Nucleation of spatiotemporal structures from defect turbulence in the two-dimensional complex Ginzburg-Landau equation
Abstract
We numerically investigate nucleation processes in the transient dynamics of the two-dimensional complex Ginzburg--Landau equation towards its "frozen'' state with quasi-stationary spiral structures. We study the transition kinetics from either the defect turbulence regime or random initial configurations to the frozen state with a well-defined low density of quasi-stationary topological defects. Nucleation events of spiral structures are monitored using the characteristic length between the emerging shock fronts. We study two distinct situations, namely either when the system is quenched far away from the transition limit or near it. In the former deeply quenched case, the average nucleation time for different system sizes is measured over many independent realizations. We employ an extrapolation method as well as a phenomenological formula to account for and eliminate finite-size effects. The non-zero (dimensionless) 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. Here, we also investigate 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 distributionmore »
- Authors:
-
[1]
- Virginia Polytechnic Inst. and State Univ. (Virginia Tech), Blacksburg, VA (United States)
- Publication Date:
- Research Org.:
- Virginia Polytechnic Inst. and State Univ. (Virginia Tech), Blacksburg, VA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22). Materials Sciences & Engineering Division
- OSTI Identifier:
- 1574685
- Grant/Contract Number:
- SC0002308
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review E
- Additional Journal Information:
- Journal Volume: 100; Journal Issue: 5; Journal ID: ISSN 2470-0045
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 97 MATHEMATICS AND COMPUTING
Citation Formats
Liu, Weigang, and Täuber, Uwe C. Nucleation of spatiotemporal structures from defect turbulence in the two-dimensional complex Ginzburg-Landau equation. United States: N. p., 2019.
Web. doi:10.1103/PhysRevE.100.052210.
Liu, Weigang, & Täuber, Uwe C. Nucleation of spatiotemporal structures from defect turbulence in the two-dimensional complex Ginzburg-Landau equation. United States. doi:10.1103/PhysRevE.100.052210.
Liu, Weigang, and Täuber, Uwe C. Wed .
"Nucleation of spatiotemporal structures from defect turbulence in the two-dimensional complex Ginzburg-Landau equation". United States. doi:10.1103/PhysRevE.100.052210. https://www.osti.gov/servlets/purl/1574685.
@article{osti_1574685,
title = {Nucleation of spatiotemporal structures from defect turbulence in the two-dimensional complex Ginzburg-Landau equation},
author = {Liu, Weigang and Täuber, Uwe C.},
abstractNote = {We numerically investigate nucleation processes in the transient dynamics of the two-dimensional complex Ginzburg--Landau equation towards its "frozen'' state with quasi-stationary spiral structures. We study the transition kinetics from either the defect turbulence regime or random initial configurations to the frozen state with a well-defined low density of quasi-stationary topological defects. Nucleation events of spiral structures are monitored using the characteristic length between the emerging shock fronts. We study two distinct situations, namely either when the system is quenched far away from the transition limit or near it. In the former deeply quenched case, the average nucleation time for different system sizes is measured over many independent realizations. We employ an extrapolation method as well as a phenomenological formula to account for and eliminate finite-size effects. The non-zero (dimensionless) 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. Here, we also investigate 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.},
doi = {10.1103/PhysRevE.100.052210},
journal = {Physical Review E},
number = 5,
volume = 100,
place = {United States},
year = {2019},
month = {11}
}
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