Journal ArticleDOI
Order and complexity in the Kuramoto-Sivashinsky model of weakly turbulent interfaces
TLDR
In this article, a large number of new geometric, ergodic and statistical properties of the Kuramoto-Sivashinsky equation were presented for modeling interfacial turbulence in various physical contexts.About:
This article is published in Physica D: Nonlinear Phenomena.The article was published on 1986-12-01. It has received 191 citations till now. The article focuses on the topics: Dissipative system & Partial differential equation.read more
Citations
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Journal ArticleDOI
Pattern formation outside of equilibrium
Michael Cross,P. C. Hohenberg +1 more
TL;DR: A comprehensive review of spatiotemporal pattern formation in systems driven away from equilibrium is presented in this article, with emphasis on comparisons between theory and quantitative experiments, and a classification of patterns in terms of the characteristic wave vector q 0 and frequency ω 0 of the instability.
Journal ArticleDOI
The dynamics of coherent structures in the wall region of a turbulent boundary layer.
TL;DR: In this article, the wall region of a turbulent boundary layer is modelled by expanding the instantaneous field in so-called empirical eigenfunctions, as permitted by the proper orthogonal decomposition theorem.
Journal ArticleDOI
Back in the saddle again: a computer assisted study of the Kuramoto-Sivashinsky equation
TL;DR: In this article, a numerical and analytical study of the Kuramoto-Sivashinsky partial differential equation (PDE) in one spatial dimension with periodic boundary conditions is presented, and the structure, stability, and bifurcation characteristics of steady state and time-dependent solutions of the PDE for values of the parameter α less than 40 are examined.
Journal ArticleDOI
Approximate inertial manifolds for the Kuramoto-Sivashinsky equation: analysis and computations
TL;DR: In this article, the approximation of inertial manifolds for the one-dimensional Kuramoto-Sivashinsky equation (KSE) has been studied and a method motivated by the dynamics originally developed for the Navier-Stokes equation is adapted for the KSE.
References
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Book
Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields
TL;DR: In this article, the authors introduce differential equations and dynamical systems, including hyperbolic sets, Sympolic Dynamics, and Strange Attractors, and global bifurcations.
A Reflection on Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields
J. Guckenheimer,P. J. Holmes +1 more
TL;DR: In this paper, the authors introduce differential equations and dynamical systems, including hyperbolic sets, Sympolic Dynamics, and Strange Attractors, and global bifurcations.
Journal ArticleDOI
Ergodic theory of chaos and strange attractors
Jean-Pierre Eckmann,David Ruelle +1 more
TL;DR: A review of the main mathematical ideas and their concrete implementation in analyzing experiments can be found in this paper, where the main subjects are the theory of dimensions (number of excited degrees of freedom), entropy (production of information), and characteristic exponents (describing sensitivity to initial conditions).
Journal ArticleDOI
Dynamic Scaling of Growing Interfaces
TL;DR: A model is proposed for the evolution of the profile of a growing interface that exhibits nontrivial relaxation patterns, and the exact dynamic scaling form obtained for a one-dimensional interface is in excellent agreement with previous numerical simulations.
BookDOI
Singularities and groups in bifurcation theory
TL;DR: Singularities and groups in bifurcation theory as mentioned in this paper have been used to solve the problem of finding a group of singularities in a set of problems with multiple solutions.
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