Vortex Velocity Probability Distributions in Phase Ordering Kinetics

TL;DR

This paper extends the calculation of vortex velocity probability distributions to include anisotropic and conserved order parameter systems, revealing scaling behaviors and decay rates of vortex speeds over time.

Contribution

It introduces a generalized approach for vortex velocity distributions applicable to a broader class of phase ordering systems, including anisotropic and conserved cases.

Findings

Vortex velocity distributions satisfy scaling with large velocity tails.

Average vortex speed decays as t^{-1} in conserved systems.

Average vortex speed decays as t^{-1/2} in nonconserved systems.

Abstract

The calculation of the point vortex velocity probability distribution function (vvpdf) is extended to a larger class of systems beyond the nonconserved TDGL model treated earlier. The range is extended to include certain anisotropic models and the conserved order parameter case. The vvpdf still satisfies scaling with large velocity tails as for the nonconserved isotropic case. It is shown that the average vortex speed can be self-consistently expressed in terms of correlation functions associated with a Gaussian auxiliary field. In the conserved order parameter case the average vortex speed decays as $t^{-1}$ compared to the $t^{-1/2}$ decay for the nonconserved case.