2004/04/27 by Hai Qian, Gene F. Mazenko · 2 citations
Mathematics · Physics and Astronomy · #Algorithm #Biology #Cold Atom Physics and Bose-Einstein Condensates #Conserved quantity #Distribution (mathematics) #Function (biology) #Geometry #Mathematical analysis #Mathematical physics #Mathematics #Mechanics #Phase space #Physics #Physics of Superconductivity and Magnetism #Position (finance) #Quantum mechanics #Scalar (mathematics) #Scaling #Statistical physics #Theoretical and Computational Physics #Vortex #cond-mat.soft #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.70.031104
published in Physical Review E 70(3), 031104 (American Physical Society) · 21 pages, 9 figures
arxiv created 2004/04/27 · openalex publication_date 2004/09/14 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.