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Updated: Jun 5, 2026

The Diffusion of Passive Tracers in Laminar Shear Flow

The Diffusion of Passive Tracers in Laminar Shear Flow

Published on: May 1, 2018

Fractional Fokker-Planck equations for subdiffusion with space- and time-dependent forces.

B I Henry¹, T A M Langlands, P Straka

¹Department of Applied Mathematics, University of New South Wales, Sydney NSW, Australia. B.Henry@unsw.edu.au

Physical Review Letters

|January 15, 2011

Summary

We derived a fractional Fokker-Planck equation for subdiffusion, applicable to complex systems with time-dependent forces. This equation models particle movement influenced by Boltzmann weights and continuous time random walks.

Related Experiment Videos

Last Updated: Jun 5, 2026

The Diffusion of Passive Tracers in Laminar Shear Flow

The Diffusion of Passive Tracers in Laminar Shear Flow

Published on: May 1, 2018

Area of Science:

Physics
Statistical Mechanics
Non-equilibrium Systems

Background:

Subdiffusion is a key transport mechanism in complex systems.
Continuous time random walks (CTRWs) model anomalous diffusion.
Force fields significantly influence particle dynamics.

Purpose of the Study:

Derive a fractional Fokker-Planck equation for subdiffusion.
Incorporate space- and time-dependent force fields.
Analyze systems biased by Boltzmann weights.

Main Methods:

Utilizing power law waiting time continuous time random walks.
Deriving the governing equation from a generalized master equation.
Establishing equivalence to a subordinated stochastic Langevin equation.

Main Results:

A fractional Fokker-Planck equation for subdiffusion was successfully derived.
The equation accounts for general space- and time-dependent force fields.
The derived equation is equivalent to a subordinated stochastic Langevin equation.

Conclusions:

The derived fractional Fokker-Planck equation provides a powerful tool for modeling subdiffusion.
This framework is applicable to diverse physical systems with complex driving forces.
The equivalence to a Langevin equation offers insights into the underlying stochastic processes.