as it provides a means to describe the essential physics of a self-propelled, spherical Brownian particle. However, the truncated or "short-time" form of the MSD equation is typically fitted, which can lead to significant problems in parameter estimation. Furthermore, heteroscedasticity and the often statistically dependent observations of an ABP's MSD lead to a situation where standard ordinary least-squares regression leads to biased estimates and unreliable confidence intervals. Instead, we propose here to revert to always fitting the full expression of an ABP's MSD at short timescales, using bootstrapping to construct confidence intervals of the fitted parameters. Additionally, after comparison between different fitting strategies, we propose to extract the physical parameters of an ABP using its mean logarithmic squared displacement. These steps improve the estimation of an ABP's physical properties and provide more reliable confidence intervals, which are critical in the context of a growing interest in the interactions of microswimmers with confining boundaries and the influence on their motion.