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We study the motion of vortices in the conserved and non-conservedphase-ordering models. We give an analytical method for computing the speed andposition distribution functions for pairs of annihilating point vortices basedon heuristic scaling arguments. In the non-conserved case this method producesa speed distribution function consistent with previous analytic results. As twospecial examples, we simulate the conserved and non-conserved O(2) model in twodimensional space numerically. The numerical results for the non-conserved caseare consistent with the theoretical predictions. The speed distribution of thevortices in the conserved case is measured for the first time. Our theoryproduces a distribution function with the correct large speed tail but does notaccurately describe the numerical data at small speeds. The positiondistribution functions for both models are measured for the first time and wefind good agreement with our analytic results. We are also able to extend thismethod to models with a scalar order parameter.Comment: 21 pages, 9 figure

physical review. e, statistical, nonlinear and soft matter physics

Vortex kinetics of conserved and nonconserved<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi mathvariant="normal">O</mml:mi><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math>models

Vortex kinetics of conserved and nonconservedO(n)models