Extraction of self-diffusivity in systems with nondiffusive short-time behavior

Area of Science:

• Physics
• Physical Chemistry
• Statistical Mechanics

Background:

• Many physical systems exhibit short-time nondiffusive behavior.
• Extracting self-diffusion coefficients from particle trajectories is crucial for understanding these systems.
• Accurate determination of the transition to diffusive behavior is often challenging.

Purpose of the Study:

• To develop and evaluate a method for extracting self-diffusivity from particle trajectories.
• To automatically detect the transition from nondiffusive to diffusive behavior.
• To identify the most accurate and efficient method for analyzing trajectory data and characterizing uncertainty.

Main Methods:

• A toy model simulating short-time nondiffusive behavior was used.
• Data sets of varying quality were generated through simulation.
• Weighted least-squares analysis with statistical bootstrap was employed.
• Methods for extracting the self-diffusion coefficient and its uncertainty were tested.

Main Results:

• Weighted least-squares with statistical bootstrap proved to be the most accurate and efficient analysis method.
• The proposed method effectively detects the transition to diffusive behavior.
• The study provides insights into characterizing the uncertainty of self-diffusion coefficients.

Conclusions:

• The weighted least-squares method with statistical bootstrap is recommended for analyzing trajectory data to determine self-diffusion coefficients.
• An iterative approach for designing simulations to achieve specific accuracy levels is suggested.
• This work offers a robust framework for studying self-diffusion in complex physical systems.