Growth of Order in An Anisotropic Swift-Hohenberg Model

TL;DR

This study investigates the ordering process in a two-dimensional anisotropic Swift-Hohenberg model, revealing defect dynamics, anisotropic defect motion, and statistical properties of dislocation trajectories.

Contribution

It introduces a numerical approach to analyze dislocation dynamics in an anisotropic SH model, highlighting defect behavior and anisotropic effects.

Findings

Dislocation motion follows power-law time dependence with different amplitudes.

Defect structures are simpler than in isotropic models, with only dislocations present.

Dislocation velocity and position distributions are weakly anisotropic.

Abstract

We have studied the ordering kinetics of a two-dimensional anisotropic Swift-Hohenberg (SH) model numerically. The defect structure for this model is simpler than for the isotropic SH model. One finds only dislocations in the aligned ordering striped system. The motion of these point defects is strongly influenced by the anisotropic nature of the system. We developed accurate numerical methods for following the trajectories of dislocations. This allows us to carry out a detailed statistical analysis of the dynamics of the dislocations. The average speeds for the motion of the dislocations in the two orthogonal directions obey power laws in time with different amplitudes but the same exponents. The position and velocity distribution functions are only weakly anisotropic.