Mezić Research Group

Dynamical Systems and Nonlinear Control Theory

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Dynamical Systems

Research Program Outline for Big Data Dynamics in Systems of Systems

Igor Mezić

The problem of design, reverse engineering and retrofitting for robust operation of large-scale interconnected dynamical systems is perhaps the engineering grand challenge of our time. Mathematics and engineering tools for treatment of individual components have been developed to a high degree of sophistication. However, when these components are connected - whether physically or by communication devices - new, collective phenomena can emerge that are not necessarily related to properties of individual components. The local consequences of such phenomena can be sensed - and the drive towards reduced cost and ubiquity of sensors leads to a massive amount of dynamically changing data. The phenomena indicated by sensed data have to be recognized, counteracted or perhaps even utilized dynamically in attempts to achieve optimal design and operation. Here are some of the critical elements of the applied problem at hand, the "Big Data Dynamics in Systems of Systems", and our viewpoint on the associated research directions.

Last Updated on Friday, 23 May 2014 12:54

Spread of Deepwater Horizon oil slick predicted using a new method

Mesohyperbolicity in Gulf Oil Spill dataIn a paper published online on September 2nd 2010, in the prestigious journal Science, Mezic, together with Sophie Loire, a postdoctoral fellow who works with Mezic and colleagues at the software development company Aimdyn, Inc. in Santa Barbara and at NASA’s Stennis Space Center in Mississippi, describe how they predicted the movement of oil spilled into the Gulf of Mexico after an explosion aboard the Deepwater Horizon rig on April 20.
UCSB Press Release:
Last Updated on Tuesday, 22 March 2011 19:56

Ergodic Quotient and Coherent Structures

Marko Budisic

Coloring of the standard map state space using ergodic quotient

Certain dynamical systems, e.g., geophysical fluid flows, can be so complicated that it is difficult to provide concise mathematical models for their behavior. Nevertheless, simulations and experiments provide us with data in which we can recognize simple patterns that resemble systems that are well studied and understood. My research aimed to extract regions of such simpler behaviors and analyze how micro-structures fit together to form larger coherent structures, taking an approach alternative to classical geometric dynamical systems analysis.

Last Updated on Thursday, 22 May 2014 09:50

The Effect of Symmetry on Spatiotemporal Resonances in Coupled Systems

Bryan Eisenhower

Conformation change

In this work we study instability in networked systems which leads to a better understanding of their sensitivities and control requirements. The networks we study range from those inspired by biology to power grids and networked control systems. We use both deterministic and stochastic Dynamical Systems tools including high dimensional internal resonance, Hamiltonian dynamics, averaging, and analysis of stochastic differential equations.

Last Updated on Saturday, 25 April 2009 10:02

Mechanical Model of Coupled Oscillators

George Gilmore

I am currently building a physical model of 20 coupled oscillators, imposing a variety of initial conditions, from which we will measure and collect behavioral information via video capture.

Last Updated on Monday, 27 April 2009 08:52