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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Symmetry in materials science models under the div
ergence constraint - Radu Ignat (Université Paul S
abatier Toulouse III)
DTSTART;TZID=Europe/London:20190117T110000
DTEND;TZID=Europe/London:20190117T114500
UID:TALK117154AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/117154
DESCRIPTION:The symmetry of the order parameter is one of the
most important features in materials science.
In this talk we will focus on the one-dimensional
symmetry of transition layers u in some variationa
l
models (such as smectic liquid crystals\,
thin film blisters\, micromagnetics...)
where
the divergence div(u) vanishes.
Namely\, we d
etermine a class of nonlinear potentials such that
the minimal transition layers are
one-dimens
ional symmetric. In particular\, this class includ
es in dimension N=2 the nonlinearities w^2
wi
th w being an harmonic function or a solution to t
he wave equation\,
while in dimensions N>\;2
\, this class contains a perturbation of the stand
ard Ginzburg-Landau potential
as well as pote
ntials having N+1 wells with prescribed transition
cost between the wells.
For that\, we develop
a theory of calibrations for divergence-free maps
in R^N (similar to the theory of entropies
f
or the Aviles-Giga model when N=2).
This is a
joint work with Antonin Monteil (Louvain\, Belgium
).
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:INI IT
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