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SUMMARY:The periodic\, multiply-connected Schwarz-Christoffel mapping - Pe
 ter Baddoo ( DAMTP)
DTSTART:20190423T100000Z
DTEND:20190423T110000Z
UID:TALK122962@talks.cam.ac.uk
CONTACT:Matthew Priddin
DESCRIPTION:Schwarz-Christoffel (S-C) formulae provide conformal mappings 
 from circular domains to polygonal domains. Consequently\, they are import
 ant tools for applied mathematicians seeking to solve problems involving c
 omplicated geometries. We present a major extension to previous S-C mappin
 gs by permitting the target domain to consist of a periodic array of polyg
 ons. Moreover\, by employing the transcendental Schottky-Klein prime funct
 ion\, the new S-C formula is valid for any number of polygons in each peri
 od window. We demonstrate several examples of the new mapping for a range 
 of connectivities and show that\, when coupled with the "new calculus of t
 wo-dimensional vortex dynamics"\, the new S-C mapping is a powerful tool f
 or the study of fluid flows in periodic domains. Finally\, we formulate th
 e accessory parameter problem of determining the pre-vertices and conforma
 l geometry in the canonical domain in order to achieve the desired target 
 domain. This work is in collaboration with Prof. Darren Crowdy (Imperial).
LOCATION:CMS\, MR15
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