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UID:20251104T075326EST-3136xuMeBO@132.216.98.100
DTSTAMP:20251104T125326Z
DESCRIPTION:Title: Computer-assisted theorems for the Ohta-Kawasaki problem
 .\n\nAbstract:\n\nIn this talk we discuss a rigorous numerical method to s
 tudy pattern formation in the Ohta-Kawasaki model in both two and three di
 mensions. This model appears in the study of di-block copolymers. The mode
 l describes\, roughly speaking\, the balance between long range attraction
  and short range repulsion.\n\nFor the two dimensional case we compare loc
 al minimizers of the Ohta-Kawasaki functional. In particular\, we validate
  part of the phase diagram\, identifying regions of parameter space where 
 rolls are favorable\, where hexagonally packed spots have lowest energy an
 d finally where the constant mixed state does. This includes determining o
 ptimal domain sizes\, which are unknown a priori. In terms of the practica
 l realities of applying the computer assisted theorems ideas\, this work r
 epresents a step forward past clean-cut test problems to more elaborate va
 riational problems in pattern formation.\n\nFor the three dimensional case
  we illustrate the work in progress by fixing a cubical domain and finding
  several highly symmetric periodic stationary states. This is based on joi
 nt work with JF Williams (SFU).\n
DTSTART:20180123T200000Z
DTEND:20180123T210000Z
LOCATION:Room 1214\, Burnside Hall\, CA\, QC\, Montreal\, H3A 0B9\, 805 rue
  Sherbrooke Ouest
SUMMARY:Jan Bouwe van den Berg ( Vrije Universiteit Amsterdam)
URL:/mathstat/channels/event/jan-bouwe-van-den-berg-vr
 ije-universiteit-amsterdam-283791
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