Directed Percolation Process Advected by Compressible Velocity Field

TL;DR

This paper investigates the directed percolation process near non-equilibrium phase transitions within a compressible environment modeled by the Kraichnan framework, using field theoretic and renormalization techniques.

Contribution

It introduces a field theoretic analysis of directed percolation in a compressible velocity field, extending previous incompressible models with one-loop renormalization results.

Findings

Differences between compressible and incompressible percolation models identified

Renormalization constants calculated to one-loop order

Model provides a basis for understanding phase transitions in compressible media

Abstract

The directed percolation process in the vicinity of non-equilibrium phase transition is studied by the means of field theoretic methods. It will be assumed that percolation takes place in a compressible environment, which will be generated by the modified Kraichnan model. We will discuss differ- ences with the incompressible case and describe how the given model can be renormalized. The renormalization constants will be given to the one-loop order.