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SUMMARY:Asymptotics of stationary points of a non-local Ginzburg-Landau en
 ergy - Oxbridge PDE Days - Dr Dorian Goldman\, DPMMS
DTSTART:20140320T150000Z
DTEND:20140320T160000Z
UID:TALK51577@talks.cam.ac.uk
CONTACT:36127
DESCRIPTION:We study a non-local Cahn-Hilliard energy arising in the study
  of di-block copolymer melts\, often referred to as the Ohta-Kawasaki ener
 gy in that context. In this model\, two phases appear\, which interact via
  a Coulombic energy. We focus on the regime where one of the phases has a 
 very small volume fraction\, thus creating ``droplets'' of the minority ph
 ase in a ``sea'' of the majority phase. In this paper\, we address the asy
 mptotic behavior of non-minimizing stationary points in dimensions $n \\ge
 q 2$ left open by the study of the $\\Gamma$-convergence of the energy est
 ablished in by Goldman-Muratov-Serfaty\, which provides information only f
 or almost minimizing sequences when $n=2$. In particular\, we prove that (
 asymptotically) stationary points satisfy a force balance condition which 
 implies that the minority phase distributes itself uniformly in the backgr
 ound majority phase. Our proof uses and generalizes the framework of Sandi
 er-Serfaty\, used in the context of stationary points of the Ginzburg-Land
 au model\, to higher dimensions. When $n=2$\, using the regularity results
  obtained in\, we also are able to conclude that the droplets in the sharp
  interface energy become asymptotically round when the number of droplets 
 is constrained to be finite and have bounded isoperimetric deficit.\n\nhtt
 p://www.maths.cam.ac.uk/postgrad/cca/oxbridgepde2014.html
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