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We numerically investigate nucleation processes in the transient dynamics ofthe two-dimensional complex Ginzburg-Landau equation towards its "frozen" statewith quasi-stationary spiral structures. We study the transition kinetics fromeither the defect turbulence regime or random initial configurations to thefrozen state with a well-defined low density of quasi-stationary topologicaldefects. Nucleation events of spiral structures are monitored using thecharacteristic length between the emerging shock fronts. We study two distinctsituations, namely either when the system is quenched far away from thetransition limit or near it. In the former deeply quenched case, the averagenucleation time for different system sizes is measured over many independentrealizations. We employ an extrapolation method as well as a phenomenologicalformula to account for and eliminate finite-size effects. The non-zero(dimensionless) barrier for the nucleation of single spiral droplets in theextrapolated infinite system size limit suggests that the transition to thefrozen state is discontinuous. We also investigate the nucleation of spiralsfor systems that are quenched close to but beyond the crossover limit, and oftarget waves which emerge if a specific spatial inhomogeneity is introduced. Ineither of these cases, we observe long, "fat" tails in the distribution ofnucleation times, which also supports a discontinuous transition scenario.

Nucleation of Spatio-Temporal Structures From Defect Turbulence in the Two-dimensional Complex Ginzburg-Landau Equation