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Subdiffusion in random compressible flows.

Konstantin Chukbar¹, Vasily Zaburdaev

¹RRC Kurchatov Institute, Pl.Kurchatova, 1, 123182 Moscow, Russia.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|August 11, 2005

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We analytically solve particle diffusion in random velocity fields, revealing conditions for subdiffusive transport. This work provides a rigorous method for understanding random compressible flows and their associated scaling estimates.

Area of Science:

Physics
Statistical Mechanics
Fluid Dynamics

Background:

Previous studies on admixture particle diffusion in random velocity fields were limited to scaling estimates.
Understanding random compressible flows is crucial for various physical phenomena.

Purpose of the Study:

To develop a general analytical approach for studying particle diffusion in a 1D random potential velocity field.
To derive the macroscopic transport equation and identify conditions for subdiffusive transport.
To analyze the Green's function and its properties under specific potential distributions.

Main Methods:

Analytical solution development for particle diffusion.
Derivation of the macroscopic transport equation.
Fourier-Laplace transform of the Green's function analysis.

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Main Results:

A general analytical approach was successfully developed.
The macroscopic transport equation was derived.
Conditions for subdiffusive transport were rigorously established.
The Green's function was found to satisfy a subdiffusive equation with a fractional time derivative for certain potential distributions.

Conclusions:

The study provides a rigorous analytical framework for understanding admixture particle diffusion in random velocity fields.
It confirms and extends previous scaling estimates for random compressible flows.
The findings highlight the potential for subdiffusive behavior governed by fractional calculus in such systems.