Numerical simulation of bubble collision and formation of vortices

We perform a numerical study of the dynamical formation of vortices in 2+1 dimensions in the collision of critical bubbles. An initial field configuration is prescribed in the form of three critical bubbles with given positions and Higgs phases. These bubbles expand and form vortices after coalescing if the Higgs phases have appropriate values. We find that if the initial Higgs-phase distribution is not uniform, or if bubbles do not collide symmetrically, then the vortices can develop large velocities at the time of their formation (about 0.5c). We also find that a subcritical bubble bounces back after each collapse, losing energy in each bounce