Hyperballistic Superdiffusion and Explosive Solutions to the Non-Linear Diffusion Equation

By means of a particle model that includes interactions only via the local particle concentration, we show that hyperballistic diffusion may result. This is done by findng the exact solution of the corresponding non-linear diffusion equation, as well as by particle simulations. The connection betwee...

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Bibliographic Details
Published in:Frontiers in Physics
Main Authors: Eirik G. Flekkøy, Alex Hansen, Beatrice Baldelli
Format: Article
Language:English
Published: Frontiers Media S.A. 2021-03-01
Subjects:
anomalous diffusion
concentration-dependent diffusivity
non-linear diffusion equation
brownian motion (wiener process)
random walks
Online Access:https://www.frontiersin.org/articles/10.3389/fphy.2021.640560/full
Description
Summary:By means of a particle model that includes interactions only via the local particle concentration, we show that hyperballistic diffusion may result. This is done by findng the exact solution of the corresponding non-linear diffusion equation, as well as by particle simulations. The connection between these levels of description is provided by the Fokker-Planck equation describing the particle dynamics. PACS numbers:
ISSN:2296-424X

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