Analysis of diffusion trajectories of anisotropic objects.

Area of Science:

• Theoretical physics
• Statistical mechanics
• Soft matter physics

Background:

• Understanding diffusion is crucial in various scientific fields.
• Anisotropic objects exhibit complex diffusion behaviors.
• Quantifying shape anisotropy's effect on diffusion is challenging.

Purpose of the Study:

• To theoretically analyze diffusion trajectories of anisotropic objects in 2D.
• To develop a novel measure for diffusion parameters linked to shape anisotropy.
• To compare the efficiency of this new measure against existing methods.

Main Methods:

• Theoretical analysis of diffusion trajectories.
• Derivation of an analytic expression for a gyration tensor-based measure.
• Comparison of statistical convergence and efficiency with the fourth cumulant of particle displacement.

Main Results:

• A novel gyration tensor-based measure for diffusion analysis was developed.
• The analytic expression for this measure was obtained exactly.
• The gyration measure demonstrated higher efficiency in estimating diffusion constants than the fourth cumulant.

Conclusions:

• The gyration tensor measure provides a more efficient method for analyzing anisotropic diffusion.
• This finding has implications for studying particle dynamics in complex systems.
• The study offers a new tool for characterizing diffusion in the absence of external fields.