Hyperballistic superdiffusion and explosive solutions to the non-linear diffusion equation

TL;DR

This paper demonstrates hyperballistic superdiffusion through exact solutions and particle simulations of a non-linear diffusion equation, revealing new insights into diffusion dynamics driven by local concentration interactions.

Contribution

It provides the first exact solution of a non-linear diffusion equation exhibiting hyperballistic superdiffusion, linking particle models with continuum descriptions.

Findings

Hyperballistic diffusion observed in particle simulations.

Exact analytical solutions for the non-linear diffusion equation.

Connection established between particle dynamics and continuum models.

Abstract

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.