Quantitative analysis of single particle trajectories: mean maximal excursion method

TL;DR

This paper introduces the mean maximal excursion method for analyzing single particle trajectories, demonstrating its advantages over traditional mean squared displacement analysis in characterizing subdiffusion phenomena.

Contribution

The authors propose and validate a new statistical method based on mean maximal excursions for better identification of anomalous diffusion exponents and underlying stochastic processes.

Findings

Mean maximal excursion analysis outperforms traditional methods in determining anomalous diffusion exponents.

Combining moments of regular and maximal excursions provides insights into the physical nature of subdiffusion.

The method is validated on experimental and simulated data from various models of anomalous diffusion.

Abstract

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.