Seminar Event Detail


Student AIM Seminar

Date:  Friday, December 11, 2015
Location:  1084 East Hall (4:10 PM to 5:00 PM)

Title:  Optimal control of a shell model for mixing

Abstract:   Optimal mixing is significant to process engineering within industries such as food, pharmaceutical, petrochemical, and more. An important question in this field is ``How should one stir to create a homogeneous mixture while being energetically efficient?" To answer this question, we consider an initially unmixed scalar field representing some concentration within a fluid on a perodic domain. This passive-scalar field is advected by the velocity field, our control variable, constrained by a some physical quantity such as energy or enstrophy. We consider two objectives: local-in-time optimization (what will maximize the mixing rate now?) and global-in-time optimization (what will maximize mixing at the end time?). In this presentation, we use the $H^{-1}$ mix-norm to measure mixing. To gain a qualitative understanding of optimal mixing, we will examine a simplified model of mixing by using a shell model of passive-scalar advection.

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Speaker:  Chris Miles
Institution:  University of Michigan

Event Organizer:   Derek Wood and Jeremy Hoskins   

 

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