Mezić Research Group

Dynamical Systems and Nonlinear Control Theory

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Events

The Mezic Research group is pleased to announce the PhD Dissertation Defense for Michael Georgescu

Date: Thursday, December 4, 2014
Time: 9:00am
Location: Materials Research Lab (MRL), Room 2048

Advisor: Prof. Igor Mezic
Title: Analysis of Systems in Buildings using Spectral Koopman Operator Methods
Abstract:

This work presents a viewpoint for analyzing data-based systems using an operator-theoretic approach based on the Koopman operator. In particular we focus on problems emerging from building systems analysis; a setting where systems are high-dimensional and described by large data-sets (either measured or generated from simulation), but for which equations describing the system often cannot be expressed analytically. In the building setting, natural cycles of operations exist that are driven by occupancy, plug load schedules and environmental conditions. Using properties of the Koopman operator, building data can be decomposed into spatial-temporal modes, and from these modes, characteristics of data can be studied at varying time-scales. In particular we present a variety of novel analysis techniques based on spectral properties of the Koopman operator that can be applied to a variety of applications ranging from the monitoring/visualization, model order reduction, and model calibration of building systems. Each chapter is dedicated to one specific application and the tools developed for it. Numerous examples are presented to illustrate the capabilities of the developed framework.

Last Updated on Wednesday, 03 December 2014 14:25
 

The Mezic Research Group is pleased to host C P Caulfield

We are pleased to have Dr Colm-cille P. Caulfield, from the University of Cambridge, visit the Mezic's research group this Tuesday, December 2, 2014.

Dr Colm-cille P. Caulfield is interested in fluid flows where density
variations play a critical dynamical role. He strives to use a combination
of mathematical modelling, numerical simulation and laboratory experimentation
to understand and quantify fundamental physical processes, particularly when
they are transient in nature.
Last Updated on Monday, 01 December 2014 13:56
 

Talk: Koopman Mode Decomposition, Mesohyperbolicity and Mixing

TUESDAY, OCTOBER 14, 2014 4:30 - 5:20

Igor Mezic (University of California, Santa Barbara (UC Santa Barbara))

Koopman Mode Decomposition, Mesohyperbolicity and Mixing

@The INSTITUTE FOR PURE AND APPLIED MATHEMATICS
Los Angeles, California
Last Updated on Tuesday, 07 October 2014 17:33 Read more...
 

The Mezic Research Group is pleased to host Kari Kuester

On the spectrum of a Koopman operator of a dynamical system

Kari Kuester

Department of Mathematics

University of Tuebingen, Germany

Engineering Building II, Room 2243

Wednesday, May 21, 2014

10:30 am - 11:30 am

Abstract:

The Koopman operator permits to linearize dynamical systems in a way that all important information of the original system is preserved. In particular it is interesting to study the eigenvalues and eigenfunctions of the Koopman operator. The so called Jacobs-Glicksberg-de Leeuw-splitting shows that unimodular eigenvalues are of particular interest. It decomposes the observable space into a structured and a random part. The structured part is spanned by the eigenfunctions corresponding to unimodular eigenvalues and gives insight into the longterm behavior of the Koopman operator.

Short bio:

Kari Kuester studies Mathematics at the University of Tuebingen, Germany. She is preparing her Master thesis on "The Koopman linearization of dynamical systems" under the supervision of Prof. Rainer Nagel and is currently working with Prof. Frank Neubrander at Louisiana State University, Baton Rouge.

Last Updated on Saturday, 31 May 2014 18:55
 

Visitor: Dr. Ophir Samson

Dr. Ophir Samson will be presenting his research on Fri Apr 29, 4pm, at E2 2319 (small ME conference room). Dr. Samson applies techniques of complex analysis to study solutions of fluid flows.

Talk abstract: Stokes flows in confined geometries have recently attracted much attention due to their relevance to both lab-on-a-chip design as well as low Reynolds number locomotion. Most two-dimensional problems have studied flows in simple geometries, such as a half plane. We present a new method of finding exact solutions for Stokes flows in more complicated domains. We also present a new way of modelling micro-swimmers and show how they interact with walls, as well as walls with gaps. This results in interesting dynamical systems which exhibit rare gluing bifurcations as well as hydrodynamical bound states, which are useful for mixing problems in Stokes flows.

Last Updated on Tuesday, 03 May 2011 11:23
 
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Acknowledgements