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Vortex velocity probability distributions in phase-ordering kinetics.

Gene F Mazenko¹

¹The James Franck Institute and Department of Physics, The University of Chicago, Chicago, Illinois 60637, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|July 13, 2004

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This study extends point vortex velocity probability distribution function (VVPDF) calculations to anisotropic and conserved systems. The findings reveal consistent scaling properties and a new method for expressing average vortex speed in conserved systems.

Area of Science:

Condensed Matter Physics
Statistical Mechanics
Nonlinear Dynamics

Background:

The time-dependent Ginzburg-Landau (TDGL) model is a standard for studying systems with vortices.
Previous work focused on nonconserved, isotropic TDGL models for vortex velocity calculations.
Understanding vortex dynamics is crucial in various physical phenomena.

Purpose of the Study:

To extend the calculation of the point vortex velocity probability distribution function (VVPDF) to broader classes of systems.
To investigate the applicability of VVPDF scaling in anisotropic and conserved order parameter systems.
To develop a self-consistent method for expressing the average vortex speed.

Main Methods:

Extended theoretical calculations beyond the nonconserved TDGL model.

Related Experiment Videos

Incorporated anisotropic models and the conserved order parameter case.

Utilized correlation functions associated with a Gaussian auxiliary field.

Main Results:

The VVPDF retains scaling properties with large velocity tails, similar to the nonconserved isotropic case.
A self-consistent expression for the average vortex speed was derived using Gaussian auxiliary field correlations.
In conserved systems, average vortex speed decays as t(-1), contrasting with t(-1/2) in nonconserved systems.

Conclusions:

The VVPDF framework is robust and applicable to a wider range of physical systems, including anisotropic and conserved ones.
The derived method provides a new perspective on calculating average vortex speeds.
The distinct decay rates highlight fundamental differences in vortex dynamics between conserved and nonconserved systems.