Anisotropic velocity statistics of topological defects under shear flow

TL;DR

This study investigates the velocity statistics of topological defects during phase ordering under shear flow, revealing a universal algebraic tail in velocity distributions and anisotropic effects due to external shear.

Contribution

It introduces an efficient defect tracking method and characterizes the velocity distribution functions, highlighting universal algebraic tails and anisotropic effects under shear flow.

Findings

Velocity fluctuation distributions have a robust inverse cube tail.

Universal algebraic tail in velocity distributions for defects of codimension two.

External shear induces anisotropic statistical properties in defect velocities.

Abstract

We report numerical results on the velocity statistics of topological defects during the dynamics of phase ordering and non-relaxational evolution assisted by an external shear ow. We propose a numerically efficient tracking method for finding the position and velocity of defects, and apply it to vortices in a uniform field and dislocations in anisotropic stripe patterns. During relaxational dynamics, the distribution function of the velocity fuctuations is characterized by a dynamical scaling with a scaling function that has a robust algebraic tail with an inverse cube power law. This is characteristic to defects of codimension two, e.g. point defects in two dimensions and filaments in three dimensions, regardless of whether the motion is isotropic (as for vortices) or highly anisotropic (as for dislocations). However, the anisotropic dislocation motion leads to anisotropic statistical properties when the interaction between defects and their motion is in infuenced by the presence of an external shear flow transverse to the stripe orientation.