Diffusion Properties of Small-Scale Fractional Transport Models

Area of Science:

• Physics
• Applied Mathematics
• Complex Systems

Background:

• Stochastic transport phenomena are crucial in various scientific fields.
• Understanding particle dynamics in complex, turbulent-like velocity fields remains a challenge.
• Fractional Gaussian Noises (FGN) offer a way to model persistent random processes.

Purpose of the Study:

• To numerically investigate stochastic transport in velocity fields driven by FGN.
• To develop a unified model for comparing different space-time structures in stochastic transport.
• To analyze the influence of FGN persistence on particle diffusion.

Main Methods:

• Numerical investigation of stochastic transport.
• Modeling velocity fields using superposition of divergence-free vector fields activated by FGN.
• Utilizing an Ornstein-Uhlenbeck approximation and taking the white noise limit for model comparison.
• Analyzing Fourier components to understand the role of spatial structures and FGN memory.

Main Results:

• A model was established to compare diverse space-time structures on equal footing by normalizing kinetic energy.
• A key finding is that mixing spatial structures combined with persistent FGN lead to classical Brownian diffusion.
• The diffusion coefficient is determined, and the memory of FGN is shown to be lost within the velocity field's spatial complexity.

Conclusions:

• The study provides a framework for analyzing stochastic transport in complex velocity fields.
• It demonstrates that spatial complexity can effectively homogenize persistent temporal correlations, leading to simple diffusion.
• This research contributes to understanding anomalous diffusion and the emergence of Brownian motion from complex dynamics.