Unified model for vortex-string network evolution

We describe and numerically test the velocity-dependent one-scale string evolution model, a simple analytic approach describing a string network with the averaged correlation length and velocity. We show that it accurately reproduces the large-scale behavior (in particular the scaling laws) of numerical simulations of both Goto-Nambu and field theory string networks. We explicitly demonstrate the relation between the high-energy physics approach and the damped and nonrelativistic limits which are relevant for condensed matter physics. We also reproduce experimental results in this context and show that the vortex-string density is significantly reduced by loop production, an effect not included in the usual "coarse-grained" approach.