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SUMMARY:Symmetry in materials science models under the divergence constrai
 nt - Radu Ignat (Université Paul Sabatier Toulouse III)
DTSTART:20190117T110000Z
DTEND:20190117T114500Z
UID:TALK117154@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:The symmetry of the order parameter is one of the most importa
 nt features in materials science.<br> In this talk we will focus on the on
 e-dimensional symmetry of transition layers u in some variational  <br> mo
 dels (such as smectic liquid crystals\, thin film blisters\, micromagnetic
 s...) <br> where the divergence div(u) vanishes.<br> Namely\, we determine
  a class of nonlinear potentials such that the minimal transition layers a
 re <br> one-dimensional symmetric. In particular\, this class includes in 
 dimension N=2 the nonlinearities w^2 <br> with w being an harmonic functio
 n or a solution to the wave equation\,<br> while in dimensions N&gt\;2\, t
 his class contains a perturbation of the standard Ginzburg-Landau potentia
 l <br> as well as potentials having N+1 wells with prescribed transition c
 ost between the wells.<br> For that\, we develop a theory of calibrations 
 for divergence-free maps in R^N (similar to the theory of entropies <br> f
 or the Aviles-Giga model when N=2).<br> This is a joint work with Antonin 
 Monteil (Louvain\, Belgium).
LOCATION:Seminar Room 1\, Newton Institute
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