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Updated: Jul 13, 2026

The Diffusion of Passive Tracers in Laminar Shear Flow
Published on: May 1, 2018
Non-Markovian Lévy diffusion in nonhomogeneous media
1Institute of Nuclear Physics, Polish Academy of Sciences, Kraków, Poland.
Abstract:
We study the diffusion equation with a position-dependent, power-law diffusion coefficient. The equation possesses the Riesz-Weyl fractional operator and includes a memory kernel. It is solved in the diffusion limit of small wave numbers. Two kernels are considered in detail: the exponential kernel, for which the problem resolves itself to the telegrapher's equation, and the power-law one. The resulting distributions have the form of the Lévy process for any kernel. The renormalized fractional moment is introduced to compare different cases with respect to the diffusion properties of the system.
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