358 research outputs found
Defect Statistics in the Two Dimensional Complex Ginsburg-Landau Model
The statistical correlations between defects in the two dimensional complex
Ginsburg-Landau model are studied in the defect-coarsening regime. In
particular the defect-velocity probability distribution is determined and has
the same high velocity tail found for the purely dissipative time-dependent
Ginsburg-Landau (TDGL) model. The spiral arms of the defects lead to a very
different behavior for the order parameter correlation function in the scaling
regime compared to the results for the TDGL model.Comment: 24 page
The Vortex Kinetics of Conserved and Non-conserved O(n) Models
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.Comment: 21 pages, 9 figure
Vortex annihilation in the ordering kinetics of the O(2) model
The vortex-vortex and vortex-antivortex correlation functions are determined
for the two-dimensional O(2) model undergoing phase ordering. We find
reasonably good agreement with simulation results for the vortex-vortex
correlation function where there is a short-scaled distance depletion zone due
to the repulsion of like-signed vortices. The vortex-antivortex correlation
function agrees well with simulation results for intermediate and long-scaled
distances. At short-scaled distances the simulations show a depletion zone not
seen in the theory.Comment: 28 pages, REVTeX, submitted to Phys. Rev.
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