The Edwards-Wilkinson equation with drift and Neumann boundary conditions

TL;DR

This paper investigates the complex scaling behavior of the Edwards-Wilkinson equation with drift under Neumann boundary conditions, revealing non-trivial effects of the diffusion term despite initial dominance assumptions.

Contribution

It provides a detailed comparison of the scaling behavior of the Edwards-Wilkinson equation with drift under Neumann versus Dirichlet boundary conditions, highlighting the subtle role of the diffusion term.

Findings

Diffusion term is dangerously irrelevant in scaling analysis.

Scaling behavior differs between Neumann and Dirichlet boundary conditions.

The presence of drift complicates the scaling, requiring refined analysis.

Abstract

The well known scaling of the Edwards-Wilkinson equation is essentially determined by dimensional analysis. Once a drift term is added, more sophisticated reasoning is required, which initially suggests that the drift term dominates over the diffusion. However, the diffusion term is dangerously irrelevant and the resulting scaling in fact non-trivial. In the present article we compare the resulting scaling of the Edwards-Wilkinson equation with drift and Neumann boundary conditions to the published case with Dirichlet boundary conditions.