Derivation of non-polynomial fractional diffusions from the generalized exclusion with a slow barrier

TL;DR

This paper derives a generalized fractional porous medium equation from a microscopic particle system with long-range interactions and a slow barrier, extending classical models to include non-polynomial functions of density.

Contribution

It introduces a novel derivation of a fractional diffusion equation with a non-polynomial density function from microscopic dynamics with long-range interactions and barriers.

Findings

Derived a generalized fractional porous medium equation in the hydrodynamic limit.

Extended fractional diffusion models to include non-polynomial functions of density.

Analyzed the effects of a slow barrier on mass flow and diffusion behavior.

Abstract

In this article we derive in the hydrodynamic limit a generalized fractional porous medium equation, in the sense that the regional fractional Laplacian is applied to a function of the density given in terms of a power series, instead of a polynomial. The hydrodynamic limit is obtained considering a microscopic dynamics of random particles with long range interactions, but the jump rate highly depends on the occupancy near the sites where the interactions take place. This system is also studied in the presence of a "slow barrier" that hinders the flow of mass between two half-spaces.