Figure 1

Comparing the standard (PRS) and our (new) velocity estimation methods, for 2D (solid line) and 3D (dashed line) radiation era runs. Each curve corresponds to an average of 10 simulations. Clearly the PRS method overestimates velocities by about 20%.Reuse & Permissions

Figure 2

Same as Fig. 1 for matter era simulations.Reuse & Permissions

Figure 3

Comparing our analytic model with field theory numerical simulations in the matter (left-side panels) and radiation (right-side panels) epochs. Top panels show the evolution of the correlation length (in fact $L/t$) whereas bottom panels show the RMS velocity. In both cases the longer solid curves correspond to 2D simulations, while the shorter solid curves correspond to 3D simulations. Each such curve is in fact an averaged curve for the outcome of 100 such simulations. The corresponding dashed curves are the outcome of our analytic model, for the initial conditions relevant to each case. For all such curves we have used $c_w=0.5$ and $k_w=0.9$, which provides the best fit.Reuse & Permissions

Figure 4

An alternative fit to the model, now using an ansatz for $k_w(v)$ that has been derived for cosmic strings—see main text for further discussion. Panel and line conventions are as in Fig. 2.Reuse & Permissions