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Multilayered noise model for transport in complex environments
1Department of Mathematics and Statistics, Washington State University, Pullman, Washington 99164, USA.
Abstract:
Transport in complex fluidic environments often exhibits transient subdiffusive dynamics accompanied by non-Gaussian probability density profiles featuring a nonmonotonic non-Gaussian parameter. Such properties cannot be adequately explained by the original theory of Brownian motion. Based on an extension of kinetic theory, this study introduces a chain of hierarchically coupled random walks approach that effectively captures all these intriguing characteristics. If the environment consists of a series of independent white noise sources, then the problem can be expressed as a system of hierarchically coupled Ornstein-Uhlenbech equations. Due to the linearity of the system, the most essential transport properties have a closed analytical form.
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In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....

