Noise-sustained structure, intermittency and the Ginzburg-Landau equation

DOI10.1007/BF01017180zbMath0625.76062OpenAlexW2064982319MaRDI QIDQ580100

Robert J. Deissler

Publication date: 1985

Published in: Journal of Statistical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01017180

zbMATH Keywords

pattern formationconvective instabilitysecondary instabilityintermittent turbulencelow-level external noisemacroscopic dynamicsnoise amplificationnoise-sustained structurespatial instabilityspatially growing wavesstationary frame of referencetime-dependent generalized Ginzburg-Landau equation

Mathematics Subject Classification ID

Absolute and convective instability and stability in hydrodynamic stability (76E15) Nonlinear effects in hydrodynamic stability (76E30) Partial differential equations of mathematical physics and other areas of application (35Q99)

Related Items (32)

Local Lyapunov exponents for spatiotemporal chaos ⋮ Spatially growing waves, intermittency, and convective chaos in an open- flow system ⋮ Periodic solutions of the Ginzburg-Landau equation ⋮ Convective instability with time scale translation of the transmitted fluctuation ⋮ Rigid transition to the stationary structure and imposed convective instability in a reaction-diffusion system with flow ⋮ Slowly varying fully nonlinear wavetrains in the Ginzburg-Landau equation ⋮ Experiments and long-term high-performance computations on amplitude modulations of strato-rotational flows ⋮ On the convective and absolute nature of instabilities in finite difference numerical simulations of open flows ⋮ Asymptotic theory of multidimensional chaos ⋮ Nonlinear analysis of instability modes in the Taylor–Dean system ⋮ Existence and uniqueness of weak solutions to Ginzburg-Landau equation with external noise and stochastic perturbation ⋮ Dissipative solitons stabilized by nonlinear gradients in one spatial dimension: from deterministic to stochastic aspects, and a perspective ⋮ Classification of solutions of a system of nonlinear diffusion equations in a neighborhood of a bifurcation point ⋮ Characterization of the spatial complex behavior and transition to chaos in flow systems ⋮ Convective and absolute instabilities of fluid flows in finite geometry ⋮ Against the wind ⋮ A mechanism for localized turbulence ⋮ The effect of Lagrangian chaos on locking bifurcations in shear flows ⋮ Convective instability and boundary driven oscillations in a reaction-diffusion-advection model ⋮ Flow and diffusion distributed structures with noise at the inlet ⋮ Solutions of the Ginzburg-Landau Equation of Interest in Shear Flow Transition ⋮ Convective instability boundary of Couette flow between rotating porous cylinders with axial and radial flows ⋮ Absolute instability of Rayleigh-Bénard convection in a time-periodic shear flow ⋮ Bistability in the complex Ginzburg-Landau equation with drift ⋮ Forced convective structures in a differential-flow reactor ⋮ Spatio-temporal structures in a differential flow reactor with cubic autocatalator kinetics ⋮ Two boundary value problems for the Ginzburg-Landau equation ⋮ Electric field induced propagating structures in a model of spatio-temporal signalling ⋮ Nonlinear dynamics of waves and modulated waves in 1D thermocapillary flows. II: Convective/absolute transitions ⋮ The development of spatial structure in an ionic chemical system induced by applied electric fields ⋮ Experiments with pattern-forming systems ⋮ Noise-induced absolute instability

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• Stability of Spatially Periodic Supercritical Flows in Hydrodynamics
• A non-linear instability theory for a wave system in plane Poiseuille flow

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