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SUMMARY:Jan Bouwe van den Berg (VU Amsterdam)
DTSTART:20200623T140000Z
DTEND:20200623T150000Z
DTSTAMP:20260423T024659Z
UID:CRM-CAMP/1
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CRM-CAMP/1/"
 >Stable periodic patterns in 3D for the Ohta-Kawasaki problem</a>\nby Jan 
 Bouwe van den Berg (VU Amsterdam) as part of CRM CAMP (Computer-Assisted M
 athematical Proofs) in Nonlinear Analysis\n\n\nAbstract\nIn this talk we d
 iscuss a mathematically rigorous computational method to compare local min
 imizers of the Ohta-Kawasaki free energy\, describing diblock copolymer me
 lts. This energy incorporates a nonlocal term to take into account the bon
 d between the monomers.\nWorking within an arbitrary space group symmetry\
 , we explore the phase space\, computing candidates both with and without 
 experimentally observed symmetries. We validate the phase diagram\, identi
 fying regions of parameter space where different spatially periodic struct
 ures have the lowest energy. These patterns may be lamellar layers\, hexag
 onally packed cylinders\, body-centered or close-packed spheres\, as well 
 as double gyroids and 'O70' arrangements. Each computation is validated by
  a mathematical theorem\, where we bound the truncation errors and apply a
  fixed point argument to establish a computer-assisted proof. The method c
 an be applied more generally to symmetric space-time periodic solution of 
 many partial differential equations.\n
LOCATION:https://researchseminars.org/talk/CRM-CAMP/1/
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