Log it: How to fit an active Brownian particle's mean squared displacement with improved parameter estimation

Abstract

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 (OLS) regression will obtain biased estimates and unreliable confidence intervals. Here, we propose 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 (MLSD). 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.

arXiv comment20 pages, 5 figures

References in corpus (14)

• Active Particles in Complex and Crowded Environments
• Self-motile colloidal particles: from directed propulsion to random walk
• Circular motion of asymmetric self-propelling particles
• Topographical pathways guide chemical microswimmers
• Brownian motion of a self-propelled particle
• Dynamics of a Brownian circle swimmer
• Inertial effects of self-propelled particles: from active Brownian to active Langevin motion
• Non-Gaussian statistics for the motion of self-propelled Janus particles: experiment versus theory
• Improved estimation of anomalous diffusion exponents in single particle tracking experiments
• Slip length dependent propulsion speed of catalytic colloidal swimmers near walls
• Active Brownian motion with orientation-dependent motility: theory and experiments
• Intermediate scattering function of an anisotropic Brownian circle swimmer
• Diffusion-based height analysis reveals robust microswimmer-wall separation
• Fitting a function to time-dependent ensemble averaged data

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• Expanding Active Matter to the Third Dimension: Exploring Short and Long-Range Particle-Wall Interactions