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Spectral analysis of nonlinear flows
- C. Rowley, I. Mezić, S. Bagheri, P. Schlatter, D. Henningson
- MathematicsJournal of Fluid Mechanics
- 18 November 2009
We present a technique for describing the global behaviour of complex nonlinear flows by decomposing the flow into modes determined from spectral analysis of the Koopman operator, an…
Chaotic Mixer for Microchannels
- A. Stroock, S. Dertinger, A. Ajdari, I. Mezić, H. Stone, G. Whitesides
- 25 January 2002
This work presents a passive method for mixing streams of steady pressure-driven flows in microchannels at low Reynolds number, and uses bas-relief structures on the floor of the channel that are easily fabricated with commonly used methods of planar lithography.
Spectral Properties of Dynamical Systems, Model Reduction and Decompositions
- I. Mezić
- 1 August 2005
In this paper we discuss two issues related to model reduction of deterministic or stochastic processes. The first is the relationship of the spectral properties of the dynamics on the attractor of…
Linear predictors for nonlinear dynamical systems: Koopman operator meets model predictive control
The Koopman framework is showing potential for crossing over from academic and theoretical use to industrial practice, and the paper highlights its strengths in applied and numerical contexts.
Analysis of Fluid Flows via Spectral Properties of the Koopman Operator
- I. Mezić
- 3 January 2013
This article reviews theory and applications of Koopman modes in fluid mechanics. Koopman mode decomposition is based on the surprising fact, discovered in Mezic (2005), that normal modes of linear…
Metrics for ergodicity and design of ergodic dynamics for multi-agent systems
Ergodic Theory, Dynamic Mode Decomposition, and Computation of Spectral Properties of the Koopman Operator
This work establishes the convergence of a class of numerical algorithms, known as dynamic mode decomposition (DMD), for computation of the eigenvalues and eigenfunctions of the infinite-dimensional Koopman operator, and shows that the singular value decomposition, which is the central part of most DMD algorithms, converges to the proper orthogonal decomposition of observables.