On phase ordering behind the propagating front of a second-order transition

In a real system the heating is nonuniform and a second-order phase transition into a broken symmetry phase occurs by propagation of the temperature front. Two parameters, the cooling rate $\tau_Q$ and the velocity $v_T$ of the transition front, determine the nucleation of topological defects. Depending on the relation of these parameters two regimes are found: in the regime of fast propagation defects are created according to the Zurek scenario for the homogeneous case, while in the slow propagation regime vortex formation is suppressed.