The Vortex Kinetics of Conserved and Non-conserved O(n) Models

Abstract

We study the motion of vortices in the conserved and non-conserved phase-ordering models. We give an analytical method for computing the speed and position distribution functions for pairs of annihilating point vortices based on heuristic scaling arguments. In the non-conserved case this method produces a speed distribution function consistent with previous analytic results. As two special examples, we simulate the conserved and non-conserved O(2) model in two dimensional space numerically. The numerical results for the non-conserved case are consistent with the theoretical predictions. The speed distribution of the vortices in the conserved case is measured for the first time. Our theory produces a distribution function with the correct large speed tail but does not accurately describe the numerical data at small speeds. The position distribution functions for both models are measured for the first time and we find good agreement with our analytic results. We are also able to extend this method to models with a scalar order parameter.

arXiv comment21 pages, 9 figures

References in corpus (6)

• Theory of Phase Ordering Kinetics
• Fast and Accurate Coarsening Simulation with an Unconditionally Stable Time Step
• Velocity Distribution of Topological Defects in Phase-Ordering Systems
• Velocity Distribution for Strings in Phase Ordering Kinetics
• Vortex Dynamics in a Coarsening Two Dimensional XY Model
• Vortex Velocity Pair Correlations

Cited by in corpus (2)

• Growth of Order in An Anisotropic Swift-Hohenberg Model
• Coarsening Kinetics of a Two Dimensional O(2) Ginzburg-Landau Model: Effect of Reversible Mode Coupling