A Singular Perturbation Analysis for \\Unstable Systems with Convective Nonlinearity

TL;DR

This paper applies a singular perturbation method to analyze interface dynamics in non-conserved order parameter systems with convection, revealing limitations of the method at high bias or convection strengths.

Contribution

It extends the singular perturbation analysis to systems with external bias, identifying the method's breakdown point under strong convection.

Findings

Method successfully analyzes interface dynamics at low convection.

Breaks down when bias or convection exceeds a critical threshold.

Highlights limitations of existing analytical techniques for strongly driven systems.

Abstract

We use a singular perturbation method to study the interface dynamics of a non-conserved order parameter (NCOP) system, of the reaction-diffusion type, for the case where an external bias field or convection is present. We find that this method, developed by Kawasaki, Yalabik and Gunton for the time-dependant Ginzburg-Landau equation and used successfully on other NCOP systems, breaks down for our system when the strength of bias/convection gets large enough.