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Accueil > Événements > Actualités

Séminaire

2012

Séminaire LPMMC

Uwe Tauber (Virginia Tech)
Nucleation and Aging Transient Dynamics in the Two-Dimensional Complex Ginzburg-Landau Equation
Lieu : Amphithéâtre,
le mercredi 28 août 2019 à 11h00
Personne à contacter : Léonie Canet ()

The complex Ginzburg-Landau equation (CGL) is a (stochastic) partial differential equation that describes a remarkably wide range of physical systems. We numerically investigate nucleation processes in the transient dynamics of the two-dimensional CGL towards its "frozen" state with stationary spiral structures, starting either from the defect turbulence regime or random initial configurations. Nucleation events of spiral structures are monitored using the characteristic length between the emerging shock fronts. We employ an extrapolation method and a phenomenological formula to account for finite-size effects. The non-zero barrier for the nucleation of single spiral droplets in the extrapolated infinite system size limit suggests that the transition to the frozen state is discontinuous. We also study the nucleation of spirals for systems that are quenched close to but beyond the crossover limit, and of target waves which emerge if a specific spatial inhomogeneity is introduced. In either of these cases, we observe long, "fat" tails in the distribution of nucleation times, which also supports a discontinuous transition scenario. Upon quenching the CGL into the "defocusing spiral quadrant", we observe slow coarsening dynamics as oppositely charged topological defects annihilate. We find the physical aging features in this system to be governed by non-universal aging scaling exponents. We also investigate systems with control parameters residing in the "focusing quadrant", and identify slow aging kinetics in that regime as well. We provide heuristic criteria for the existence of slow coarsening dynamics and physical aging behavior in the CGL.
Reference: W. Liu and U.C. Täuber, arXiv:1905.07317;