Mezić Research Group

Dynamical Systems and Nonlinear Control Theory

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Activities

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
 

Review article "Applied Koopmanism" made the cover of AIP Chaos

An invited review article "Applied Koopmanism", co-written by M. Budisic, R. Mohr, and I. Mezic, has just been published in journal Chaos in the focus issue Fifty Years of Chaos: Applied and Theoretical. Additionally, one of the images from the article has been featured on the cover page of the special issue.

The PDF version is available from the Chaos website, while the pre-print can be downloaded from arXiv:1206.3164.

Reference: Applied Koopmanism, Marko Budisic, Ryan Mohr, and Igor Mezic, Chaos 22, 047510 (2012), DOI:10.1063/1.4772195

Last Updated on Wednesday, 09 January 2013 14:49
 

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
 

PNAS publishes article about Deepwater Horizon plumes

Proceedings of National Academy of Sciences has published a paper which establishes that the shape of underwater plumes, released by Deepwater Horizon spill, resembles underwater clouds, not rivers, as it was previously thought. This finding reconciles seemingly incongruent measurements of bacterial activity, seen by other researchers.

Our group has contributed in the analysis of hydromechanics of the Gulf, where study of mesohyperbolic structures of fluid flows from measured data played the central role. Coupling these results with Dave Valentine's insights about bacterial activity explained the motion of hydrocarbones after the oil spill. Paper is, among others, coauthored by Igor Mezic, postdoctoral researcher Sophie Loire, and Stefan Ivic, graduate student at University of Rijeka, who visited the group during summer 2011.

Coverage:

Last Updated on Sunday, 15 January 2012 10:49
 

Visitor: Dr. Tuhin Sahai

Dr. Tuhin SahaiDr. Tuhin Sahai, a Staff Research Scientist at United Technologies Research Center, will be visiting the research group on Wed, May 4, 2011. His research interest is in managing uncertainty, nonlinear dynamics and control, and scientific and distributed computation. [website]
Dr. Sahai will present a lecture at 11am in E2 2243 (old CAD lab), with the title "Hearing the Clusters in a Graph and other Scalable Algorithms for Complex Networks". All group members are encouraged to attend. The talk summary can be found in the remainder of this announcement.
Last Updated on Monday, 09 May 2011 10:21 Read more...
 

Visitor: Dr. Matthew West

Dr. Matthew WestDr. Matthew West, an Associate Professor at Dept. of Mechanical Science and Engineering at University of Illinois - Urbana-Champaign, will be visiting the research group on Tue, Mar 22, 2011. Dr. West's research is in numerical simulation of mechanical systems and multiscale methods in consensus and control [website].
Dr. West will give a talk on Tue, Mar 22, 2011 from 10.30a-12.00p at EII 1335. All group members are encouraged to attend.
Last Updated on Tuesday, 22 March 2011 19:39
 

Visitor: Dr. Stefan Siegmund

Dr. SiegmundOn Thu, 18 Mar, 2010, Dr. Stefan Siegmund, of TU Dresden [link], will be visiting our group, and giving a talk on the same day between 4 and 5pm, titled "Dynamics and Control in Fluids, Engineering and Biochemistry". The room is tentatively scheduled as ESB 1001.
Last Updated on Thursday, 25 March 2010 10:23 Read more...
 



Acknowledgements