Phase chaos in the anisotropic complex Ginzburg-Landau equation

Faller, Roland; Kramer, Lorenz

doi:10.1103/physreve.57.r6249

Cited by 19 publications

(9 citation statements)

References 31 publications

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“…A summary of the scaling exponents obtained in the various systems is shown in Table I. So far, there exists no theory that would capture the power laws, let alone predict the values of the exponents. 45 The exponents obtained in the experimental system differ noticeably from those found in the computations. The agreement between the exponents obtained for the three computational systems is therefore quite remarkable, since these systems differ substantially from each other.…”

Section: Discussionmentioning

confidence: 57%

Statistics of defect trajectories in spatio-temporal chaos in inclined layer convection and the complex Ginzburg–Landau equation

Huepe

Riecke

Daniels

et al. 2004

Chaos: An Interdisciplinary Journal of Nonlinear Science

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For spatio-temporal chaos observed in numerical simulations of the complex Ginzburg-Landau equation (CGL) and in experiments on inclined-layer convection (ILC) we report numerical and experimental data on the statistics of defects and of defect loops. These loops consist of defect trajectories in space-time that are connected to each other through the pairwise annihilation or creation of the associated defects. While most such loops are small and contain only a few defects, the loop distribution functions decay only slowly with the quantities associated with the loop size, consistent with power-law behavior. For the CGL, two of the three power-law exponents are found to agree, within our computational precision, with those from previous investigations of a simple lattice model. In certain parameter regimes of the CGL and ILC, our results for the single-defect statistics show significant deviations from the previously reported findings that the defect dynamics are consistent with those of random walkers that are created with fixed probability and annihilated through random collisions.

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Section: Discussionmentioning

confidence: 57%

Statistics of defect trajectories in spatio-temporal chaos in inclined layer convection and the complex Ginzburg–Landau equation

Huepe

Riecke

Daniels

et al. 2004

Chaos: An Interdisciplinary Journal of Nonlinear Science

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“…Numerical simulations of the anisotropic CGLE have presented a class of solutions where the defects were aligned spontaneously along chains (Weber et al 1991). These chains, which bear some resemblance with chevron patterns, have been observed in liquid crystal convection (Rossberg & Kramer 1998) and have been discussed in more detail by Weber et al (1992) and Faller & Kramer (1999). We should emphasize that periodic amplitude defects can be obtained only for homogeneous boundary conditions, and cannot be found for periodic boundary conditions.…”

Section: Discussionmentioning

confidence: 99%

Secondary structures in a one-dimensional complex Ginzburg–Landau equation with homogeneous boundary conditions

2009

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Experiments in extended systems, such as the counter-rotating Couette-Taylor flow or the Taylor-Dean flow system, have shown that patterns with vanishing amplitude may exhibit periodic spatio-temporal defects for some range of control parameters. These observations could not be interpreted by the complex Ginzburg-Landau equation (CGLE) with periodic boundary conditions. We have investigated the one-dimensional CGLE with homogeneous boundary conditions. We found that, in the 'Benjamin-Feir stable' region, the basic wave train bifurcates to state with periodic spatio-temporal defects. The numerical results match the observations quite well. We have built a new state diagram in the parameter plane spanned by the criticality (or equivalently the linear group velocity) and the nonlinear frequency detuning.

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“…[7]). In another context, symmetry breaking of STC in anisotropic liquid crystals with different diffusion constants for different spatial directions [8] can be also interpreted as the synchronization transition in STC.…”

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confidence: 99%

Critical Properties of the Synchronization Transition in Space-Time Chaos

2002

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We study two coupled spatially extended dynamical systems which exhibit space-time chaos. The transition to the synchronized state is treated as a nonequilibrium phase transition, where the average synchronization error is the order parameter. The transition in one-dimensional systems is found to be generically in the universality class of the Kardar-Parisi-Zhang equation with a growth-limiting term ("bounded KPZ"). For systems with very strong nonlinearities in the local dynamics, however, the transition is found to be in the universality class of directed percolation.

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Phase chaos in the anisotropic complex Ginzburg-Landau equation

Cited by 19 publications

References 31 publications

Statistics of defect trajectories in spatio-temporal chaos in inclined layer convection and the complex Ginzburg–Landau equation

Statistics of defect trajectories in spatio-temporal chaos in inclined layer convection and the complex Ginzburg–Landau equation

Secondary structures in a one-dimensional complex Ginzburg–Landau equation with homogeneous boundary conditions

Critical Properties of the Synchronization Transition in Space-Time Chaos

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