单粒子轨迹的定量分析：平均最大漂移法
Quantitative analysis of single particle trajectories: mean maximal excursion method
摘要：
越来越多的实验研究采用单粒子跟踪来探测复杂系统中的物理环境。在这里，我们提出并讨论了新的方法来分析的粒子轨迹的时间序列，特别是子扩散现象。我们讨论平均最大偏移的统计特性，即，测试粒子在时间t之前所覆盖的最大距离。与传统的均方位移分析方法相比，平均最大偏移分析方法在确定反常扩散指数方面有更好的效果。我们还表明，经常矩与矩的平均最大偏移方法的组合提供了额外的标准，以确定确切的物理性质的基础随机subdiffusion过程。我们把测试的方法，使用实验数据以及模拟的时间序列从不同的模型为正常和异常的动力学，如扩散分形，连续时间随机游走，和分数布朗运动。
英文摘要：
An increasing number of experimental studies employ single particle tracking to probe the physical environment in complex systems. We here propose and discuss new methods to analyze the time series of the particle traces, in particular, for subdiffusion phenomena. We discuss the statistical properties of mean maximal excursions, i.e., the maximal distance covered by a test particle up to time t. Compared to traditional methods focusing on the mean squared displacement we show that the mean maximal excursion analysis performs better in the determination of the anomalous diffusion exponent. We also demonstrate that combination of regular moments with moments of the mean maximal excursion method provides additional criteria to determine the exact physical nature of the underlying stochastic subdiffusion processes. We put the methods to test using experimental data as well as simulated time series from different models for normal and anomalous dynamics, such as diffusion on fractals, continuous time random walks, and fractional Brownian motion.
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