Defect formation in the Swift-Hohenberg equation

TL;DR

This paper investigates defect formation in the two-dimensional Swift-Hohenberg model during finite-time quenches, applying the Kibble-Zurek mechanism and analyzing the roles of local pattern variations and defect types.

Contribution

It combines numerical and analytical methods to connect defect density with the quench process, considering local pattern effects and defect types in the Swift-Hohenberg model.

Findings

Kibble-Zurek mechanism applies to defect density during quenches

Local pattern variations influence defect formation

Both point-like and extended defects are significant

Abstract

We study numerically and analytically the dynamics of defect formation during a finite-time quench of the two dimensional Swift-Hohenberg (SH) model of Rayleigh-Benard convection. We find that the Kibble-Zurek picture of defect formation can be applied to describe the density of defects produced during the quench. Our study reveals the relevance of two factors: the effect of local variations of the striped patterns within defect-free domains and the presence of both point-like and extended defects. Taking into account these two aspects we are able to identify the characteristic length scale selected during the quench and to relate it to the density of defects. We discuss possible consequences of our study for the analysis of the coarsening process of the SH model.