Mixing: Visualization, norms, and control

Thursday, April 15, 2010 - 4:00pm - 4:45pm
EE/CS 3-180
Igor Mezic (University of California)
Keywords: mixing, mix-norm, optimal stirring, ergodicity

Abstract: I will discuss several issues in analyzing kinematics of a purely advective mixing process:

1) Determine whether the scalar quantity, such as dye, introduced into the flow field is - asymptotically - in time thoroughly mixed.

2) Determine how good is the mixture at any finite time.

3) Provide methods for open-loop optimization or feedback control of the mixture.

The concept of ergodic partition allows us to discuss 1) precisely, and I will discuss some new results that allow us to compute it effectively. Concerning 2), the problem of an effective norm for mixing has attracted a lot of work over the last decade. I will discuss one family of norms - the so called mix-norm that connects to negative Sobolev space norms - that allows us to pursue study of opimization and control, thus covering 3).

I will also discuss the question of ergodicity of a system and how to measure it. This is a departure from the standard off-on definition of ergodicity providing a measure of how close to ergodicity a system is. In all of the above, ergodic theory plays a prominent role.
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