Journal ArticleDOI
Chaotic dynamics of coherent structures
TLDR
In this paper, a variety of chaotic flows evolving in relatively high-dimensional spaces are considered, and it is shown through the use of an optimal choice of basis functions, which are consequence of the Karhunen-Loeve procedure, that an accurate description can be given in a relatively low-dimensional space.About:
This article is published in Physica D: Nonlinear Phenomena.The article was published on 1989-08-01. It has received 221 citations till now. The article focuses on the topics: Chaotic & Basis function.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 Proper Orthogonal Decomposition in the Analysis of Turbulent Flows
TL;DR: The Navier-Stokes equations are well-known to be a good model for turbulence as discussed by the authors, and the results of well over a century of increasingly sophisticated experiments are available at our disposal.
Journal ArticleDOI
Spectral proper orthogonal decomposition and its relationship to dynamic mode decomposition and resolvent analysis
TL;DR: In this article, the spectral proper orthogonal decomposition (SPOD) has been studied in the context of the analysis of the Ginzburg-Landau equation and a turbulent jet.
Journal ArticleDOI
Modeling and control of physical processes using proper orthogonal decomposition
Hung V. Ly,Hien T. Tran +1 more
TL;DR: The aim of the paper is to show that, using the obtained ensemble of data, POD can be used to model accurately the natural convection and this approach is very efficient in the sense that it uses the smallest possible number of parameters, and thus, is suited for process control.
Journal ArticleDOI
The proper orthogonal decomposition of pressure fluctuations surrounding a turbulent jet
TL;DR: In this paper, the authors present an approach to solve the problem of the "missing link" problem in the context of artificial neural networks, and propose a method to solve it.
References
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Journal ArticleDOI
Deterministic nonperiodic flow
TL;DR: In this paper, it was shown that nonperiodic solutions are ordinarily unstable with respect to small modifications, so that slightly differing initial states can evolve into considerably different states, and systems with bounded solutions are shown to possess bounded numerical solutions.
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.
Book
Probability theory
TL;DR: These notes cover the basic definitions of discrete probability theory, and then present some results including Bayes' rule, inclusion-exclusion formula, Chebyshev's inequality, and the weak law of large numbers.