Defect Structures in the Growth Kinetics of the Swift-Hohenberg Model

TL;DR

This study investigates defect dynamics and coarsening behavior in the Swift-Hohenberg model's stripe growth, introducing an algorithm to track defects and analyzing their scaling laws and velocities.

Contribution

We develop a novel algorithm to identify and track defects in the Swift-Hohenberg model, revealing detailed scaling laws and defect velocity distributions during stripe coarsening.

Findings

Defect coarsening follows a growth law with exponent ~1/3.

Disclinations are rare compared to dislocations and grain boundaries.

Defect speeds exhibit power-law tail distributions and decrease over time.

Abstract

The growth of striped order resulting from a quench of the two-dimensional Swift-Hohenberg model is studied in the regime of a small control parameter and quenches to zero temperature. We introduce an algorithm for finding and identifying the disordering defects (dislocations, disclinations and grain boundaries) at a given time. We can track their trajectories separately. We find that the coarsening of the defects and lowering of the effective free energy in the system are governed by a growth law $L(t)\approx t^{x}$ with an exponent x near 1/3. We obtain scaling for the correlations of the nematic order parameter with the same growth law. The scaling for the order parameter structure factor is governed, as found by others, by a growth law with an exponent smaller than x and near to 1/4. By comparing two systems with different sizes, we clarify the finite size effect. We find that the system has a very low density of disclinations compared to that for dislocations and fraction of points in grain boundaries. We also measure the speed distributions of the defects at different times and find that they all have power-law tails and the average speed decreases as a power law.