Different behaviors of diffusing diffusivity dynamics based on three different definitions of fractional Brownian...

Area of Science:

• Statistical Mechanics
• Soft Matter Physics
• Biophysics

Background:

• Diffusing diffusivity (DD) models random fluctuations in diffusion coefficients.
• Fractional Brownian motion (FBM) is used to model anomalous diffusion.
• Understanding DD within FBM frameworks is crucial for complex systems.

Purpose of the Study:

• To investigate the effects of DD on three distinct FBM models.
• To analyze statistical properties like MSD, MSI, ACVF, and PDF.
• To compare the behavior of Langevin equation (LE-FBM-DD), Weyl (MN-FBM-DD), and Riemann-Liouville (RL-FBM-DD) integral representations.

Main Methods:

• Formulating three FBM-generalized DD models: LE-FBM-DD, MN-FBM-DD, and RL-FBM-DD.
• Examining statistical properties: mean-squared displacement (MSD), mean-squared increment (MSI), autocovariance function (ACVF), and probability density function (PDF).
• Analyzing the impact of correlations in random diffusivity on model behavior.

Main Results:

• MN-FBM-DD and LE-FBM-DD models exhibit distinct MSD and MSI, contrary to prior assumptions.
• LE-FBM-DD shows crossover behavior due to diffusivity correlations.
• MSI and ACVF are nonstationary in RL-FBM-DD but stationary in MN-FBM-DD and LE-FBM-DD.
• All models display a transition from non-Gaussian to Gaussian PDFs over time.

Conclusions:

• The choice of FBM framework significantly impacts DD model behavior.
• Correlations in diffusivity introduce complex dynamics not captured by simpler models.
• Findings guide the selection of appropriate FBM-generalized models for heterogeneous bio- and soft-matter systems.