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Multilayered noise model for transport in complex environments.

Nikolaos K Voulgarakis¹

¹Department of Mathematics and Statistics, Washington State University, Pullman, Washington 99164, USA.

Physical Review. E

|January 20, 2024

Summary

This study introduces a novel random walks model to explain complex fluid transport dynamics, moving beyond traditional Brownian motion limitations. The approach captures transient subdiffusion and non-Gaussian profiles, offering new insights into particle movement in challenging environments.

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Area of Science:

Physics
Physical Chemistry
Complex Systems

Background:

Transport in complex fluids shows transient subdiffusive dynamics.
Non-Gaussian probability density profiles with nonmonotonic parameters are observed.
Standard Brownian motion theory fails to explain these phenomena.

Purpose of the Study:

To develop a theoretical framework for understanding anomalous transport in complex fluidic environments.
To explain transient subdiffusion and non-Gaussian behavior.
To provide analytical solutions for key transport properties.

Main Methods:

Extension of kinetic theory.
Development of a chain of hierarchically coupled random walks.
Modeling the environment as independent white noise sources.
Formulation as a system of hierarchically coupled Ornstein-Uhlenbeck equations.

Main Results:

The proposed model effectively captures transient subdiffusive dynamics.
Non-Gaussian probability density profiles are accurately reproduced.
The nonmonotonic non-Gaussian parameter is explained.
Closed analytical forms for essential transport properties were derived due to system linearity.

Conclusions:

The hierarchically coupled random walks approach provides a robust explanation for anomalous transport in complex fluids.
This framework extends beyond the limitations of classical Brownian motion.
The derived analytical solutions offer significant advantages for predicting transport behavior.