Analysis of diffusion trajectories of anisotropic objects

TL;DR

This paper provides an exact analytical method to analyze diffusion trajectories of anisotropic objects, demonstrating that the gyration tensor-based measure offers more efficient estimation of diffusion parameters than traditional cumulant methods.

Contribution

It introduces a novel gyration tensor-based measure for estimating diffusion parameters of anisotropic objects, with proven efficiency and statistical convergence.

Findings

Gyration tensor measure yields more efficient diffusion constant estimates.

Analytic expression for the gyration measure derived exactly.

Comparison shows improved efficiency over fourth cumulant analysis.

Abstract

We theoretically analyze diffusion trajectories of an anisotropic object moving on a two dimensional space in the absence of an external field. In determining diffusion parameters associated with the shape anisotropy, we devise a measure based on the gyration tensor, and obtain its analytic expression exactly. Its efficiency and statistical convergence are examined in comparison with the fourth cumulant of particle displacement. We find that the estimation of diffusion constants based on the gyration measure is more efficient than analysis adopting the fourth cumulant.