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DTSTART:20190331T030000
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DTSTAMP:20260406T042021Z
UID:5b3b5421d7c51352294898@ist.ac.at
DTSTART:20190111T093000
DTEND:20190111T103000
DESCRIPTION:Speaker: Thilo Simon\nhosted by Julian Fischer\nAbstract: A num
 ber of fundamental questions about the structure of matter can be formulat
 ed as problems in energy-driven pattern formation. For example\, Gamow's l
 iquid drop model addresses the shape and stability properties of atomic nu
 clei as arising from competition between long-range Coulomb repulsion and 
 short-range attraction modeled by surface tension. We discuss a related mo
 del for perpendicularly oriented dipoles in the plane\, and in which perim
 eter (representing line tension) and regularized 3D dipolar repulsion comp
 ete under a volume constraint. Examples of such situations are Langmuir mo
 nolayers and the patterns formed in ultrathin ferromagnetic films with per
 pendicular anisotropy.In contrast to previously studied similar problems\,
  the nonlocal term contributes to the perimeter term to leading order for 
 small regularization cutoffs. For subcritical dipolar strengths we prove t
 hat the limiting functional is a renormalized perimeter and that for small
  cutoff lengths all minimizers are disks. For critical dipolar strength\, 
 we identify the next-order ?-limit when sending the cutoff length to zero 
 and prove that with a slight modification of the dipolar kernel there exis
 t masses for which classical minimizers are not disks.This talk is joint w
 ork with Cyrill B. Muratov
LOCATION:Big Seminar room Ground floor / Office Bldg West (I21.EG.101)\, IS
 TA
ORGANIZER:jdeanton@ist.ac.at
SUMMARY:Thilo Simon: A nonlocal isoperimetric problem with dipolar repulsio
 n
URL:https://talks-calendar.ista.ac.at/events/1701
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