This is a supplementary material for arxiv:1303.3044,
These results were shown at the workshop Quantised Flux in Tightly Knotted and Linked Systems, held in Cambridge, UK (Dec. 3-7 2012). See the corresponding talk of M. S. Volkov. See the published version in Phys. Rev. Lett.
Introduction
Description of the simulations: Movies show the relativistic evolution (wave equation) in 3+1 with a semi-implicit time discretization using $\beta$-Newmark method. The spatial discretization is done with a Finite-Element decomposition over spherical domain, equipped with tetrahedral mesh obtain by Delaunay-Voronoi tetrahedrizations. The initial configuration by minimization of the axially symmetric configuration. At the boundary, the fields are fixed to their initial (vacuum) value, that is $\partial_t\phi_a=0$. Thus the integration domain is a `confining box'. This means that the vorton cannot escape the box.
Stable regimes is run much longer than unstable ones, just to make sure they are not just longer-lived.
The displayed quantities are: The isosurfaces are surfaces of constant density of the second scalar field $|\phi_2|^2$. Blue to Red colors shows small to big densities. The arrows represent the associated Noether current (supercurrent) $~\mathrm{Im}(\phi_2^*\partial_k\phi_2)$. Some simulations just show one (outter) isosurface of $|\phi_2|^2$ (in blue).
1. Unstable vortons :
This shows the time evolution of thin unstable vortons. Note that the evolution reflects the fact that simulation is done in a closed box. Indeed, after destruction due to the pinching instability, the three lumps should escape. But since they live in a closed box, they can bounce and recombine to form a bigger lump.


This shows the time evolution of a thin unstable vorton. It corresponds to the first line displayed in Fig. 3 of tha paper. This is a $m=6$, $Q=24000$ vorton.


This shows the time evolution of a thin unstable vorton. It corresponds to the second line displayed in Fig. 3 of tha paper. This is a $m=3$, $Q=12000$ vorton.
2. Stable vorton :
This shows the (relativistic) dynamical evolution of a thick, stable vorton.

This shows the time evolution of a thick stable vorton. It correspond to the third line displayed in Fig. 3 of tha paper. This is a $m=1$, $Q=6000$ vorton.
References and useful readings
  1. J. Garaud, E. Radu and M. S. Volkov,
    Stable cosmic vortons
    Phys. Rev. Lett. 111, 171602, (2013). Link , arXiv
  2. E. Radu and M. S. Volkov,
    Existence of stationary, non-radiating ring solitons in field theory: knots and vortons.
    Phys. Rept. 468, 101-151, (2008). Link , arXiv
  3. R. A. Battye and P. M. Sutcliffe,
    Vorton construction and dynamics.
    Nucl. Phys. B 814, 180-194, (2009). Link , arXiv