Order and complexity in the Kuramoto-Sivashinsky model of weakly turbulent interfaces
From MaRDI portal
Publication:1090550
DOI10.1016/0167-2789(86)90136-3zbMath0621.76065OpenAlexW2022491062MaRDI QIDQ1090550
Basil Nicolaenko, James M. Hyman, Stéphane Zaleski
Publication date: 1986
Published in: Physica D (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/0167-2789(86)90136-3
bifurcationsKuramoto-Sivashinsky equationcorrelation functionsnumerical simulationsdiffusive relaxationinertial manifoldsdeveloped turbulencerandom interfaceslong time tailschaotic regimesfinite-dimensional dynamical systeminfinite-dimensional partial differential equationinterfacial turbulencelarge-scale fluctuationslow-dimensional vector field skeletonweakly turbulent interface
Related Items
ADI schemes for higher-order nonlinear diffusion equations., Finite-dimensional behavior in dissipative partial differential equations, On the well-posedness of an anisotropically-reduced two-dimensional Kuramoto-Sivashinsky equation, Interactions of coherent structures in a film flow: Simulations of a highly nonlinear evolution equation, Implicit-explicit BDF methods for the Kuramoto-Sivashinsky equation, A nonequilibrium-to-equilibrium mapping and its application to the perturbed sine-Gordon equation, On the nonlinear stability of the 1:1:1 ABC flow, Defect-mediated stability: An effective hydrodynamic theory of spatiotemporal chaos, Order parameter equations for long-wavelength instabilities, Robust heteroclinic cycles, A particle model for the Kuramoto-Sivashinsky equation, New Bounds for the Inhomogenous Burgers and the Kuramoto-Sivashinsky Equations, Archetypal analysis of spatio-temporal dynamics, The anomalous diffusion of wave disturbances in hydrodynamic-type systems, Spatio-temporal symmetries and bifurcations via bi-orthogonal decompositions, A stochastic model for the large scale dynamics of some fluctuating interfaces, Modelling the dynamics of nonlinear partial differential equations using neural networks, Higher-order incremental unknowns, hiearchical basis, and nonlinear dissipative evolutionary equations, Macrodynamics: Large-scale structures in turbulent media, Homoclinic Bifurcations for Partial Differential Equations in Unbounded Domains, Transient chaotic rotating waves in a ring of unidirectionally coupled symmetric Bonhoeffer-van der Pol oscillators near a codimension-two bifurcation point, Group classification and conservation laws for a two-dimensional generalized Kuramoto-Sivashinsky equation, Super convergence analysis of fully discrete Hermite splines to simulate wave behaviour of Kuramoto-Sivashinsky equation, A unified framework for mesh refinement in random and physical space, NOISE-INDUCED INTERMITTENCY IN CELLULAR PATTERN-FORMING SYSTEMS, Continuum modeling of particle redeposition during ion-beam erosion. Continuum modeling of particle redeposition during ion-beam erosion, one-dimensional case, The dynamics of coherent structures in the wall region of a turbulent boundary layer, Approximate inertial manifolds for the Kuramoto-Sivashinsky equation: Analysis and computations, Symmetry and chaos in the complex Ginzburg-Landau equation. II: Translational symmetries, Chaotic dynamics of an unstable Burgers equation, Inertial manifolds for the Kuramoto-Sivashinsky equation, On some dissipative fully discrete nonlinear Galerkin schemes for the Kuramoto-Sivashinsky equation, Modeling the dynamics of PDE systems with physics-constrained deep auto-regressive networks, Preserving dissipation in approximate inertial forms for the Kuramoto- Sivashinsky equation, Optimal parameter-dependent bounds for Kuramoto-Sivashinsky-type equations, Bounds on mean energy in the Kuramoto–Sivashinsky equation computed using semidefinite programming, Hierarchy of bifurcations of space-periodic structures in a nonlinear model of active dissipative media, Construction of an optimal background profile for the Kuramoto-Sivashinsky equation using semidefinite programming, Two-periodical and quasi-periodical wave solutions of the Kuramoto- Sivashinsky equation and their stability and bifurcations, Symmetry breaking Hopf bifurcations in equation with O(2) symmetry with application to the Kuramoto-Sivashinsky equation, Asymptotic expansion of the solutions to time-space fractional Kuramoto-Sivashinsky equations, A dynamical systems approach to simulating macroscale spatial dynamics in multiple dimensions, Spectral methods in time for a class of parabolic partial differential equations, Nonlinear evolution and breaking of interfacial Rayleigh–Taylor waves, Minimal dynamial systems from PDEs using Sobolev eigenfunctions, Reconstructing phase space from PDE simulations, Traveling waves for a model of gravity-driven film flows in cylindrical domains, Reduced-order-based feedback control of the Kuramoto--Sivashinsky equation, Dimensionality reduction using secant-based projection methods: the induced dynamics in projected systems, A discrete model for an ill-posed nonlinear parabolic PDE, Shear-flow and thermocapillary interfacial instabilities in a two-layer viscous flow, LYAPUNOV EXPONENTS OF THE KURAMOTO–SIVASHINSKY PDE, Stabilizing steady and periodic behavior in propagating flame fronts, Cubic Hermite collocation solution of Kuramoto–Sivashinsky equation, Numerical solutions of the generalized Kuramoto-Sivashinsky equation by Chebyshev spectral collocation methods, Nonlinear stability of oscillatory core-annular flow: A generalized Kuramoto-Sivashinsky equation with time periodic coefficients, Traveling wave oscillatory patterns in a signed Kuramoto-Sivashinsky equation with absorption, When Bifidelity Meets CoKriging: An Efficient Physics-Informed MultiFidelity Method, Organization of spatially periodic solutions of the steady Kuramoto-Sivashinsky equation, Coupled KS-CGL and coupled Burgers-CGL equations for flames governed by a sequential reaction, A form of turbulence associated with defects, Travelling waves exhibiting spatio-temporal chaos on the surface of a vertically falling thin film, INTERMITTENCY NEAR A CODIMENSION THREE STEADY-STATE BIFURCATION, The steady states of the Kuramoto-Sivashinsky equation, An intermittency route to chaos via attractor merging in the Laser-Kuramoto-Sivashinsky equation, Reconstruction equations and the Karhunen-Loève expansion for systems with symmetry, The Numerical Computation of Unstable Manifolds for Infinite Dimensional Dynamical Systems by Embedding Techniques, Bifurcations of finite difference schemes and their approximate inertial forms, Longwave instability of two-layer dielectric fluid flows in a transverse electrostatic field, A note on the computation of bifurcation diagrams of the Kuramoto- Sivashinsky equation by pseudospectral methods, Attractors and transients for a perturbed periodic KdV equation: A nonlinear spectral analysis, Doubly periodic and quasiperiodic wave regimes in a liquid film flowing down an inclined plane, their stability and bifurcations, On the hidden beauty of the proper orthogonal decomposition, Gradient pattern analysis of short nonstationary time series: an application to Lagrangian data from satellite tracked drifters, On the stability of traveling wave solutions to thin-film and long-wave models for film flows inside a tube
Cites Work
- Inertial manifolds for the Kuramoto-Sivashinsky equation and an estimate of their lowest dimension
- Structure and crises of fractal basin boundaries.
- Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
- Remarks on the Kuramoto-Sivashinsky equation
- Fractal basin boundaries
- Some global dynamical properties of the Kuramoto-Sivashinsky equations: nonlinear stability and attractors
- The Kuramoto-Sivashinsky equation: a bridge between PDE's and dynamical systems
- Steady solutions of the Kuramoto-Sivashinsky equation
- Singularities and groups in bifurcation theory. Volume I
- On the solidification front of a dilute binary alloy: Thermal diffusivity effects and breathing solutions
- Dynamic Scaling of Growing Interfaces
- Determination of the Solutions of the Navier-Stokes Equations by a Set of Nodal Values
- Attractors representing turbulent flows
- Global lyapunov exponents, kaplan-yorke formulas and the dimension of the attractors for 2D navier-stokes equations
- Super persistent chaotic transients
- Determining modes and fractal dimension of turbulent flows
- Ergodic theory of chaos and strange attractors
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item