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Vortex kinetics of conserved and nonconserved On models.

We study the motion of vortices in the conserved and nonconserved 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 nonconserved case this method produces a speed distribution function consistent with previous analytic results. As two special examples, we simulate numerically the conserved and nonconserved O(2) model in two-dimensional space. The numerical results for the nonconserved case are consistent with the theoretical predictions. The speed distribution of the vortices in the conserved case is measured. 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 and we find good agreement with our analytic results. We are also able to extend this method to models with a scalar order parameter.