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UID:5df3fb6c1e71c0e264406e027f5ce8ee
CATEGORIES:Applied and Computational Math Seminar
CREATED:20230424T195618
SUMMARY:Bifurcation points induced by cyclic symmetries
LOCATION:Hill 705
DESCRIPTION:<p><span style="color: #000000; font-family: Calibri, Arial, Helvetica, san
 s-serif; font-size: 16px; font-style: normal; font-weight: 400; letter-spac
 ing: normal; orphans: 2; text-align: start; text-indent: 0px; text-transfor
 m: none; white-space: normal; widows: 2; word-spacing: 0px; background-colo
 r: #ffffff; float: none;">Diblock copolymers are a class of materials forme
 d by the reaction of two linear polymers. The different structures taken on
  by these polymers grant them special properties, which can prove useful in
  applications such as the development of new adhesives and asphalt additive
 s. We consider a model for the formation of diblock copolymers first propos
 ed by Ohta and Kawasaki, which is a Cahn-Hilliard-like equation together wi
 th a nonlocal term. Unlike the Cahn-Hilliard model, even on one-dimensional
  spatial domains the steady state bifurcation diagram of the Ohta-Kawasaki 
 model is still not fully understood. We therefore present computer-assisted
  proof techniques which can be used to validate and continue its bifurcatio
 n points. This includes not only fold points, but also pitchfork bifurcatio
 ns&nbsp;</span><span class="x_x_ContentPasted0 x_ContentPasted1" style="bor
 der: 0px; font-style: normal; font-weight: 400; font-size: 16px; line-heigh
 t: inherit; font-family: Calibri, Arial, Helvetica, sans-serif; margin: 0px
 ; padding: 0px; vertical-align: baseline; color: #000000; letter-spacing: n
 ormal; orphans: 2; text-align: start; text-indent: 0px; text-transform: non
 e; white-space: normal; widows: 2; word-spacing: 0px; background-color: #ff
 ffff;">which are the result of a cyclic group action beyond forcing through
  $\Z_2$ symmetries.</span></p>
CONTACT:Thomas Wanner (George Mason University)
DTSTAMP:20260830T170628
DTSTART;TZID=America/New_York:20230425T110000
DTEND;TZID=America/New_York:20230425T120000
SEQUENCE:0
TRANSP:OPAQUE
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