TIME-DOMAIN METHODS FOR DIFFUSIVE TRANSPORT IN SOFT MATTER.

Area of Science:

• Soft Matter Physics
• Rheology
• Statistical Mechanics

Background:

• Passive microrheology uses particle fluctuations to determine material properties.
• Existing methods often rely on frequency-domain analysis of mean-squared displacement.
• Generalized Langevin Equation (GLE) describes particle diffusion in complex media.

Purpose of the Study:

• To develop and present statistically exact, time-domain algorithms for modeling particle diffusion in viscoelastic media.
• To apply time series analysis, specifically maximum likelihood estimators via the Kalman filter, for inferring memory kernel properties directly from particle position data.
• To decouple the inference of bulk viscoelastic moduli from the analysis of particle diffusion.

Main Methods:

• Discrete formulation of the Generalized Langevin Equation (GLE) as an autoregressive stochastic process.
• Application of time series analysis (Kalman filter) to bead position data for inverse problem solving (memory kernel recovery).
• Development of statistically exact GLE algorithms for direct modeling of individual particle paths and their correlations.

Main Results:

• Demonstration of a novel time-domain approach for analyzing particle diffusion in viscoelastic media.
• Successful recovery of the memory kernel using Kalman filter applied directly to time-series position data.
• Generalization of GLE modeling to arbitrary M-mode exponential series, transforming the process into a vector Ornstein-Uhlenbeck process.

Conclusions:

• The developed time-domain methods offer an alternative and effective approach to microrheology analysis.
• Direct analysis of particle trajectories provides a robust way to infer material's viscoelastic properties.
• The framework allows for accurate modeling and analysis of complex diffusive dynamics in soft materials.