Asymptotics of stationary points of a non-local Ginzburg-Landau energy - Oxbridge PDE Days

Add to your list(s) Download to your calendar using vCal

• Dr Dorian Goldman, DPMMS
• Thursday 20 March 2014, 15:00-16:00
• MR2.

If you have a question about this talk, please contact sk789.

We study a non-local Cahn-Hilliard energy arising in the study of di-block copolymer melts, often referred to as the Ohta-Kawasaki energy 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 phase in a ``sea’’ of the majority phase. In this paper, we address the asymptotic behavior of non-minimizing stationary points in dimensions $n \geq 2$ left open by the study of the $\Gamma$-convergence of the energy established in by Goldman-Muratov-Serfaty, which provides information only for 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 background majority phase. Our proof uses and generalizes the framework of Sandier-Serfaty, used in the context of stationary points of the Ginzburg-Landau 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.

http://www.maths.cam.ac.uk/postgrad/cca/oxbridgepde2014.html

This talk is part of the Cambridge Centre for Analysis talks series.

This talk is included in these lists:

• All CMS events
• CMS Events
• Cambridge Centre for Analysis talks
• DPMMS info aggregator
• Hanchen DaDaDash
• Interested Talks
• MR2
• My seminars
• bld31

Note that ex-directory lists are not shown.