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SUMMARY:Design principles for mixers motivated by ergodic theory\, or: How
  fluids mix\, and how to make that happen without having to know the answe
 r ahead of time - Stephen Wiggins (University of Bristol)
DTSTART:20101029T150000Z
DTEND:20101029T160000Z
UID:TALK27006@talks.cam.ac.uk
CONTACT:Dr C. P.  Caulfield
DESCRIPTION:I will begin by talking briefly about what makes fluids mix (w
 hich has been known for a long time)\, and some examples of efforts to mak
 e this happen in practical devices. Then I will introduce the mathematical
  theory of mixing from ergodic theory and talk about why it is a useful gu
 ide\, but why there are practical obstacles to applying the theory in "rea
 l life" and how this opens up a wealth of new mathematical questions. The 
 mixers that I will mostly be concerned with are ‘’micromixers’’ an
 d to motivate the general ideas that I wish to develop I will survey a num
 ber of micromixers with an idea of extracting the common features. This wi
 ll provide a good entry for going back to the theory (a bit) and extractin
 g "Eulerian and Lagrangian" aspects  that influence mixing. Basically\, wh
 at I would “ideally’’ like to do is completely bypass the Lagrangian
  aspect of mixing (which sounds contradictory\, especially with respect to
  what I would have talked about earlier) but if it's possible (and I will 
 discuss the extent that it is) it offers great promise for a priori design
 \, i.e. designing a mixer without simulating its mixing properties first. 
 I will then give one or two examples from biotechnology (sensor arrays) wh
 ere this approach can be practically implemented\, and I will describe the
  advantages of this approach for  “optimizing” the performance of a mi
 xing device.\nThe talk will emphasize ideas and not go into technical deta
 ils. However\, a general point that I hope to make in this talk is that ma
 ny current designs for micromixers naturally fit into a common framework w
 here (smooth) ergodic theory can not only yield practical results\, such a
 s design principles\, but the design of the mixing devices themselves are 
 suggesting  interesting theorems and directions for research in ergodic th
 eory.
LOCATION:MR2\, Centre for Mathematical Sciences\, Wilberforce Road\, Cambr
 idge
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