Dislocation dynamics in a dodecagonal quasiperiodic structure

TL;DR

This paper introduces numerical tools to analyze defect dynamics in quasiperiodic structures, specifically studying dislocation motion in a dodecagonal pattern, revealing unique pinning behavior under certain conditions.

Contribution

The paper develops new numerical methods for analyzing defect dynamics in quasiperiodic structures and applies them to study dislocation motion in dodecagonal patterns.

Findings

Dislocation climb velocity is similar in dodecagonal and hexagonal patterns under strong diffusion.

Weak diffusion causes unique pinning of dislocations in dodecagonal structures.

Tools enable real-time tracking of dislocation evolution in quasiperiodic systems.

Abstract

We have developed a set of numerical tools for the quantitative analysis of defect dynamics in quasiperiodic structures. We have applied these tools to study dislocation motion in the dynamical equation of Lifshitz and Petrich [Phys. Rev. Lett. 79 (1997) 1261] whose steady state solutions include a quasiperiodic structure with dodecagonal symmetry. Arbitrary dislocations, parameterized by the homotopy group of the D-torus, are injected as initial conditions and quantitatively followed as the equation evolves in real time. We show that for strong diffusion the results for dislocation climb velocity are similar for the dodecagonal and the hexagonal patterns, but that for weak diffusion the dodecagonal pattern exhibits a unique pinning of the dislocation, reflecting its quasiperiodic nature.